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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.

The resurgence of infectious diseases due to vaccine refusal has highlighted the role of interactions between disease dynamics and the spread of vaccine opinion on social networks. Shifts between disease elimination and outbreak regimes often occur through tipping points. It is known that tipping points can be predicted by early warning signals (EWS) based on characteristic dynamics near the critical transition, but the study of EWS in coupled behaviour-disease networks has received little attention. Here, we test several EWS indicators measuring spatial coherence and autocorrelation for their ability to predict a critical transition corresponding to disease outbreaks and vaccine refusal in a multiplex network model. The model couples paediatric infectious disease spread through a contact network to binary opinion dynamics of vaccine opinion on a social network. Through change point detection, we find that mutual information and join count indicators provided the best EWS. We also show the paediatric infectious disease natural history generates a discrepancy between population-level vaccine opinions and vaccine immunity status, such that transitions in the social network may occur before epidemiological transitions. These results suggest that monitoring social media for EWS of paediatric infectious disease outbreaks using these spatial indicators could be successful.

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.

ObjectivesAs COVID-19 vaccinations accelerate in many countries, narratives skeptical of vaccination have also spread through social media. Open online forums like Reddit provide an opportunity to quantitatively examine COVID-19 vaccine perceptions over time. We examine COVID-19 misinformation on Reddit following vaccine scientific announcements.MethodsWe collected all posts on Reddit from January 1 2020 - December 14 2020 (n=266,840) that contained both COVID-19 and vaccine-related keywords. We used topic modeling to understand changes in word prevalence within topics after the release of vaccine trial data. Social network analysis was also conducted to determine the relationship between Reddit communities (subreddits) that shared COVID-19 vaccine posts, and the movement of posts between subreddits.ResultsThere was an association between a Pfizer press release reporting 90% efficacy and increased discussion on vaccine misinformation. We observed an association between Johnson and Johnson temporarily halting its vaccine trials and reduced misinformation. We found that information skeptical of vaccination was first posted in a subreddit (r/Coronavirus) which favored accurate information and then reposted in subreddits associated with antivaccine beliefs and conspiracy theories (e.g. conspiracy, LockdownSkepticism).ConclusionsOur findings can inform the development of interventions where individuals determine the accuracy of vaccine information, and communications campaigns to improve COVID-19 vaccine perceptions. Such efforts can increase individual- and population-level awareness of accurate and scientifically sound information regarding vaccines and thereby improve attitudes about vaccines. Further research is needed to understand how social media can contribute to COVID-19 vaccination services.FundingStudy was funded by the Yale Institute for Global Health and the Whitney and Betty MacMillan Center for International and Area Studies at Yale University. The funding bodies had no role in the design, analysis or interpretation of the data in the study.

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.

Sudden shifts in population health and vaccination rates occur as the dynamics of some epidemiological models go through a critical point; literature shows that this is sometimes foreshadowed by early warning signals (EWS). We investigate different structural measures of a network as candidate EWS of infectious disease outbreaks and changes in popular vaccine sentiment. We construct a multiplex disease model coupling infectious disease spread and social contact dynamics. We find that the number and mean size of echo chambers predict transitions in the infection dynamics, as do opinion-based communities. Graph modularity also gives early warnings, though the clustering coefficient shows no significant pre-outbreak changes. Change point tests applied to the EWS show decreasing efficacy as social norms strengthen. Therefore, many measures of social network connectivity can predict approaching critical changes in vaccine uptake and aggregate health, thereby providing valuable tools for improving public health.

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.

Dynamic transmission models of influenza are sometimes used in decision-making to identify which vaccination strategies might best reduce influenza-associated health burdens. Our goal was to use laboratory confirmed influenza cases to fit model parameters in an age-structured, two-type (influenza A/B) dynamic model of influenza. We compared the fitted model under two fitting methodologies: using longitudinal weekly case notification data versus using cross-sectional age-stratified cumulative case notification data. The longitudinal data came from a Canadian province (Ontario)whereasthecross-sectionaldatacamefromthenationallevel(allofCanada). Wefindthatthe longitudinal fitting method provides best fitting parameter sets that have a higher variance between the respective parameters in each set than the cross-sectional cumulative case method. Model predictions-particularly for influenza A-are very different for the two fitting methodologies under hypothetical vaccination scenarios that expand coverage in either younger age classes or older age classes: the cross-sectional method predicts much larger decreases in total cases under expanded vaccine coverage than the longitudinal method. Also, the longitudinal method predicts that vaccinating younger age groups yields greater declines in total cases than vaccinating older age groups, whereas the cross- sectional method predicts the opposite. We conclude that model predictions of vaccination impacts under different strategies may differ at national versus provincial levels. Finally, we discuss whether usinglongitudinalversuscross-sectionaldatainmodelfittingmaygeneratefurtherdifferencesinmodel predictions (above and beyond population-specific differences) and how such a hypothesis could be tested in future studies.

