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Bark beetle outbreaks and forest fires have imposed severe ecological damage and caused billions of dollars in lost resources in recent decades. The impact of such combined disturbances is projected to become more severe, especially as climate change takes its toll on forest ecosystems in the coming years. Here, we investigate the impact of multiple disturbances in a demographically heterogeneous tree population, using an age-structured difference equation model of bark beetle outbreaks and forest fires. We identify two dynamical regimes for beetle and fire dynamics. The model predicts that fire helps dampen beetle outbreaks not only by removing host trees but also by altering the demographic structure of forest stands. We show that a stand thinning protocol, which reduces the population size of the largest few juvenile classes by a small percentage, is able to significantly reduce beetle-induced tree mortality. Our research demonstrates one approach to capturing compound disturbances in a mathematical model. Electronic supplementary material The online version of this article (10.1007/s12080-021-00520-y) contains supplementary material, which is available to authorized users.

Objective The analysis estimates projected population outcomes resulting from the introduction of a plant-derived influenza vaccine formulated as quadrivalent virus-like particles (QVLP) in Canada. Methods Using Monte Carlo simulations, the number of influenza cases, general practitioner visits, inpatient admissions, intensive care unit (ICU) admissions, and deaths due to influenza-associated illness were estimated under no vaccination, plant-derived QVLP vaccines only, or egg-derived vaccines only. The base case analysis examined the adult Canadian population in two subgroups: 18–64 years of age during the 2017/18 season and 65+ years of age during the 2018/19 season. Efficacy data were obtained from QVLP clinical trials. Vaccine effectiveness data for egg-derived vaccines were calculated from observational studies from the corresponding influenza seasons. Scenario analyses examined the impact of varying absolute vaccine effectiveness or vaccination coverage from base case inputs. Results In the base case analysis, plant-derived QVLP vaccines led to an additional reduction in the burden of influenza over egg-derived vaccines for both population subgroups. In the 18–64 subgroup, QVLP vaccines were associated with 2.63% (48,029; 95% credible interval [Crl]: 42,723–53,336) fewer influenza cases than egg-derived vaccines. In the 65+ subgroup, QVLP vaccines led to 4.82% (27,918; 95% Crl: 25,440–30,397) fewer influenza cases, and reductions in the number of inpatient admissions by 4.77% (1167; 95% CrI: 851–1483) and deaths by 4.75% (326; 95% CrI: 107–546) compared to egg-derived vaccines. Further reductions were observed in scenario analyses considering the potential increase in vaccine coverage. Conclusion Use of plant-derived QVLP influenza vaccines may contribute to greater reductions in influenza cases and influenza-related outcomes, including inpatient admissions and deaths, compared to egg-derived vaccines currently available in Canada.

Significance An individual’s decision to vaccinate can be motivated by both self-interest and prosociality, making it difficult to delineate the contribution of prosociality to vaccination uptake. A silent polio epidemic in Israel in which the primary purpose of vaccination was to avert transmission to the general community provides a unique case study through which we quantify, using game-theoretical models, the contribution of prosociality to vaccination decisions. We find that prosociality was a significant driver to rapidly achieving a high coverage of polio vaccination. To further boost coverage, public health communication efforts should be directed toward allaying fears about vaccine risks. Our approach is useful for enhancing participation in diverse disease control measures, Regions with insufficient vaccination have hindered worldwide poliomyelitis eradication, as they are vulnerable to sporadic outbreaks through reintroduction of the disease. Despite Israel’s having been declared polio-free in 1988, a routine sewage surveillance program detected polio in 2013. To curtail transmission, the Israel Ministry of Health launched a vaccine campaign to vaccinate children—who had only received the inactivated polio vaccine—with the oral polio vaccine (OPV). Determining the degree of prosocial motivation in vaccination behavior is challenging because vaccination typically provides direct benefits to the individual as well as indirect benefits to the community by curtailing transmission. However, the Israel OPV campaign provides a unique and excellent opportunity to quantify and model prosocial vaccination as its primary objective was to avert transmission. Using primary survey data and a game-theoretical model, we examine and quantify prosocial behavior during the OPV campaign. We found that the observed vaccination behavior in the Israeli OPV campaign is attributable to prosocial behavior and heterogeneous perceived risk of paralysis based on the individual’s comprehension of the prosocial nature of the campaign. We also found that the benefit of increasing comprehension of the prosocial nature of the campaign would be limited if even 24% of the population acts primarily from self-interest, as greater vaccination coverage provides no personal utility to them. Our results suggest that to improve coverage, communication efforts should also focus on alleviating perceived fears surrounding the vaccine.

Dietary patterns have long been a driver of global land use. Increasingly, they also respond to it, in part because of social processes that support adoption of eco-conscious diets. Here we develop a coupled social-and-land use mathematical model parameterised for 153 countries. We project global land use for future population, income, and agricultural yield using our coupled dynamical model. We find that coupled social-and-land feedbacks can alter the peak global land use for agriculture by up to 2 billion hectares, depending on the parameter regime. Across all yield scenarios, the model projects that social dynamics will cause an increase in eco-conscious dietary behaviour until the middle of the 21st century, after which it will decline in response to declining land use caused by a shrinking global population. The model also exhibits a regime of synergistic effects whereby simultaneous changes to multiple socio-economic parameters are required to change land use projections. This research demonstrates the value of including coupled social-and-land feedbacks in land use projections. Social learning processes regarding eco-conscious dietary choices can substantially alter projections of global peak land use for agriculture, according to a coupled social-and-land use dynamics model

Decision-making about pandemic mitigation often relies upon simulation modelling. Models of disease transmission through networks of contacts--between individuals or between population centres--are increasingly used for these purposes. Real-world contact networks are rich in structural features that influence infection transmission, such as tightly-knit local communities that are weakly connected to one another. In this paper, we propose a new flow-based edge-betweenness centrality method for detecting bottleneck edges that connect nodes in contact networks. In particular, we utilize convex optimization formulations based on the idea of diffusion with p-norm network flow. Using simulation models of COVID-19 transmission through real network data at both individual and county levels, we demonstrate that targeting bottleneck edges identified by the proposed method reduces the number of infected cases by up to 10% more than state-of-the-art edge-betweenness methods. Furthermore, the proposed method is orders of magnitude faster than existing methods., Comment: 38 pages, 21 figures

The continued growth of the world’s population and increased interconnectivity heighten the risk that infectious diseases pose for human health worldwide. Epidemiological modelling is a tool that can be used to mitigate this risk by predicting disease spread or quantifying the impact of different intervention strategies on disease transmission dynamics. We illustrate how four decades of methodological advances and improved data quality have facilitated the contribution of modelling to address global health challenges, exemplified by models for the HIV crisis, emerging pathogens and pandemic preparedness. Throughout, we discuss the importance of designing a model that is appropriate to the research question and the available data. We highlight pitfalls that can arise in model development, validation and interpretation. Close collaboration between empiricists and modellers continues to improve the accuracy of predictions and the optimization of models for public health decision-making.

Given trade’s importance to maintaining food security, it is crucial to understand the relationship between human population growth, land use, food supply, and trade. We develop a metapopulation model coupling human population dynamics to agricultural land use and food production in “patches” (regions and countries) connected via trade networks. Patches that import sparingly or fail to adjust their demand sharply in response to changes in food per capita experience food insecurity. They fall into a feedback loop between increasing population growth and decreasing food per capita, particularly if they are peripheral to the network. A displacement effect is also evident; patches that are more central and/or import more heavily preserve their natural land states. Their reliance on imports means other patches must expand their agricultural land. These results emphasize that strategies for improving food security and equality must account for the combined effects of network topology and patch-level characteristics.

The critical community size (CCS) is the minimum closed population size in which a pathogen can persist indefinitely. Below this threshold, stochastic extinction eventually causes pathogen extinction. Here we use a simulation model to explore behaviour-mediated persistence: a novel mechanism by which the population response to the pathogen determines the CCS. We model severe coronavirus 2 (SARS-CoV-2) transmission and non-pharmaceutical interventions (NPIs) in a population where both individuals and government authorities restrict transmission more strongly when SARS-CoV-2 case numbers are higher. This results in a coupled human-environment feedback between disease dynamics and population behaviour. In a parameter regime corresponding to a moderate population response, this feedback allows SARS-CoV-2 to avoid extinction in the trough of pandemic waves. The result is a very low CCS that allows long term pathogen persistence. Hence, an incomplete pandemic response represents a “sour spot” that not only ensures relatively high case incidence and unnecessarily long lockdown, but also promotes long-term persistence of the pathogen by reducing the CCS. Given the worldwide prevalence of small, isolated populations in which a pathogen with low CCS can persist, these results emphasize the need for a global approach to coronavirus disease 2019 (COVID-19) vaccination.