The propagation of rumours about rare but severe adverse vaccination or infection events through social networks can strongly impact vaccination uptake. Here we model a coupled behaviour-disease system where individual risk perception regarding vaccines and infection are shaped by their personal experiences and the experiences of others. Information about vaccines and infection either propagates through the network or becomes available through globally available sources. Dynamics are studied on a range of network types. Individuals choose to vaccinate according to their personal perception of risk and information about infection prevalence. We study events ranging from common and mild, to severe and rare. We find that vaccine and infection adverse events have asymmetric impacts. Vaccine (but not infection) adverse events may significantly prolong the tail of an outbreak. Similarly, introducing a small risk of a vaccine adverse event may cause a steep decline in vaccine coverage, especially on scale-free networks. Global dissemination of information about infection prevalence boosts vaccine coverage more than local dissemination. Taken together, these findings highlight the dangers associated with vaccine rumour propagation through scale-free networks such as those exhibited by online social media, as well as the benefits of disseminating public health information through mass media.

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.

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.

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.

Seasonal influenza imposes a significant worldwide health burden each year. Mathematical models help us to understand how changes in vaccination affect this burden. Here, we develop a new dynamic transmission model which directly tracks the four dominant seasonal influenza strains/lineages, and use it to retrospectively examine the impact of the switch from a targeted to a universal influenza immunization program (UIIP) in the Canadian province of Ontario in 2000. According to our model results, averaged over the first four seasons post-UIIP, the rates of influenza-associated health outcomes in Ontario were reduced to about half of their pre-UIIP values. This is conservative compared to the results of a study estimating the UIIP impact from administrative data, though that study finds age-specific trends similar to those presented here. The strain interaction in our model, together with its flexible parameter calibration scheme, make it readily extensible to studying scenarios beyond the one explored here.

The controversy over whether vaccine-targeted HPV types will be replaced by other oncogenic, non-vaccine-targeted types remains unresolved. This is in part because little is known about the ecology of HPV types. Patient data has been interpreted to suggest independence or facilitative interactions between types and therefore replacement is believed to be unlikely. With a novel mathematical model, we investigated which HPV type interactions and their immune responses gave qualitatively similar patterns frequently observed in patients. To assess the possibility of type replacement, vaccination was added to see if non-vaccine-targeted types increased their 'niche'. Our model predicts that independence and facilitation are not necessary for the coexistence of types inside hosts, especially given the patchy nature of HPV infection. In fact, independence and facilitation inadequately represented co-infected patients. We found that some form of competition is likely in natural co-infections. Hence, non-vaccine-targeted types that are not cross-reactive with the vaccine could spread to more patches and can increase their viral load in vaccinated hosts. The degree to which this happens will depend on replication and patch colonization rates. Our results suggest that independence between types could be a fallacy, and so without conclusively untangling HPV within-host ecology, type replacement remains theoretically viable. More ecological thinking is needed in future studies.

Every year in the United States more than 12,000 women are diagnosed with cervical cancer, a disease principally caused by human papillomavirus (HPV). Bivalent and quadrivalent HPV vaccines protect against 66% of HPV-associated cervical cancers, and a new nonavalent vaccine protects against an additional 15% of cervical cancers. However, vaccination policy varies across states, and migration between states interdependently dilutes state-specific vaccination policies. To quantify the economic and epidemiological impacts of switching to the nonavalent vaccine both for individual states and for the nation as a whole, we developed a model of HPV transmission and cervical cancer incidence that incorporates state-specific demographic dynamics, sexual behavior, and migratory patterns. At the national level, the nonavalent vaccine was shown to be cost-effective compared with the bivalent and quadrivalent vaccines at any coverage despite the greater per-dose cost of the new vaccine. Furthermore, the nonavalent vaccine remains cost-effective with up to an additional 40% coverage of the adolescent population, representing 80% of girls and 62% of boys. We find that expansion of coverage would have the greatest health impact in states with the lowest coverage because of the decreasing marginal returns of herd immunity. Our results show that if policies promoting nonavalent vaccine implementation and expansion of coverage are coordinated across multiple states, all states benefit both in health and in economic terms.

Behavior-incidence models have been used to model phenomena such as free-riding vaccinating behavior, where nonvaccinators free ride on herd immunity generated by vaccinators. Here, we develop and analyze a simulation model of voluntary ring vaccination on an evolving social contact network. Individuals make vaccination decisions by examining their expected payoffs, which are influenced by the infection status of their neighbors. We find that stochasticity can make outcomes extremely variable (near critical thresholds) and thus unpredictable: some stochastic realizations result in rapid control through ring vaccination while others result in widespread transmission. We also explore the phenomenon of outcome inelasticity, wherein behavioral responses result in certain outcome measures remaining relatively unchanged. Finally, we explore examples where ineffective or risky vaccines are more widely adopted than safe, effective vaccines. This occurs when such a vaccine is unattractive to a sufficient number of contacts of an index case to cause failure of ring vaccination. As a result, the infection percolates through the entire network, causing the final epidemic size and vaccine coverage to be higher than would otherwise occur. Effects such as extreme outcome variability and outcome inelasticity have implications for vaccination policies that depend on individual choice for their success and predictability.

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.

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.

Mathematical models have been used extensively in the evaluation of chronic diseases and in exploring the health economics of vaccination. In this study, we examine the value of having two different cohort models based on similar assumptions, one comprehensive and one simplified, which can be used to evaluate the impact of cervical cancer vaccination. To compare models, we ran cost-effectiveness analyses in four geographical regions (Italy, the UK, Taiwan and Canada). We show that the models produce comparable results and therefore can be used independently. However, as they require different complexities of data inputs, they are more suited to different circumstances depending on the level of data inputs available or the complexity of the research question asked.

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.

Vaccination against Hepatitis A virus (HAV) in Canada is currently targeted toward high-risk groups. However, universal vaccination has been adopted in several other countries with a similar disease burden. Here we develop an age-structured compartmental model of HAV transmission and vaccination in Canada to assess potential universal vaccination strategies. The model predicts that universal vaccination at age 1 (respectively 4, 9, 15), with phasing out of targeted vaccination, would reduce reported incidence by 60% (respectively 52, 36, 31%) and mortality attributable to HAV by 56% (respectively 45, 26, 25%), relative to continued targeted vaccination, over 80 years.

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.

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.

In non-mandatory vaccination policies, individual choice can be a major driver of vaccine uptake. Choice thereby influences whether public health targets can be achieved. Individual vaccinating decisions can be influenced by perceptions of vaccine risks or infection risks. There is also the potential for non-vaccinators to strategically 'free-ride' on herd immunity provided by vaccinators. This strategic interaction between individuals generates a social dilemma--a conflict between self-interest and what is best for the group as a whole. Game theory and related mathematical approaches that couple mechanistic models of vaccinating decisions with mechanistic models of disease spread can capture this social dilemma and address relevant questions. The past decade has seen significant growth in the theoretical literature developing and analyzing such models. Here, we argue that using these models to address specific public health challenges will require more work that integrates information from empirical studies into the development and validation of such models, as well as more collaboration between mathematical modelers, psychologists, economists and public health experts.

We propose a model describing the synergetic feedback between word-of-mouth (WoM) and epidemic dynamics controlled by voluntary vaccination. We combine a game-theoretic model for the spread of WoM and a compartmental model describing $SIR$ disease dynamics in the presence of a program of voluntary vaccination. We evaluate and compare two scenarios, depending on what WoM disseminates: (1) vaccine advertising, which may occur whether or not an epidemic is ongoing and (2) epidemic status, notably disease prevalence. Understanding the synergy between the two strategies could be particularly important for organizing voluntary vaccination campaigns. We find that, in the initial phase of an epidemic, vaccination uptake is determined more by vaccine advertising than the epidemic status. As the epidemic progresses, epidemic status become increasingly important for vaccination uptake, considerably accelerating vaccination uptake toward a stable vaccination coverage., Comment: 10 pages, 2 figures

Interactions between disease dynamics and vaccinating behavior have been explored in many coupled behavior-disease models. Cognitive effects such as risk perception, framing and subjective probabilities of adverse events can be important determinants of the vaccinating behaviour and represent departures from the pure “rational” decision model that are often described as “bounded rationality”. However, the impact of such cognitive effects in the context of paediatric infectious disease vaccines has received relatively little attention. Here, we develop a disease-behavior model that accounts for bounded rationality through prospect theory. We analyze the model and compare its predictions to a reduced model that lacks bounded rationality. We find that, in general, introducing bounded rationality increases the dynamical richness of the model and makes it harder to eliminate a paediatric infectious disease. In contrast, in other cases, a low cost, highly efficacious vaccine can be refused, even when the rational decision model predicts acceptance. Injunctive social norms can prevent vaccine refusal, if vaccine acceptance is sufficiently high in the beginning of the vaccination campaign. Cognitive processes can have major impacts on the predictions of behaviour-disease models and further study of such processes in the context of vaccination is thus warranted.

Mathematical models that couple disease dynamics and vaccinating behaviour often assume that the incentive to vaccinate disappears if disease prevalence is zero. Hence, they predict that vaccine refusal should be the rule, and elimination should be difficult or impossible. In reality, countries with non-mandatory vaccination policies have usually been able to maintain elimination or very low incidence of paediatric infectious diseases for long periods of time. Here, we show that including injunctive social norms can reconcile such behaviour-incidence models to observations. Adding social norms to a coupled behaviour-incidence model enables the model to better explain pertussis vaccine uptake and disease dynamics in the UK from 1967 to 2010, in both the vaccine-scare years and the years of high vaccine coverage. The model also illustrates how a vaccine scare can perpetuate suboptimal vaccine coverage long after perceived risk has returned to baseline, pre-vaccine-scare levels. However, at other model parameter values, social norms can perpetuate depressed vaccine coverage during a vaccine scare well beyond the time when the population's baseline vaccine risk perception returns to pre-scare levels. Social norms can strongly suppress vaccine uptake despite frequent outbreaks, as observed in some small communities. Significant portions of the parameter space also exhibit bistability, meaning long-term outcomes depend on the initial conditions. Depending on the context, social norms can either support or hinder immunization goals.