Summary Background During the COVID-19 pandemic, authorities must decide which groups to prioritise for vaccination in a shifting social–epidemiological landscape in which the success of large-scale non-pharmaceutical interventions requires broad social acceptance. We aimed to compare projected COVID-19 mortality under four different strategies for the prioritisation of SARS-CoV-2 vaccines. Methods We developed a coupled social–epidemiological model of SARS-CoV-2 transmission in which social and epidemiological dynamics interact with one another. We modelled how population adherence to non-pharmaceutical interventions responds to case incidence. In the model, schools and workplaces are also closed and reopened on the basis of reported cases. The model was parameterised with data on COVID-19 cases and mortality, SARS-CoV-2 seroprevalence, population mobility, and demography from Ontario, Canada (population 14·5 million). Disease progression parameters came from the SARS-CoV-2 epidemiological literature. We assumed a vaccine with 75% efficacy against disease and transmissibility. We compared vaccinating those aged 60 years and older first (oldest-first strategy), vaccinating those younger than 20 years first (youngest-first strategy), vaccinating uniformly by age (uniform strategy), and a novel contact-based strategy. The latter three strategies interrupt transmission, whereas the first targets a vulnerable group to reduce disease. Vaccination rates ranged from 0·5% to 5% of the population per week, beginning on either Jan 1 or Sept 1, 2021. Findings Case notifications, non-pharmaceutical intervention adherence, and lockdown undergo successive waves that interact with the timing of the vaccine programme to determine the relative effectiveness of the four strategies. Transmission-interrupting strategies become relatively more effective with time as herd immunity builds. The model predicts that, in the absence of vaccination, 72 000 deaths (95% credible interval 40 000–122 000) would occur in Ontario from Jan 1, 2021, to March 14, 2025, and at a vaccination rate of 1·5% of the population per week, the oldest-first strategy would reduce COVID-19 mortality by 90·8% on average (followed by 89·5% in the uniform, 88·9% in the contact-based, and 88·2% in the youngest-first strategies). 60 000 deaths (31 000–108 000) would occur from Sept 1, 2021, to March 14, 2025, in the absence of vaccination, and the contact-based strategy would reduce COVID-19 mortality by 92·6% on average (followed by 92·1% in the uniform, 91·0% in the oldest-first, and 88·3% in the youngest-first strategies) at a vaccination rate of 1·5% of the population per week. Interpretation The most effective vaccination strategy for reducing mortality due to COVID-19 depends on the time course of the pandemic in the population. For later vaccination start dates, use of SARS-CoV-2 vaccines to interrupt transmission might prevent more deaths than prioritising vulnerable age groups. Funding Ontario Ministry of Colleges and Universities.

The results of COVID-19 vaccine clinical trials suggest that an end to the pandemic is within reach. However, public health authorities world-wide are faced with the difficult task of prioritizing their allocation [17, 10, 2]. Theory indicates that prioritizing vaccination of individuals with more contacts can be disproportionately effective [25, 8, 5, 3]. However, implementation of such strategies has been hampered by inability to determine population contact structure. One of the novel tools introduced during the pandemic has been the use of Bluetooth technology to assist in contact tracing and exposure notification [6, 13, 12]. Here we show that the technology underlying these Bluetooth exposure notification applications can be leveraged to efficiently prioritise vaccine allocation. Our approach is based on the insight that these apps also act as local sensing devices measuring each user’s total exposure time to other app users, thereby enabling the implementation of a previously impossible vaccine strategy that prioritises potential super-spreaders based on total exposure time. To compare vaccination strategies we introduce a novel and widely generalizable measure of vaccination efficiency. By extending percolation theory we furthermore demonstrate that our proposed “hot-spotting” strategy can achieve herd immunity with less than half as many vaccines as distributing the vaccines uniformly in the population.

Vaccinating individuals with more exposure to others can be disproportionately effective, in theory, but identifying these individuals is difficult and has long prevented implementation of such strategies. Here, we propose how the technology underlying digital contact tracing could be harnessed to boost vaccine coverage among these individuals. In order to assess the impact of this “hot-spotting” proposal we model the spread of disease using percolation theory, a collection of analytical techniques from statistical physics. Furthermore, we introduce a novel measure which we call the efficiency, defined as the percentage decrease in the reproduction number per percentage of the population vaccinated. We find that optimal implementations of the proposal can achieve herd immunity with as little as half as many vaccine doses as a non-targeted strategy, and is attractive even for relatively low rates of app usage.

Sudden shifts in vaccine uptake, vaccine opinion, and infection incidence can occur in coupled behaviour-disease systems going through a bifurcation as the perceived risk of the vaccine increases. Literature shows that such regime shifts are sometimes foreshadowed by early warning signals (EWS). We propose and compare the performance of various measures of network structure as potential EWS indicators of epidemics and changes in population vaccine opinion. We construct a multiplex model coupling transmission of a vaccine-preventable childhood infectious disease and social dynamics concerning vaccine opinion. We find that the modularity of pro- and anti-vaccine network communities perform well as EWS, as do several measures of the number and size of opinion-based communities, and the size of pro-vaccine echo chambers. The number of opinion changes also gives early warnings, although the clustering coefficient and metrics concerning anti-vaccine echo chambers provide little warning. Stronger social norms are found to compromise the ability of all EWS metrics to provide advance warning. These exploratory results suggest that EWS indicators based on the network structure of online social media communities might assist public health preparedness by providing early warning of potential regime shifts.

SummaryBackgroundDuring the COVID-19 pandemic, authorities must decide which groups to prioritise for vaccination. These decision will occur in a constantly shifting social-epidemiological landscape where the success of large-scale non-pharmaceutical interventions (NPIs) like physical distancing requires broad population acceptance.MethodsWe developed a coupled social-epidemiological model of SARS-CoV-2 transmission. Schools and workplaces are closed and re-opened based on reported cases. We used evolutionary game theory and mobility data to model individual adherence to NPIs. We explored the impact of vaccinating 60+ year-olds first; FindingsCase notifications, NPI adherence, and lockdown periods undergo successive waves during the simulated pandemic. Vaccination reduces median deaths by 32% – 77% (22% – 63%) for January (July) availability, depending on the scenario. Vaccinating 60+ year-olds first prevents more deaths (up to 8% more) than transmission-interrupting strategies for January vaccine availability across most parameter regimes. In contrast, transmission-interrupting strategies prevent up to 33% more deaths than vaccinating 60+ year-olds first for July availability, due to higher levels of natural immunity by that time. Sensitivity analysis supports the findings.InterpretationFurther research is urgently needed to determine which populations can benefit from using SARS-CoV-2 vaccines to interrupt transmission.FundingOntario Ministry of Colleges and Universities.Research in contextEvidence before this studyWhether to vaccinate individuals who cause the most transmission or those who are at highest risk of death is relevant to prioritizing COVID-19 vaccination. We searched PubMed and medRxiv for the terms COVID19, vaccin*, model, and priorit* up to September 24, 2020, with no date or language restrictions. We identified 4 papers on mathematical models of COVID-19 vaccine prioritization that explored the conditions under which different age groups should be vaccinated first. We did not find any coupled social-epidemiological models that capture feedback between social dynamics and epidemic trajectories.Added value of this studyThe dynamic interaction between SARS-CoV-2 epidemics and the population response through scalable non-pharmaceutical interventions will continue to play a large role in the course of the pandemic, both before and after vaccines become available. Hence, social-epidemiological models may be useful. Our social-epidemiological model identifies the conditions under which COVID-19 deaths can be reduced most effectively by prioritizing older individuals first, versus other strategies designed to interrupt transmission. We explore how the best vaccination strategy varies depending on a wide range of socio-epidemiological and vaccine program parameters. We identify clear and interpretable conditions under which using COVID-19 vaccines to interrupt transmission can reduce mortality most effectively.Implications of all the available evidenceSeroprevalence surveys before the onset of vaccination could measure population-level SARS-CoV-2 immunity. In populations where seropositivity is high due to previous waves, vaccinating to interrupt transmission may reduce deaths more effectively than targeting older individuals. More research is urgently required to evaluate how to prioritise vaccination in populations that have experienced one or more waves of COVID-19.