Previous mathematical models of spatial farm-to-farm transmission of foot and mouth disease (FMD) have explored the impacts of control measures such as culling and vaccination during a single outbreak in a country normally free of FMD. As a result, these models do not include factors that are relevant to countries where FMD is endemic in some regions, like long-term waning natural and vaccine immunity, use of prophylactic vaccination and disease re-importations. These factors may have implications for disease dynamics and control, yet few models have been developed for FMD-endemic settings. Here we develop and study an SEIRV (susceptible-exposed-infectious-recovered-vaccinated) pair approximation model of FMD. We focus on long term dynamics by exploring characteristics of repeated outbreaks of FMD and their dependence on disease re-importation, loss of natural immunity, and vaccine waning. We find that the effectiveness of ring and prophylactic vaccination strongly depends on duration of natural immunity, rate of vaccine waning, and disease re-introduction rate. However, the number and magnitude of FMD outbreaks are generally more sensitive to the duration of natural immunity than the duration of vaccine immunity. If loss of natural immunity and/or vaccine waning happen rapidly, then multiple epidemic outbreaks result, making it difficult to eliminate the disease. Prophylactic vaccination is more effective than ring vaccination, at the same per capita vaccination rate. Finally, more frequent disease re-importation causes a higher cumulative number of infections, although a lower average epidemic peak. Our analysis demonstrates significant differences between dynamics in FMD-free settings versus FMD-endemic settings, and that dynamics in FMD-endemic settings can vary widely depending on factors such as the duration of natural and vaccine immunity and the rate of disease re-importations. We conclude that more mathematical models tailored to FMD-endemic countries should be developed that include these factors.

Objective Advisory committees in Canada and the United States have updated recommendations for quadrivalent meningococcal conjugate vaccines against serogroups A, C, W135, and Y. Our objective was to evaluate optimally effective meningococcal vaccination policies using a stochastic dynamic model. Canada was used as an example. Methods Our stochastic dynamic model of Neisseria meningitidis (Nm) transmission in an age-structured population assumed partial cross-immunity among two aggregated serogroup categories: ‘AWY’ containing A, W135, and Y; and ‘Other’ containing B, C, and ungroupable types. We compared the impact of monovalent C versus quadrivalent ACWY vaccination on Nm carriage and invasive meningococcal disease (IMD). Our model was parameterized with Canadian epidemiological and demographic data and employed probabilistic sensitivity analysis. Results Routine infant immunization at 12 months and boosting at 15 years with a quadrivalent vaccine is projected to have the largest impact on total IMD incidence: a 74% reduction over 40 years. Routine infant immunization with a monovalent vaccine at 12 months only has much less impact and also generates strain replacement appearing after approximately ten years of continuous use. Conclusions Immunizing infants at 12 months and boosting adolescents at 15 years with an ACWY vaccine is predicted to be most effective at reducing IMD incidence.

The focus of the growing discipline of behavioral epidemiology (BE) of infectious diseases is on individual behavior as a key determinant of infection trajectories. This overview departs from the central, but static, role of human behavior in traditional mathematical models of infection to motivate the importance of including behavior into epidemiological models. Our aim is threefold. First, we attempt to motivate the historical and cultural background underpinning the BE revolution, focusing on the issue of rational opposition to vaccines as a natural endpoint of the changed relation between man and disease in modern industrialized countries. Second, we review those contributions, from both mathematical epidemiology and economics, that forerun the current “epidemic” of studies on BE. Last, we offer a more detailed overview of the current epidemic phase of BE studies and, still motivated by the issue of immunization choices, introduce some baseline ideas and models.

Personal experiences with past infection events, or perceived vaccine failures and complications, are known to drive vaccine uptake. We coupled a model of individual vaccinating decisions, influenced by these drivers, with a contact network model of influenza transmission dynamics. The impact of non-influenzal influenza-like illness (niILI) on decision-making was also incorporated: it was possible for individuals to mistake niILI for true influenza. Our objectives were to (1) evaluate the impact of personal experiences on vaccine coverage; (2) understand the impact of niILI on behaviour–incidence dynamics; (3) determine which factors influence vaccine coverage stability; and (4) determine whether vaccination strategies can become correlated on the network in the absence of social influence. We found that certain aspects of personal experience can significantly impact behaviour–incidence dynamics. For instance, longer term memory for past events had a strong stabilising effect on vaccine coverage dynamics, although it could either increase or decrease average vaccine coverage depending on whether memory of past infections or past vaccine failures dominated. When vaccine immunity wanes slowly, vaccine coverage is low and stable, and infection incidence is also very low, unless the effects of niILI are ignored. Strategy correlations can occur in the absence of imitation, on account of the neighbour–neighbour transmission of infection and history-dependent decision making. Finally, niILI weakens the behaviour–incidence coupling and therefore tends to stabilise dynamics, as well as breaking up strategy correlations. Behavioural feedbacks, and the quality of self-diagnosis of niILI, may need to be considered in future programs adopting “universal” flu vaccines conferring long-term immunity. Public health interventions that focus on reminding individuals about their previous influenza infections, as well as communicating facts about vaccine efficacy and the difference between influenza and niILI, may be an effective way to increase vaccine coverage and prevent unexpected drops in coverage.