Climate dynamics are inextricably linked to processes in social systems that are highly unequal. This suggests a need for coupled social-climate models that capture pervasive real-world asymmetries in the population distribution of the consequences of anthropogenic climate change and climate (in)action. Here we develop a simple social-climate model with group structure to investigate how anthropogenic climate change and population heterogeneity co-evolve. We find that greater homophily and resource inequality cause an increase in the global peak temperature anomaly by as much as 0.7°C. Also, climate change can structure human populations by driving opinion polarization. Finally, climate mitigation achieved by reducing the cost of mitigation measures paid by individuals tends to be contingent upon socio-economic conditions, whereas policies that achieve communication between different strata of society show climate mitigation benefits across a broad socio-economic regime. We conclude that advancing climate change mitigation efforts can benefit from a social-climate systems perspective.

Significance During the COVID-19 pandemic, decision makers are grappling with how to reopen (and possibly reclose) their jurisdictions as the number of cases ebbs and flows. Establishing a criterion for each county/municipality to open and close based on their case count has appeal, given the wide disparity in COVID-19 rates in urban versus rural settings. Our simulation model is based on the geography, epidemiology, and travel patterns of Ontario, Canada. It shows that the county-by-county approach causes fewer days of closure and impacts fewer people than a strategy that opens or closes the entire province together. This is true even if individuals begin traveling to reopened counties with higher frequency. The county-by-county strategy is most effective when the criteria are coordinated., In the late stages of an epidemic, infections are often sporadic and geographically distributed. Spatially structured stochastic models can capture these important features of disease dynamics, thereby allowing a broader exploration of interventions. Here we develop a stochastic model of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission among an interconnected group of population centers representing counties, municipalities, and districts (collectively, “counties”). The model is parameterized with demographic, epidemiological, testing, and travel data from Ontario, Canada. We explore the effects of different control strategies after the epidemic curve has been flattened. We compare a local strategy of reopening (and reclosing, as needed) schools and workplaces county by county, according to triggers for county-specific infection prevalence, to a global strategy of province-wide reopening and reclosing, according to triggers for province-wide infection prevalence. For trigger levels that result in the same number of COVID-19 cases between the two strategies, the local strategy causes significantly fewer person-days of closure, even under high intercounty travel scenarios. However, both cases and person-days lost to closure rise when county triggers are not coordinated and when testing rates vary among counties. Finally, we show that local strategies can also do better in the early epidemic stage, but only if testing rates are high and the trigger prevalence is low. Our results suggest that pandemic planning for the far side of the COVID-19 epidemic curve should consider local strategies for reopening and reclosing.

Pre-exposure prophylaxis (PrEP) has been shown to be highly effective in reducing the risk of HIV infection in gay and bisexual men who have sex with men (GbMSM). However, PrEP does not protect against other sexually transmitted infections (STIs). In some populations, PrEP has also led to riskier behaviour such as reduced condom usage, with the result that the prevalence of bacterial STIs like gonorrhea has increased. Here we develop a compartmental model of the transmission of HIV and gonorrhea, and the impacts of PrEP, condom usage, STI testing frequency and potential changes in sexual risk behaviour stemming from the introduction of PrEP in a population of GbMSM. We find that introducing PrEP causes an increase in gonorrhea prevalence for a wide range of parameter values, including at the current recommended frequency of STI testing once every 3 months for individuals on PrEP. Moreover, the model predicts that a higher STI testing frequency alone is not enough to prevent a rise in gonorrhea prevalence, unless the testing frequency is increased to impractical levels. However, testing every 2 months in combination with sufficiently high condom usage by individuals on PrEP would be successful in maintaining gonorrhea prevalence at pre-PrEP levels. The results emphasize that programs making PrEP more available should be accompanied by efforts to support condom usage and frequent STI testing, in order to avoid an increase in the prevalence of gonorrhea and other bacterial STIs.

In May 2020, many jurisdictions around the world began lifting physical distancing restrictions against the spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), giving rise to concerns about a possible second wave of coronavirus disease 2019 (COVID-19). These restrictions were imposed as a collective population response to the presence of COVID-19 in communities. However, lifting restrictions is also a population response to their socio-economic impacts, and is expected to increase COVID-19 cases, in turn. This suggests that the COVID-19 pandemic exemplifies a coupled behaviour-disease system. Here we develop a minimal mathematical model of the interaction between social support for school and workplace closure and the transmission dynamics of SARS-CoV-2. We find that a second wave of COVID-19 occurs across a broad range of plausible model input parameters, on account of instabilities generated by behaviour-disease interactions. We conclude that second waves of COVID-19–should they materialize–can be interpreted as the outcomes of nonlinear interactions between disease dynamics and population behaviour.

In the late stages of an epidemic, infections are often sporadic and geographically distributed. Spatially structured stochastic models can capture these important features of disease dynamics, thereby allowing a broader exploration of interventions. Here we develop a stochastic model of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission amongst an interconnected group of population centres representing counties, municipalities and districts (collectively, “counties”). The model is parameterized with demographic, epidemiological, testing, and travel data from Ontario, Canada. We explore the effects of different control strategies after the epidemic curve has been flattened. We compare a local strategy of re-opening (and re-closing, as needed) schools and workplaces county-by-county according to triggers for county-specific infection prevalence, to a global strategy of province-wide re-opening and re-closing according to triggers for province-wide infection prevalence. We find that the local strategy results in a similar number coronavirus disease (COVID-19) cases but significantly fewer person-days of closure, even under high inter-county travel scenarios. However, both cases and person-days lost to closure rise when county triggers are not coordinated and when testing rates vary among counties. Finally, we show that local strategies can also do better in the early epidemic stage but only if testing rates are high and the trigger prevalence is low. Our results suggest that pandemic planning for the far side of the COVID-19 epidemic curve should consider local strategies for re-opening and re-closing.

It is widely recognized that coupled socio-ecological dynamics can be qualitatively different from the dynamics of social or ecological systems in isolation from one another. The influence of the type of ecological dynamics on the dynamics of the larger socio-ecological system is less well studied, however. Here, we carry out such a comparison using a mathematical model of a common pool resource problem. A population must make decisions about harvesting a renewable resource. Individuals may either be cooperators, who harvest at a sustainable level, or defectors, who overharvest. Cooperators punish defectors through social ostracism. Individuals can switch strategies according to the costs and benefits of harvesting and the strength of social ostracism. These mechanisms are represented by a differential equation for social dynamics, which is coupled to three different types of resource dynamics: logistic growth, constant inflow, and threshold growth. We find that when human influence is sufficiently weak, the form of resource dynamics leaves a strong imprint on the socio-ecological dynamics, and human social dynamics are qualitatively very different from resource dynamics. However, stronger human influence introduces a broad intermediate parameter regime where dynamical patterns converge to a common type: the three types of ecological systems exhibit similar dynamics, but also, social and ecological dynamics mirror one another. This regime of strong human influence includes generation of stable limit cycles at high rates of social learning. Such oscillations are a consequence of stronger coupling and are reminiscent of synchrony in other fields, such as the classic problem of coupled oscillators. Socio-ecological convergence has implications for how we understand and manage complex socio-ecological systems. In an era of growing human influence on ecological systems, further empirical and theoretical work is required to determine whether socio-ecological convergence is present in real systems.