Previous game-theoretic studies of vaccination behavior typically have often assumed that populations are homogeneously mixed and that individuals are fully rational. In reality, there is heterogeneity in the number of contacts per individual, and individuals tend to imitate others who appear to have adopted successful strategies. Here, we use network-based mathematical models to study the effects of both imitation behavior and contact heterogeneity on vaccination coverage and disease dynamics. We integrate contact network epidemiological models with a framework for decision-making, within which individuals make their decisions either based purely on payoff maximization or by imitating the vaccination behavior of a social contact. Simulations suggest that when the cost of vaccination is high imitation behavior may decrease vaccination coverage. However, when the cost of vaccination is small relative to that of infection, imitation behavior increases vaccination coverage, but, surprisingly, also increases the magnitude of epidemics through the clustering of non-vaccinators within the network. Thus, imitation behavior may impede the eradication of infectious diseases. Calculations that ignore behavioral clustering caused by imitation may significantly underestimate the levels of vaccination coverage required to attain herd immunity., Author Summary Both infectious diseases and behavioral traits can spread via social contacts. Using network-based mathematical models, our study addresses the interplay between these two processes, as disease spreads through a population and individuals copy their social contacts when making vaccination decisions. Imitation can produce clusters of non-vaccinating, susceptible individuals that facilitate relatively large outbreaks of infectious diseases despite high overall vaccination coverage. This may explain, for example, recent measles outbreaks observed in many countries with universal measles vaccination policies. Given that vaccine decisions are likely to be influenced by social contacts and that such imitation can have detrimental epidemiological effects, it is important that policy makers understand its causes, magnitude and implications for disease eradication.

Vaccination is a cornerstone of infectious disease prevention. However, individual vaccinating behaviour does not always result in population-level vaccine coverage patterns that are optimal for protecting public health. For example, vaccine coverage may fall below the elimination threshold due to nonvaccinators who “free-ride” on the herd immunity provided by vaccinators. Routine vaccination programs for many paediatric infectious diseases now have an almost worldwide coverage, but vaccine scares fuelled by such behaviours threaten eradication goals. This free-riding behaviour can be seen as a manifestation of policy resistance, where humans respond to an intervention in such a way that tends to undermine the intervention. However, policy resistance is only one such example of the types of dynamics that emerge from the interaction between vaccinating behaviour and disease incidence or prevalence. Here we explore four types of emergent dynamics of behaviour-incidence systems: policy resistance, policy reinforcement, outcome inelasticity, and outcome variability. We discuss examples of each of these dynamics in the behaviour-incidence modelling literature, and suggest potential implications for vaccination policy.

Immunization programs have often been impeded by vaccine scares, as evidenced by the measles-mumps-rubella (MMR) autism vaccine scare in Britain. A “free rider” effect may be partly responsible: vaccine-generated herd immunity can reduce disease incidence to such low levels that real or imagined vaccine risks appear large in comparison, causing individuals to cease vaccinating. This implies a feedback loop between disease prevalence and strategic individual vaccinating behavior. Here, we analyze a model based on evolutionary game theory that captures this feedback in the context of vaccine scares, and that also includes social learning. Vaccine risk perception evolves over time according to an exogenously imposed curve. We test the model against vaccine coverage data and disease incidence data from two vaccine scares in England & Wales: the whole cell pertussis vaccine scare and the MMR vaccine scare. The model fits vaccine coverage data from both vaccine scares relatively well. Moreover, the model can explain the vaccine coverage data more parsimoniously than most competing models without social learning and/or feedback (hence, adding social learning and feedback to a vaccine scare model improves model fit with little or no parsimony penalty). Under some circumstances, the model can predict future vaccine coverage and disease incidence—up to 10 years in advance in the case of pertussis—including specific qualitative features of the dynamics, such as future incidence peaks and undulations in vaccine coverage due to the population's response to changing disease incidence. Vaccine scares could become more common as eradication goals are approached for more vaccine-preventable diseases. Such models could help us predict how vaccine scares might unfold and assist mitigation efforts., Author Summary “Herd immunity” is a phenomenon whereby an entire population—including unvaccinated individuals—can be protected from infection by vaccinating only a certain percentage of the population. This suggests that immunization programs can be victims of their own success: past vaccinations can drive disease incidence to such low levels that as-yet unvaccinated individuals feel no incentive to get vaccinated, which creates conditions for future outbreaks. “Behavior-incidence” models capture this interplay between disease dynamics and vaccinating behavior. However, the predictive and explanatory value of these models is rarely tested against empirical data, and it is not clear whether the implied strategic interaction between individuals drives vaccinating behavior in real populations. Here we develop a behavior-incidence model based on evolutionary game theory and social learning. We show it often explains vaccine coverage data during a vaccine scare better than most competing models without strategic interactions and/or social learning. It can also predict future vaccine coverage and disease incidence peaks to a significant extent. Thus, strategic interactions between individuals via herd immunity appear to be a significant driver of behavior during a vaccine scare. It may be possible to harness behavior-incidence models to predict how future vaccine scares might unfold and possibly also to mitigate them.

Background Several potential measles vaccine innovations are in development to address the shortcomings of the current vaccine. Funders need to prioritize their scarce research and development resources. This article demonstrates the usefulness of cost-effectiveness analysis to support these decisions. Methods This study had 4 major components: (1) identifying potential innovations, (2) developing transmission models to assess mortality and morbidity impacts, (3) estimating the unit cost impacts, and (4) assessing aggregate cost-effectiveness in United Nations Children's Fund countries through 2049. Results Four promising technologies were evaluated: aerosol delivery, needle-free injection, inhalable dry powder, and early administration DNA vaccine. They are projected to have a small absolute impact in terms of reducing the number of measles cases in most scenarios because of already improving vaccine coverage. Three are projected to reduce unit cost per dose by $0.024 to $0.170 and would improve overall cost-effectiveness. Each will require additional investments to reach the market. Over the next 40 years, the aggregate cost savings could be substantial, ranging from $98.4 million to $689.4 million. Conclusions Cost-effectiveness analysis can help to inform research and development portfolio prioritization decisions. Three new measles vaccination technologies under development hold promise to be cost-saving from a global perspective over the long-term, even after considering additional investment costs.

Vaccination can delay the peak of a pandemic influenza wave by reducing the number of individuals initially susceptible to influenza infection. Emerging evidence indicates that susceptibility to severe secondary bacterial infections following a primary influenza infection may vary seasonally, with peak susceptibility occurring in winter. Taken together, these two observations suggest that vaccinating to prevent a fall pandemic wave might delay it long enough to inadvertently increase influenza infections in winter, when primary influenza infection is more likely to cause severe outcomes. This could potentially cause a net increase in severe outcomes. Most pandemic models implicitly assume that the probability of severe outcomes does not vary seasonally and hence cannot capture this effect. Here we show that the probability of intensive care unit (ICU) admission per influenza infection in the 2009 H1N1 pandemic followed a seasonal pattern. We combine this with an influenza transmission model to investigate conditions under which a vaccination program could inadvertently shift influenza susceptibility to months where the risk of ICU admission due to influenza is higher. We find that vaccination in advance of a fall pandemic wave can actually increase the number of ICU admissions in situations where antigenic drift is sufficiently rapid or where importation of a cross-reactive strain is possible. Moreover, this effect is stronger for vaccination programs that prevent more primary influenza infections. Sensitivity analysis indicates several mechanisms that may cause this effect. We also find that the predicted number of ICU admissions changes dramatically depending on whether the probability of ICU admission varies seasonally, or whether it is held constant. These results suggest that pandemic planning should explore the potential interactions between seasonally varying susceptibility to severe influenza outcomes and the timing of vaccine-altered pandemic influenza waves.

Ring vaccination can be a highly effective control strategy for an emerging disease or in the final phase of disease eradication, as witnessed in the eradication of smallpox. However, the impact of behavioural dynamics on the effectiveness of ring vaccination has not been explored in mathematical models. Here, we analyze a series of stochastic models of voluntary ring vaccination. Contacts of an index case base vaccinating decisions on their own individual payoffs to vaccinate or not vaccinate, and they can also imitate the behaviour of other contacts of the index case. We find that including imitation changes the probability of containment through ring vaccination considerably. Imitation can cause a strong majority of contacts to choose vaccination in some cases, or to choose non-vaccination in other cases—even when the equivalent solution under perfectly rational (non-imitative) behaviour yields mixed choices. Moreover, imitation processes can result in very different outcomes in different stochastic realizations sampled from the same parameter distributions, by magnifying moderate tendencies toward one behaviour or the other: in some realizations, imitation causes a strong majority of contacts not to vaccinate, while in others, imitation promotes vaccination and reduces the number of secondary infections. Hence, the effectiveness of ring vaccination can depend significantly and unpredictably on imitation processes. Therefore, our results suggest that risk communication efforts should be initiated early in an outbreak when ring vaccination is to be applied, especially among subpopulations that are heavily influenced by peer opinions.