The Nilgiri Hills in the Western Ghats of India constitute a region of high biological and cultural diversity, and include an endangered shola forest-grassland mosaic ecosystem. A mosaic ecosystem is one consisting of adjacent, coexisting patches of highly distinct naturally occurring land states (in this case, shola forest and natural grassland). Changes in the landscape since the nineteenth century have severely impacted the shola-grassland mosaic and challenged the traditional lifestyles of the indigenous Toda people. However, the responses of traditional Toda socio-ecological perspectives and landscape management to these changes have not been explored through population surveys. Here, using a survey method, the article explores traditional Toda perspectives of ecosystem value and landmanagement practices. The survey consists of interviews of 50 respondents belonging to 24 munds (villages), covering ten clans, neighbouring mosaic lands, plantations and agricultural areas. The findings show that traditional socio-ecological landscape management is robust and has persisted despite marked ecological and socio-economic changes during the nineteenth and twenty-first centuries, and despite frequent gathering of land management advice from non-Toda. Elements of traditional socio-ecological knowledge that have persisted include prevalent collective traditional decision-making and long-held preferences for a landscape composition with a strong mosaic component. The highly robust nature of Toda socio-ecological culture and land management suggests that the Todas have a valuable role to play in supporting the long-term persistence of the shola-grassland mosaic. Increasing their stewardship role would help conserve this endangered and highly biodiverse ecosystem, while at the same time preserving a unique indigenous culture.

Significance Complex adaptive systems exhibit characteristic dynamics near tipping points such as critical slowing down (declining resilience to perturbations). We studied Twitter and Google search data about measles from California and the United States before and after the 2014–2015 Disneyland, California measles outbreak. We find critical slowing down starting a few years before the outbreak. However, population response to the outbreak causes resilience to increase afterward. A mathematical model of measles transmission and population vaccine sentiment predicts the same patterns. Crucially, critical slowing down begins long before a system actually reaches a tipping point. Thus, it may be possible to develop analytical tools to detect populations at heightened risk of a future episode of widespread vaccine refusal., Vaccine refusal can lead to renewed outbreaks of previously eliminated diseases and even delay global eradication. Vaccinating decisions exemplify a complex, coupled system where vaccinating behavior and disease dynamics influence one another. Such systems often exhibit critical phenomena—special dynamics close to a tipping point leading to a new dynamical regime. For instance, critical slowing down (declining rate of recovery from small perturbations) may emerge as a tipping point is approached. Here, we collected and geocoded tweets about measles–mumps–rubella vaccine and classified their sentiment using machine-learning algorithms. We also extracted data on measles-related Google searches. We find critical slowing down in the data at the level of California and the United States in the years before and after the 2014–2015 Disneyland, California measles outbreak. Critical slowing down starts growing appreciably several years before the Disneyland outbreak as vaccine uptake declines and the population approaches the tipping point. However, due to the adaptive nature of coupled behavior–disease systems, the population responds to the outbreak by moving away from the tipping point, causing “critical speeding up” whereby resilience to perturbations increases. A mathematical model of measles transmission and vaccine sentiment predicts the same qualitative patterns in the neighborhood of a tipping point to greatly reduced vaccine uptake and large epidemics. These results support the hypothesis that population vaccinating behavior near the disease elimination threshold is a critical phenomenon. Developing new analytical tools to detect these patterns in digital social data might help us identify populations at heightened risk of widespread vaccine refusal.

Human and environmental systems are often treated as existing in isolation from one another, whereas in fact they are often two parts of a single, coupled human-environment system. Developing theoretical models of coupled human-environment systems is a continuing area of research, although relatively few of these models are based on differential equations. Here we develop a simple differential equation coupled human-environment system model of forest growth dynamics and conservationist opinion dynamics in a human population. The model assumes logistic growth and harvesting in the forest. Opinion spread in the human population is based on the interplay between conservation values stimulated by forest rarity, and injunctive social norms that tend to support population conformity. We find that injunctive social norms drive the system to the boundaries of phase space, whereas rarity-based conservation priorities drive the system to the interior. The result is complex dynamics including limit cycles and alternative stable states that do not occur if injunctive social norms are absent. We found that the model with injunctive social norms had five possible observable outcomes, whereas the model without social norms had only two stable states. Thus social norms and have dramatic influence in conservation dynamics. We also find that increasing the conservation value of forests is the best way to boost and stabilize forest cover while also boosting conservationist opinion in the population, although for some parameter regimes it can also give rise to long-term oscillations in opinions and forest cover. We conclude that simple models can provide insights and reveal patterns that might be difficult to see with high-dimensional computational models, and therefore should be used more often in research on coupled human-environment systems.

Background: The potential for emergence of antiviral drug resistance during influenza pandemics has raised great concern for public health. Widespread use of antiviral drugs is a significant factor in producing resistant strains. Recent studies show that some influenza viruses may gain antiviral drug resistance without a fitness penalty. This creates the possibility of strategic interaction between populations considering antiviral drug use strategies. Methods: To explain why, we develop and analyze a classical 2-player game theoretical model where each player chooses from a range of possible rates of antiviral drug use, and payoffs are derived as a function of final size of epidemic with the regular and mutant strain. Final sizes are derived from a stochastic compartmental epidemic model that captures transmission within each population and between populations, and the stochastic emergence of antiviral drug resistance. High treatment levels not only increase the spread of the resistant strain in the subject population but also affect the other population by increasing the density of the resistant strain infectious individuals due to travel between populations. Results: We found two Nash equilibria where both populations treat at a high rate, or both treat at a low rate. Hence the game theoretical analysis predicts that populations will not choose different treatment strategies than other populations, under these assumptions. The populations may choose to cooperate by maintaining a low treatment rate that does not increase the incidence of mutant strain infections or cause case importations to the other population. Alternatively, if one population is treating at a high rate, this will generate a large number of mutant infections that spread to the other population, in turn incentivizing that population to also treat at a high rate. The prediction of two separate Nash equilibria is robust to the mutation rate and the effectiveness of the drug in preventing transmission, but it is sensitive to the volume of travel between the two populations. Conclusions: Model-based evaluations of antiviral influenza drug use during a pandemic usually consider populations in isolation from one another, but our results show that strategic interactions could strongly influence a population's choice of antiviral drug use policy. Furthermore, the high treatment rate Nash equilibrium has the potential to become socially suboptimal (i.e. non-Pareto optimal) under model assumptions that might apply under other conditions. Because of the need for players to coordinate their actions, we conclude that communication and coordination between jurisdictions during influenza pandemics is a priority, especially for influenza strains that do not evolve a fitness penalty under antiviral drug resistance. Keywords: Game theory, Stochastic compartmental model, Antiviral drugs, Drug resistance, H1N1, Fitness penalty

The replicator equation has been frequently used in the theoretical literature to explain a diverse array of biological phenomena. However, it makes several simplifying assumptions, namely complete mixing, an infinite population, asexual reproduction, proportional selection, and mean payoffs. Here, we relax the conditions of mean payoffs and proportional selection by incorporating payoff distributions and truncation selection into extensions of the replicator equation and agent-based models. In truncation selection, replicators with fitnesses above a threshold survive. The reproduction rate is equal for all survivors and is sufficient to replace the replicators that did not survive. We distinguish between two types of truncation: independent and dependent with respect to the fitness threshold. If the payoff variances from all strategy pairing are the same, then we recover the replicator equation from the independent truncation equation. However, if all payoff variances are not equal, then any boundary fixed point can be made stable (or unstable) if only the fitness threshold is chosen appropriately. We observed transient and complex dynamics in our models, which are not observed in replicator equations incorporating the same games. We conclude that the assumptions of mean payoffs and proportional selection in the replicator equation significantly impact replicator dynamics.