During the 2009 H1N1 pandemic, many individuals did not seek vaccination immediately but rather decided to "wait and see" until further information was available on vaccination costs. This behaviour implies two sources of strategic interaction: as more individuals become vaccinated, both the perceived vaccination cost and the probability that susceptible individuals become infected decline. Here we analyze the outcome of these two strategic interactions by combining game theory with a disease transmission model during an outbreak of a novel influenza strain. The model exhibits a "wait and see" Nash equilibrium strategy, with vaccine delayers relying on herd immunity and vaccine safety information generated by early vaccinators. This strategic behaviour causes the timing of the epidemic peak to be strongly conserved across a broad range of plausible transmission rates, in contrast to models without such adaptive behaviour. The model exhibits not only feedback mechanisms but also a feed-forward mechanism: a high initial perceived vaccination cost perpetuates high perceived vaccine costs (and lower vaccine coverage) throughout the remainder of the outbreak. This suggests that any effect of risk communication at the start of a pandemic outbreak will be amplified compared to the same amount of risk communication effort distributed throughout the outbreak.

We describe the application of mathematical models in the study of disease epidemics with particular focus on pandemic influenza. We outline the general mathematical approach and the complications arising from attempts to apply it for disease outbreak management in a real public health context.

The effectiveness of seasonal influenza vaccination programs depends on individual-level compliance. Perceptions about risks associated with infection and vaccination can strongly influence vaccination decisions and thus the ultimate course of an epidemic. Here we investigate the interplay between contact patterns, influenza-related behavior, and disease dynamics by incorporating game theory into network models. When individuals make decisions based on past epidemics, we find that individuals with many contacts vaccinate, whereas individuals with few contacts do not. However, the threshold number of contacts above which to vaccinate is highly dependent on the overall network structure of the population and has the potential to oscillate more wildly than has been observed empirically. When we increase the number of prior seasons that individuals recall when making vaccination decisions, behavior and thus disease dynamics become less variable. For some networks, we also find that higher flu transmission rates may, counterintuitively, lead to lower (vaccine-mediated) disease prevalence. Our work demonstrates that rich and complex dynamics can result from the interaction between infectious diseases, human contact patterns, and behavior., Author Summary When influenza spreads through a human population, its dynamics are shaped by both the complex patterns of contact that arise through our daily activities and individual decisions about the prevention and treatment of flu infections. However, until recently, mathematical models of flu transmission have ignored complex interaction and behavioral patterns in order to facilitate mathematical analyses. Here, we combine two recent approaches to modeling flu–network theory and game theory–to address the interplay between contact patterns and host vaccination decisions during seasonal flu outbreaks. Intuitively, the more contacts one has, the more likely he or she is to vaccinate. However, under the assumption that people make rational decisions based on complete information about the prior seasonal epidemic, vaccination decisions are predicted to vacillate dramatically. A severe epidemic in one year inspires high vaccination rates in the following year; this causes a milder epidemic which then leads to lower vaccination rates in the following year; and the cycle begins anew. We find further that the more homogeneous the contact patterns, the more pronounced the vacillations will be, and that decision-making based on multiple past seasons (rather than just one) leads to much more consistent behavior.

Several studies have found that some parents delay the age at which their children receive pediatric vaccines due to perception of higher vaccine risk at the recommended age of vaccination. This has been particularly apparently during the Measles-Mumps-Rubella scare in the United Kingdom. Under a voluntary vaccination policy, vaccine coverage in certain age groups is a potentially complex interplay between vaccinating behaviour, disease dynamics, and age-specific risk factors. Here, we construct an age-structured game dynamic model, where individuals decide whether to vaccinate according to imitation dynamics depending on age-dependent disease prevalence and perceived risk of vaccination. Individuals may be timely vaccinators, delayers, or non-vaccinators. The model exhibits multiple equilibria and a broad range of possible dynamics. For certain parameter regimes, the proportion of timely vaccinators and delayers oscillate in an anti-phase fashion in response to oscillations in infection prevalence. Under an exogenous change to the perceived risk of vaccination as might occur during a vaccine scare, the model can also capture an increase in delayer strategists similar in magnitude to that observed during the Measles-Mumps-Rubella vaccine scare in the United Kingdom. Our model also shows that number of delayers steadily increases with increasing severity of the scare, whereas it saturates to specific value with increases in duration of the scare. Finally, by comparing the model dynamics with and without the option of a delayer strategy, we show that adding a third delayer strategy can have a stabilizing effect on model dynamics. In an era where individual choice--rather than accessibility--is becoming an increasingly important determinant of vaccine uptake, more infectious disease models may need to use game theory or related techniques to determine vaccine uptake.