Mathematical models of the interplay between disease dynamics and human behavioural dynamics can improve our understanding of how diseases spread when individuals adapt their behaviour in response to an epidemic. Accounting for behavioural mechanisms that determine uptake of infectious disease interventions such as vaccination and non-pharmaceutical interventions (NPIs) can significantly alter predicted health outcomes in a population. However, most previous approaches that model interactions between human behaviour and disease dynamics have modelled behaviour of these two interventions separately. Here, we develop and analyze an agent based network model to gain insights into how behaviour toward both interventions interact adaptively with disease dynamics (and therefore, indirectly, with one another) during the course of a single epidemic where an SIRV infection spreads through a contact network. In the model, individuals decide to become vaccinated and/or practice NPIs based on perceived infection prevalence (locally or globally) and on what other individuals in the network are doing. We find that introducing adaptive NPI behaviour lowers vaccine uptake on account of behavioural feedbacks, and also decreases epidemic final size. When transmission rates are low, NPIs alone are as effective in reducing epidemic final size as NPIs and vaccination combined. Also, NPIs can compensate for delays in vaccine availability by hindering early disease spread, decreasing epidemic size significantly compared to the case where NPI behaviour does not adapt to mitigate early surges in infection prevalence. We also find that including adaptive NPI behaviour strongly mitigates the vaccine behavioural feedbacks that would otherwise result in higher vaccine uptake at lower vaccine efficacy as predicted by most previous models, and the same feedbacks cause epidemic final size to remain approximately constant across a broad range of values for vaccine efficacy. Finally, when individuals use local information about others’ behaviour and infection prevalence, instead of population-level information, infection is controlled more efficiently through ring vaccination, and this is reflected in the time evolution of pair correlations on the network. This model shows that accounting for both adaptive NPI behaviour and adaptive vaccinating behaviour regarding social effects and infection prevalence can result in qualitatively different predictions than if only one type of adaptive behaviour is modelled., Highlights • We create an agent based network model that simulates an epidemic. • We combine population decisions for vaccination and non-pharmaceutical interventions. • Vaccination mitigates epidemic final size effectively for high transmission rates. • Non-pharmaceutical interventions compensate for delays in vaccine availability. • Non-pharmaceutical interventions can lower vaccine uptake and reduce epidemic size.

Shared resource extraction among profit-seeking individuals involves a tension between individual benefit and the collective well-being represented by the persistence of the resource. Many game theoretic models explore this scenario, but these models tend to assume either best response dynamics (where individuals instantly switch to better paying strategies) or imitation dynamics (where individuals copy successful strategies from neighbours), and do not systematically compare predictions under the two assumptions. Here we propose an iterated game on a social network with payoff functions that depend on the state of the resource. Agents harvest the resource, and the strategy composition of the population evolves until an equilibrium is reached. The system is then repeatedly perturbed and allowed to re-equilibrate. We compare model predictions under best response and imitation dynamics. Compared to imitation dynamics, best response dynamics increase sustainability of the system, the persistence of cooperation while decreasing inequality and debt corresponding to the Gini index in the agents' cumulative payoffs. Additionally, for best response dynamics, the number of strategy switches before equilibrium fits a power-law distribution under a subset of the parameter space, suggesting the system is in a state of self-organized criticality. We find little variation in most mean results over different network topologies; however, there is significant variation in the distributions of the raw data, equality of payoff, clustering of like strategies and power-law fit. We suggest the primary mechanisms driving the difference in sustainability between the two strategy update rules to be the clustering of like strategies as well as the time delay imposed by an imitation processes. Given the strikingly different outcomes for best response versus imitation dynamics for common-pool resource systems, our results suggest that modellers should choose strategy update rules that best represent decision-making in their study systems.

Visitors can play an important role in the spread of infections. Here, we incorporate an epidemic model into a game theoretical framework to investigate the effects of travel strategies on infection control. Potential visitors must decide whether to travel to a destination that is at risk of infectious disease outbreaks. We compare the individually optimal (Nash equilibrium) strategy to the group optimal strategy that maximizes the overall population utility. Economic epidemiological models often find that individual and group optimal strategies are very different. By contrast, we find perfect agreement between individual and group optimal strategies across a wide parameter regime. For more limited regimes where disagreement does occur, the disagreement is (i) generally very extreme; (ii) highly sensitive to small changes in infection transmissibility and visitor costs/benefits; and (iii) can manifest either in a higher travel volume for individual optimal than group optimal strategies, or vice versa. The simulations show qualitative agreement with the 2003 severe acute respiratory syndrome (SARS) outbreak in Beijing, China. We conclude that a conflict between individual and group optimal visitor travel strategies during outbreaks may not generally be a problem, although extreme differences could emerge suddenly under certain changes in economic and epidemiological conditions.

It is widely recognized that coupled socio-ecological dynamics can be qualitatively different from the dynamics of social or ecological systems in isolation from one another. The influence of the type of ecological dynamics on the dynamics of the larger socio-ecological system is less well studied, however. Here, we carry out such a comparison using a mathematical model of a common pool resource problem. A population must make decisions about harvesting a renewable resource. Individuals may either be cooperators, who harvest at a sustainable level, or defectors, who over-harvest. Cooperators punish defectors through social ostracism. Individuals can switch strategies according the costs and benefits of harvesting and the strength of social ostracism. These mechanisms are represented by a differential equation for social dynamics which is coupled to three different types of resource dynamics: logistic growth, constant inflow, and threshold growth. We find that when human influence is sufficiently weak, the form of natural dynamics leaves a strong imprint on the socio-ecological dynamics, and human social dynamics are qualitatively very different from natural dynamics. However, stronger human influence introduces a broad intermediate parameter regime where dynamical patterns converge to a common type: the three types of ecological systems exhibit similar dynamics, but also, social and ecological dynamics strongly mirror one another. This is a consequence of stronger coupling and is reminiscent of synchrony from other fields, such as the classic problem of coupled oscillators in physics. Socio-ecological convergence has implications for how we understand and manage complex socio-ecological systems. In an era of growing human influence on ecological systems, further empirical and theoretical work is required to determine whether socio-ecological convergence is present in real systems.

Virulence measures the degree of harm inflicted by a pathogen on its host, and mathematical models including features of pathogens such as virulence have long been studied in an effort to better understand disease dynamics. Interventions like social distancing or vaccination have proven effective in reducing the size of epidemics and in some cases eliminating a disease from a population. Such interventions depend partly for their success on social processes that respond adaptively to disease dynamics, but mathematical models of virulence evolution typically assume that human behaviour is fixed. Here, our objective is to model the influence of social behaviour on the competition between pathogen strains with differing virulence. We couple a compartmental Susceptible-Infectious-Recovered model for a resident pathogen strain and a mutant strain with higher virulence, with a differential equation of a population where individuals learn to adopt protective behaviour from others according to the prevalence of infection of the two strains and the perceived severity of the respective strains in the population. We perform invasion analysis, time series analysis and phase plane analysis to show that perceived severities of pathogen strains and the efficacy of infection control against them can greatly impact the invasion of more virulent strain. We demonstrate that adaptive social behaviour enables invasion of the mutant strain under plausible epidemiological scenarios, even when the mutant strain has a lower basic reproductive number than the resident strain. Surprisingly, in some situations, increasing the perceived severity of the resident strain can facilitate invasion of the more virulent mutant strain. Our results demonstrate that for certain applications, it may be necessary to include adaptive social behaviour in models of the emergence of virulent pathogens, so that the models can better assist public health efforts to control infectious diseases.

It is increasingly recognized that a key component of successful infection control efforts is understanding the complex, two-way interaction between disease dynamics and human behavioral and social dynamics. Human behavior such as contact precautions and social distancing clearly influence disease prevalence, but disease prevalence can in turn alter human behavior, forming a coupled, nonlinear system. Moreover, in many cases, the spatial structure of the population cannot be ignored, such that social and behavioral processes and/or transmission of infection must be represented with complex networks. Research on studying coupled disease–behavior dynamics in complex networks in particular is growing rapidly, and frequently makes use of analysis methods and concepts from statistical physics. Here, we review some of the growing literature in this area. We contrast network-based approaches to homogeneous-mixing approaches, point out how their predictions differ, and describe the rich and often surprising behavior of disease–behavior dynamics on complex networks, and compare them to processes in statistical physics. We discuss how these models can capture the dynamics that characterize many real-world scenarios, thereby suggesting ways that policy makers can better design effective prevention strategies. We also describe the growing sources of digital data that are facilitating research in this area. Finally, we suggest pitfalls which might be faced by researchers in the field, and we suggest several ways in which the field could move forward in the coming years., Highlights • We systematically survey how the behavior affects disease spreading and prevention in well-mixed and networked populations. • The coupled disease–behavior dynamics is closely related with evolution or economic rules, and further influences the pattern formation. • Theoretical prediction gets the empirical validation via digital data or experiments. • Many novel findings or phenomena need the support of methods in statistical physics.

The relationship between socioeconomic development and environmental degradation measures such as SO2, CO, and NOx emissions and deforestation has sometimes been claimed to follow an environmental Kuznets curve. However, in an era of globalization where the populations that experience economic benefits may be geographically distant from the populations that experience the resulting environmental degradation, it is not clear whether mechanisms which may have supported an environmental Kuznets curve (EKC) previously can still be relied upon. Game theory—the mathematical formalization of strategic interactions in groups of two or more—can be useful in such situations. Here we present a game theoretical framework for thinking about strategic dimensions of the EKC, wherein each agent is a population. The framework captures how economic activities can impact ecosystem services for one or both agents, depending on degree of globalization. We show how the EKC can give way to undesirable outcomes such as an increasing curve (IC), or even an N-shaped curve (NC), as externalities due to globalization increase and/or as the perceived maximum environmental impact decreases.

Pair approximation models have been used to study the spread of infectious diseases in spatially distributed host populations, and to explore disease control strategies such as vaccination and case isolation. Here we introduce a pair approximation model of individual uptake of non-pharmaceutical interventions (NPIs) for an acute self-limiting infection, where susceptible individuals can learn the NPIs either from other susceptible individuals who are already practicing NPIs ("social learning"), or their uptake of NPIs can be stimulated by being neighbours of an infectious person ("exposure learning"). NPIs include individual measures such as hand-washing and respiratory etiquette. Individuals can also drop the habit of using NPIs at a certain rate. We derive a spatially defined expression of the basic reproduction number R0 and we also numerically simulate the model equations. We find that exposure learning is generally more efficient than social learning, since exposure learning generates NPI uptake in the individuals at immediate risk of infection. However, if social learning is pre-emptive, beginning a sufficient amount of time before the epidemic, then it can be more effective than exposure learning. Interestingly, varying the initial number of individuals practicing NPIs does not significantly impact the epidemic final size. Also, if initial source infections are surrounded by protective individuals, there are parameter regimes where increasing the initial number of source infections actually decreases the infection peak (instead of increasing it) and makes it occur sooner. The peak prevalence increases with the rate at which individuals drop the habit of using NPIs, but the response of peak prevalence to changes in the forgetting rate are qualitatively different for the two forms of learning. The pair approximation methodology developed here illustrates how analytical approaches for studying interactions between social processes and disease dynamics in a spatially structured population should be further pursued.

Many countries have eliminated foot and mouth disease (FMD), but outbreaks remain common in other countries. Rapid development of international trade in animals and animal products has increased the risk of disease introduction to FMD-free countries. Most mathematical models of FMD are tailored to settings that are normally disease-free, and few models have explored the impact of constrained control measures in a ‘near-endemic’ spatially distributed host population subject to frequent FMD re-introductions from nearby endemic wild populations, as characterizes many low-income, resource-limited countries. Here we construct a pair approximation model of FMD and investigate the impact of constraints on total vaccine supply for prophylactic and ring vaccination, and constraints on culling rates and cumulative culls. We incorporate natural immunity waning and vaccine waning, which are important factors for near-endemic populations. We find that, when vaccine supply is sufficiently limited, the optimal approach for minimizing cumulative infections combines rapid deployment of ring vaccination during outbreaks with a contrasting approach of careful rationing of prophylactic vaccination over the year, such that supplies last as long as possible (and with the bulk of vaccines dedicated toward prophylactic vaccination). Thus, for optimal long-term control of the disease by vaccination in near-endemic settings when vaccine supply is limited, it is best to spread out prophylactic vaccination as much as possible. Regardless of culling constraints, the optimal culling strategy is rapid identification of infected premises and their immediate contacts at the initial stages of an outbreak, and rapid culling of infected premises and farms deemed to be at high risk of infection (as opposed to culling only the infected farms). Optimal culling strategies are similar when social impact is the outcome of interest. We conclude that more FMD transmission models should be developed that are specific to the challenges of FMD control in near-endemic, low-income countries.

Nitrogen runoff in certain southeastern Australian grasslands promotes the invasion of exotic grassland species at the expense of native species. Mitigation programs can reduce runoff and thus support native species, but their success may require the awareness and support of local populations. This situation represents a coupled socio-ecological system, since nitrogen runoff caused by local populations can enable the invasion of exotic grassland species, which can in turn stimulate a social response to restore the native species. Our objective is to use a mathematical model to identify potential socio-ecological mechanisms for the persistence of native grassland species, and the parameter regimes for which these mechanisms operate. We couple a model of southeastern Australian grassland dynamics with a model of human social dynamics concerning runoff mitigation. Nitrogen runoff can enter the ecosystem either through local sources under control of a human population, or through global sources not under their control. Humans learn mitigating behaviour socially, and respond to the prevalence of native and exotic grassland species. We find that socio-ecological dynamics introduce broad parameter regimes that are not present in the ecological system in isolation from the human system. We identify two mechanisms for native grassland persistence: one is associated with significant reductions in runoff rates and/or cost of runoff mitigation programs, resulting in a stable state where the native grassland species exists or dominates, with or without the support of socio-ecological feedback. A second mechanism associated with higher rates of nitrogen input supports persistence of the native species through oscillations in species abundance and mitigation behaviour in the human population. However, this state is less favourable to the native species because the oscillations may become extreme in amplitude. Finally, we find that increasing the cost of mitigation programs not only reduces mitigating behaviour in the population but also (more surprisingly) increases the tendency for the system to destabilize into a regime of oscillations in native species biomass. We conclude that multiple socio-ecological mechanisms could potentially support native species in grassland ecosystems under stress from nitrogen runoff and invasive species. Further research can refine such models to inform policy in the face of nonlinear socio-ecological responses.

Over-exploitation of natural resources can have profound effects on both ecosystems and their resident human populations. Simple theoretical models of the dynamics of a population of human harvesters and the abundance of a natural resource being harvested have been studied previously, but relatively few models consider the effect of metapopulation structure (i.e., a population distributed across discrete patches). Here we analyze a socio-ecological metapopulation model based on an existing single-population model used to study persistence and collapse in human populations. Resources grow logistically on each patch. Each population harvests resources on its own patch to support population growth, but can also harvest resources from other patches when their own patch resources become scarce. We show that when populations are allowed to harvest resources from other patches, the peak population size is higher, but subsequent population collapse is significantly accelerated and across a broader parameter regime. As the number of patches in the metapopulation increases, collapse is more sudden, more severe, and occurs sooner. These effects persist under scenarios of asymmetry and inequality between patches. Our model makes simplifying assumptions in order to facilitate insight and understanding of model dynamics. However, the robustness of the model prediction suggests that more sophisticated models should be developed to ascertain the impact of metapopulation structure on socio-ecological sustainability.

As the global human population continues to grow, so too does our impact on the environment. The ingenuity with which our species has harnessed natural resources to fulfill our needs is dazzling. Even as we tighten our grip on the environment, however, the escalating extent of anthropogenic actions destabilizes long-standing ecological balances (1, 2). The dangers of mining, refining, and fossil fuel consumption now extend beyond occupational or proximate risks to global climate change (3). Among a plethora of environmental problems, extreme climate events are intensifying (4, 5). Storms, droughts, and floods cause direct destruction, but also have pervasive repercussions on food security, infectious disease transmission, and economic stability that take their toll for many years. For example, within weeks of the catastrophic wind and flood damage from the 2016 Hurricane Matthew in Haiti, there was a dramatic surge in cholera, among other devastating repercussions (6, 7). In a world where 1% of the population possesses 50% of the wealth (8), those worst affected by extreme climatic events and the aftermath are also the least able to rebound. Compounding the impact of natural disasters, our progressively more intimate interactions with fragmented environments (9) have given rise to an era of disease emergence and re-emergence at unprecedented rates, as exemplified by recent outbreaks of the Ebola and Zika viruses. Furthermore, globalization to an extent that includes the airline travel of over eight million people every day has enabled such disease outbreaks to disseminate rapidly and pose a threat far beyond their areas of origin (10). Addressing these challenges requires an understanding of coupled human–environment dynamics, whereby human activity modifies an environmental system (often detrimentally), and the resulting environmental repercussions then impact humans. In turn, these impacts can potentially spur a shift in human activity toward protection and restoration. … [↵][1]1To whom correspondence should be addressed. Email: alison.galvani{at}yale.edu. [1]: #xref-corresp-1-1

Many plants reproduce clonally through vegetative extensions (spacers). This results in a patch of clones connected through a network of spacers. The resulting network has a nontrivial spatial pattern that can be an important determinant of survival and fitness of the clonal plant. Here, we develop general growth rules that dictate how individual clones under local density-dependent conditions add spacers, giving rise to emergent population-level spatial patterns. A population subject to these growth rules is simulated using a stochastic individual-based model. The dependence of network structure on various architectural parameters is explored. The growth rules generate networks similar to those observed in natural populations, and can replicate real-world phenomena such as central die-back with regeneration, ‘fairy rings', and branch entrapment. A shorter spacer length results in higher population density (which may confer resistance to invasion in real populations), while longer spacer length allows the population to spread more quickly. The lateral branching angle, node-by-node angle, and spacer length appear to be the most influential parameters for determining the spatial architecture of the clonal patch. The number of daughter branches per mother branch follows a power law distribution in a diverse set of simulated networks. Continually growing computational power will make such simulation models increasingly useful for understanding the spatial growth of clonal plants, and power law behaviour may be a very common feature of both simulated and real clonal plant populations.

Animal Birth Control (ABC) is a program by which stray dogs are sterilized and vaccinated against rabies with the aim of controlling both dog population size and rabies. Population size and demographics of stray dogs were measured before and after implementation of an ABC program in Jodhpur, India. Dog population size declined (p0.05) in three of five areas surveyed, showed a decreasing trend (p0.05) in 1 area, and remained stable in 1 area between 2005 and 2007. By 2007, 61.8-86.5% of the free-roaming dog population was surgically sterilized and vaccinated for rabies in the areas surveyed. In March-May, 2007, adults comprised 80-96% of the free-roaming dog population, while subadults and puppies comprised 0-18 and 0-4%, respectively. The male:female ratio among dogs3 months old was 1.4:1. A population demographic model predicted that at the current level of sterilization/rabies vaccination, vaccination coverage would remain above 70%, and the dog population would decrease by 69% reaching stability after 13-18 years. A surgical sterilization coverage under 40% would maintain the dog population at current levels.

Birth rates have been declining in higher-income countries since the middle of the 19th century. A growing number of other countries have entered this demographic transition to lower fertility, as socioeconomic development continues. Analyses of this demographic transition vary widely, but most analyze individual populations in isolation from others, and most come from fields outside the biological sciences. Here, we develop a population biological model of population dynamics in higher-income countries. Individual countries evolve through density-regulated growth, where gradual evolution toward higher population densities boosts productivity (and hence socioeconomic growth) through economics of agglomeration and scale, in turn reducing birth rates. The exchange of technology and capital between countries can further boost productivity gains in any given country, thus contributing to its demographic transition. As a result, countries can down-regulate one another's population growth through mutual improvements in productivity. The model is fitted to time series data on population size, GDP per capita, and birth rates for the United States, the United Kingdom, and France. The metapopulation dynamics are also characterized across a range of parameter values close to the fitted values. This work may help advance population biological approaches to understanding the implications of the fertility demographic transition for modern human populations. This is relevant to developing long-term predictions of the earth's total population size, which must be based upon a model that incorporates underlying mechanisms.

Human papillomavirus vaccine prevents infection by two major oncogenic types of the virus. Continued screening is needed in vaccinated women to prevent cancers caused by high-risk types not included in the vaccine. An exaggerated sense of protection from the vaccine could lead to a decline in the rate of screening among vaccinated women, which in principle could lead to an increase in the incidence of cervical cancer. We present a simple mathematical model of vaccination, screening, and disease incidence, including an analysis of the effect of data uncertainties. For a population with opportunistic screening and 30% vaccine coverage, screening rates in vaccinated women would have to decline by at least 80% (median value of probabilistic uncertainty analysis) before the incidence of cervical cancer would increase in the era since the introduction of the vaccine. By comparison, the decline needed is at least 49% in a population with organised screening and 70% vaccine coverage. In populations that have highly effective cervical screening programmes, incidence of cervical cancer starts to increase after smaller, but still substantial, decreases in screening. Introduction of vaccine is unlikely to lead to an increased incidence of cervical cancer as a result of diminished screening.

Background: The 2009 influenza A (H1N1) pandemic has required decision-makers to act in the face of substantial uncertainties. Simulation models can be used to project the effectiveness of mitigation strategies, but the choice of the best scenario may change depending on model assumptions and uncertainties. Methods: We developed a simulation model of a pandemic (H1N1) 2009 outbreak in a structured population using demographic data from a medium-sized city in Ontario and epidemiologic influenza pandemic data. We projected the attack rate under different combinations of vaccination, school closure and antiviral drug strategies (with corresponding “trigger” conditions). To assess the impact of epidemiologic and program uncertainty, we used “combinatorial uncertainty analysis.” This permitted us to identify the general features of public health response programs that resulted in the lowest attack rates. Results: Delays in vaccination of 30 days or more reduced the effectiveness of vaccination in lowering the attack rate. However, pre-existing immunity in 15% or more of the population kept the attack rates low, even if the whole population was not vaccinated or vaccination was delayed. School closure was effective in reducing the attack rate, especially if applied early in the outbreak, but this is not necessary if vaccine is available early or if pre-existing immunity is strong. Interpretation: Early action, especially rapid vaccine deployment, is disproportionately effective in reducing the attack rate. This finding is particularly important given the early appearance of pandemic (H1N1) 2009 in many schools in September 2009.

The timing of introduction of a new species into an ecosystem can be critical in determining the invasibility (i.e. the sensitivity to invasion) of a resident population. Here, we use an individual-based model to test how (1) the type of competition (symmetric versus asymmetric) and (2) seed masting influence the success of invasion by producing oscillatory dynamics in resident tree populations. We focus on a case where two species (one resident, one invader introduced at low density) do not differ in terms of competitive abilities. By varying the time of introduction of the invader, we show that oscillations in the resident population favour invasion, by creating “invasibility windows” during which resource is available for the invader due to transiently depressed resident population density. We discuss this result in the context of current knowledge on forest dynamics and invasions, emphasizing the importance of variability in population dynamics.

In modern industrialized countries, human birth rates have been declining persistently for decades. In many cases they have now fallen below the replacement threshold. However, unlike in natural populations where population growth is constrained by limited resources, birth rates in modern industrialized countries are negatively correlated with resource availability. Here, declining birth rates in human populations are shown to be a manifestation of density-dependent population growth brought on by socioeconomic development. This is demonstrated by combining empirical power law relations between population size, gross domestic product (GDP) per capita, and fertility in a simple theoretical model describing population dynamics in developed countries. For a closed population, the model exhibits growth to a globally stable equilibrium population size, for both national and city populations. A version of the model that is open with respect to immigration and the influence of foreign technology and capital exhibits a good fit to long-term time series data on population size, GDP per capita, and birth rates for the United States, France and Japan.

Endogenous ecological memory (EEM) refers to the phenomenon where past states of a system (i.e. population density) can influence present states. In this paper, we address the effects of EEM on qualitative changes in population dynamics over time. The goal was to determine the effects of EEM on the stability and resilience of a population. Since natural populations do not live in isolation, we analyze the discrete-time Ricker model S t +1 = S t exp ( R ) exp (− RS t / K ) with environmental stochasticity. We explore the model when time-delays are restricted to the density-dependent exp( −RS t / K ) component of the model and lognormal multiplicative noise is incorporated as well. Simulation results show that population stability, as measured by the standard deviation of population density about the carrying capacity, decreases as the duration of EEM increases. We observe boom–bust cycles in population density for significantly long time-delays in density-dependence. These cycles become more extreme as the regulating effects of density-dependence are increasingly delayed, resulting in decreased population stability. Simulation results also show that population resilience, as measured by the return time to equilibrium after perturbation ( T r ), decrease with increasing fecundity R in a pattern that differs from the predictions of some theoretical work where memory is absent. Finally, the presence of environmental stochasticity changes the resilience properties of the model, relative to the equivalent noise-free model.

Hepatitis A (HA) vaccination in Canada is currently targeted toward high-risk groups. The cost-effectiveness and expected health outcomes of universal vaccination relative to targeted vaccination in low-incidence countries such as Canada are currently unknown. Here, we conducted a cost-utility analysis for this situation, with Canada as the study population. We included vaccine costs, time costs, infection costs, and public health costs. We assessed a range of possible universal vaccination strategies over an 80-year time horizon using multiple cost perspectives. A dynamic model was used to account for herd immunity. Aggregate health gains from switching to universal vaccination are modest (10-30 QALYs per year). However, a "9+9" strategy that replaces two doses of monovalent hepatitis B (HB) vaccine at 9/10 years (universally administered in most provinces) with two doses of bivalent HA/HB vaccine is cost-saving from the societal perspective. At a willingness to pay threshold of $50,000/QALY, mean net benefit is +49.4 QALYs (S.D. 12.6) from the societal perspective and +3.8 QALYS (S.D. 3.0) from the payer perspective for the "9+9" strategy. Net benefit from the payer perspective is sensitive to the marginal cost of HA/HB vaccine relative to HB vaccine. Similar conclusions may apply in other countries with low incidence and a targeted vaccination policy.

There has been growing use of highly active antiretroviral treatment (HAART) for HIV and significant progress in developing prophylactic HIV vaccines. The simplest theories of counterproductive behavioral responses to such interventions tend to focus on single feedback mechanisms: for instance, HAART optimism makes infection less scary and thus promotes risky sexual behavior. Here, we develop an agent based, age-structured model of HIV transmission, risk perception and partner selection in a core group to explore behavioral responses to interventions. We find that interventions can activate not one, but several feedback mechanisms that could potentially influence decision-making and HIV prevalence. In the model, HAART increases the attractiveness of unprotected sex, but it also increases perceived risk of infection and, on longer timescales, causes demographic impacts that partially counteract HAART optimism. Both HAART and vaccination usually lead to lower rates of unprotected sex on the whole, but intervention effectiveness depends strongly on whether individuals over- or under-estimate intervention coverage. Age-specific effects cause sexual behavior and HIV prevalence to change in opposite ways in old and young age groups. For complex infections like HIV—where interventions influence transmission, demography, sexual behavior and risk perception—we conclude that evaluations of behavioral responses should consider multiple feedback mechanisms.

Background The transportation of camp firewood infested by non-native forest pests such as Asian long-horned beetle (ALB) and emerald ash borer (EAB) has severe impacts on North American forests. Once invasive forest pests are established, it can be difficult to eradicate them. Hence, preventing the long-distance transport of firewood by individuals is crucial. Methods Here we develop a stochastic simulation model that captures the interaction between forest pest infestations and human decisions regarding firewood transportation. The population of trees is distributed across 10 patches (parks) comprising a “low volume” partition of 5 patches that experience a low volume of park visitors, and a “high volume” partition of 5 patches experiencing a high visitor volume. The infestation spreads within a patch—and also between patches—according to the probability of between-patch firewood transportation. Individuals decide to transport firewood or buy it locally based on the costs of locally purchased versus transported firewood, social norms, social learning, and level of concern for observed infestations. Results We find that the average time until a patch becomes infested depends nonlinearly on many model parameters. In particular, modest increases in the tree removal rate, modest increases in public concern for infestation, and modest decreases in the cost of locally purchased firewood, relative to baseline (current) values, cause very large increases in the average time until a patch becomes infested due to firewood transport from other patches, thereby better preventing long-distance spread. Patches that experience lower visitor volumes benefit more from firewood movement restrictions than patches that experience higher visitor volumes. Also, cross–patch infestations not only seed new infestations, they can also worsen existing infestations to a surprising extent: long-term infestations are more intense in the high volume patches than the low volume patches, even when infestation is already endemic everywhere. Conclusions The success of efforts to prevent long-distance spread of forest pests may depend sensitively on the interaction between outbreak dynamics and human social processes, with similar levels of effort producing very different outcomes depending on where the coupled human and natural system exists in parameter space. Further development of such modeling approaches through better empirical validation should yield more precise recommendations for ways to optimally prevent the long-distance spread of invasive forest pests.

Theoretical models of disease dynamics on networks can aid our understanding of how infectious diseases spread through a population. Models that incorporate decision-making mechanisms can furthermore capture how behaviour-driven aspects of transmission such as vaccination choices and the use of non-pharmaceutical interventions (NPIs) interact with disease dynamics. However, these two interventions are usually modelled separately. Here, we construct a simulation model of influenza transmission through a contact network, where individuals can choose whether to become vaccinated and/or practice NPIs. These decisions are based on previous experience with the disease, the current state of infection amongst one's contacts, and the personal and social impacts of the choices they make. We find that the interventions interfere with one another: because of negative feedback between intervention uptake and infection prevalence, it is difficult to simultaneously increase uptake of all interventions by changing utilities or perceived risks. However, on account of vaccine efficacy being higher than NPI efficacy, measures to expand NPI practice have only a small net impact on influenza incidence due to strongly mitigating feedback from vaccinating behaviour, whereas expanding vaccine uptake causes a significant net reduction in influenza incidence, despite the reduction of NPI practice in response. As a result, measures that support expansion of only vaccination (such as reducing vaccine cost), or measures that simultaneously support vaccination and NPIs (such as emphasizing harms of influenza infection, or satisfaction from preventing infection in others through both interventions) can significantly reduce influenza incidence, whereas measures that only support expansion of NPI practice (such as making hand sanitizers more available) have little net impact on influenza incidence. (However, measures that improve NPI efficacy may fare better.) We conclude that the impact of interference on programs relying on multiple interventions should be more carefully studied, for both influenza and other infectious diseases., Author Summary The spread of infectious diseases can be inhibited by both vaccines and non-pharmaceutical interventions (NPIs) such as hand-washing, respiratory etiquette, and social distancing. Theoretical models of disease spread have incorporated how individuals make decisions concerning these interventions in the face of disease risks and intervention costs. However, most previous models have considered these two interventions separately from one another. Here we combine decision-making processes for both interventions in a single model that simulates influenza spread through a network. Individuals choose interventions based on their past and present experiences with influenza, and the personal and social impacts of their choices. Our model indicates that, due to feedback loops between the interventions via their mutual impact on disease levels, efforts to reduce influenza spread by expanding NPI practice are almost completely mitigated by the resulting drop in vaccine coverage, whereas efforts to expand vaccine coverage are only weakly affected by the response of NPI practice. Furthermore, strategies such as making vaccines more available, stressing the harms of being infected, or stressing the social benefits of preventing infection through both interventions will prevent more disease than only expanding NPI practice through making hand sanitizers more widely available, for example.

Tags are conspicuous attributes of organisms that affect the behaviour of other organisms toward the holder, and have previously been used to explore group formation and altruism. Homophilic imitation, a form of tag-based selection, occurs when organisms imitate those with similar tags. Here we further explore the use of tag-based selection by developing homophilic replicator equations to model homophilic imitation dynamics. We assume that replicators have both tags (sometimes called traits) and strategies. Fitnesses are determined by the strategy profile of the population, and imitation is based upon the strategy profile, fitness differences, and similarity in tag space. We show the characteristics of resulting fixed manifolds and conditions for stability. We discuss the phenomenon of coat-tailing (where tags associated with successful strategies increase in abundance, even though the tags are not inherently beneficial) and its implications for population diversity. We extend our model to incorporate recurrent mutations and invasions to explore their implications upon tag and strategy diversity. We find that homophilic imitation based upon tags significantly affects the diversity of the population, although not the ESS. We classify two different types of invasion scenarios by the strategy and tag compositions of the invaders and invaded. In one scenario, we find that novel tags introduced by invaders become more readily established with homophilic imitation than without it. In the other, diversity decreases. Lastly, we find a negative correlation between homophily and the rate of convergence.

There exists an interplay between vaccine coverage, disease prevalence and the vaccinating behaviour of individuals. Moreover, because of herd immunity, there is also a strategic interaction between individuals when they are deciding whether or not to vaccinate, because the probability that an individual becomes infected depends upon how many other individuals are vaccinated. To understand this potentially complex interplay, a game dynamic model is developed in which individuals adopt strategies according to an imitation dynamic (a learning process), and base vaccination decisions on disease prevalence and perceived risks of vaccines and disease. The model predicts that oscillations in vaccine uptake are more likely in populations where individuals imitate others more readily or where vaccinating behaviour is more sensitive to changes in disease prevalence. Oscillations are also more likely when the perceived risk of vaccines is high. The model reproduces salient features of the time evolution of vaccine uptake and disease prevalence during the whole-cell pertussis vaccine scare in England and Wales during the 1970s. This suggests that using game theoretical models to predict, and even manage, the population dynamics of vaccinating behaviour may be feasible.