Background Despite the fact that approximately 70% of Canadian women undergo cervical cancer screening at least once every 3 years, approximately 1,300 women were diagnosed with cervical cancer and approximately 380 died from it in 2008. This study estimates the effectiveness and cost-effectiveness of vaccinating 12-year old Canadian females with an AS04-adjuvanted cervical cancer vaccine. The indirect effect of vaccination, via herd immunity, is also estimated. Methods A 12-health-state 1-year-cycle Markov model was developed to estimate lifetime HPV related events for a cohort of 12-year old females. Annual transition probabilities between health-states were derived from published literature and Canadian population statistics. The model was calibrated using Canadian cancer statistics. From a healthcare perspective, the cost-effectiveness of introducing a vaccine with efficacy against HPV-16/18 and evidence of cross-protection against other oncogenic HPV types was evaluated in a population undergoing current screening practices. The base-case analysis included 70% screening coverage, 75% vaccination coverage, $135/dose for vaccine, and 3% discount rate on future costs and health effects. Conservative herd immunity effects were taken into account by estimated HPV incidence using a mathematical model parameterized by reported age-stratified sexual mixing data. Sensitivity analyses were performed to address parameter uncertainties. Results Vaccinating 12-year old females (n = 100,000) was estimated to prevent between 390-633 undiscounted cervical cancer cases (reduction of 47%-77%) and 168-275 undiscounted deaths (48%-78%) over their lifetime, depending on whether or not herd immunity and cross-protection against other oncogenic HPV types were included. Vaccination was estimated to cost $18,672-$31,687 per QALY-gained, the lower range representing inclusion of cross-protective efficacy and herd immunity. The cost per QALY-gained was most sensitive to duration of vaccine protection, discount rate, and the correlation between probability of screening and probability of vaccination. Conclusion In the context of current screening patterns, vaccination of 12-year old Canadian females with an ASO4-ajuvanted cervical cancer vaccine is estimated to significantly reduce cervical cancer and mortality, and is a cost-effective option. However, the economic attractiveness of vaccination is impacted by the vaccine's duration of protection and the discount rate used in the analysis.

Background. Cohort models are often used in cost-effectiveness analysis (CEA) of vaccination. However, because they cannot capture herd immunity effects, cohort models underestimate the reduction in incidence caused by vaccination. Dynamic models capture herd immunity effects but are often not adopted in vaccine CEA. Objective. The objective was to develop a pseudo-dynamic approximation that can be incorporated into an existing cohort model to capture herd immunity effects. Methods. The authors approximated changing force of infection due to universal vaccination for a pediatric infectious disease. The projected lifetime cases in a cohort were compared under 1) a cohort model, 2) a cohort model with pseudo-dynamic approximation, and 3) an age-structured susceptible-exposed-infectious-recovered compartmental (dynamic) model. The authors extended the methodology to sexually transmitted infections. Results. For average to high values of vaccine coverage (P > 60%) and small to average values of the basic reproduction number (R 0 < 10), which describes school-based vaccination programs for many common infections, the pseudo-dynamic approximation significantly improved projected lifetime cases and was close to projections of the full dynamic model. For large values of R0 (R0 > 15), projected lifetime cases were similar under the dynamic model and the cohort model, both with and without pseudo-dynamic approximation. The approximation captures changes in the mean age at infection in the 1st vaccinated cohort. Conclusions. This methodology allows for preliminary assessment of herd immunity effects on CEA of universal vaccination for pediatric infectious diseases. The method requires simple adjustments to an existing cohort model and less data than a full dynamic model.

Certain theories suggest that it should be difficult or impossible to eradicate a vaccine-preventable disease under voluntary vaccination: Herd immunity implies that the individual incentive to vaccinate disappears at high coverage levels. Historically, there have been examples of declining coverage for vaccines, such as MMR vaccine and whole-cell pertussis vaccine, that are consistent with this theory. On the other hand, smallpox was globally eradicated by 1980 despite voluntary vaccination policies in many jurisdictions. Previous modeling studies of the interplay between disease dynamics and individual vaccinating behavior have assumed that infection is transmitted in a homogeneously mixing population. By comparison, here we simulate transmission of a vaccine-preventable SEIR infection through a random, static contact network. Individuals choose whether to vaccinate based on infection risks from neighbors, and based on vaccine risks. When neighborhood size is small, rational vaccinating behavior results in rapid containment of the infection through voluntary ring vaccination. As neighborhood size increases (while the average force of infection is held constant), a threshold is reached beyond which the infection can break through partially vaccinated rings, percolating through the whole population and resulting in considerable epidemic final sizes and a large number vaccinated. The former outcome represents convergence between individually and socially optimal outcomes, whereas the latter represents their divergence, as observed in most models of individual vaccinating behavior that assume homogeneous mixing. Similar effects are observed in an extended model using smallpox-specific natural history and transmissibility assumptions. This work illustrates the significant qualitative differences between behavior–infection dynamics in discrete contact-structured populations versus continuous unstructured populations. This work also shows how disease eradicability in populations where voluntary vaccination is the primary control mechanism may depend partly on whether the disease is transmissible only to a few close social contacts or to a larger subset of the population., Author Summary Interest in infectious disease models that incorporate the effects of human behavior has been growing in recent years. However, most of these models predict that it should never be possible to eradicate a disease under voluntary vaccination, due to nonvaccinating “free riders” that emerge when vaccine coverage is high. This prediction contradicts the fact that smallpox was eradicated under a voluntary vaccination policy in many jurisdictions, and that other diseases such as polio are likewise near eradication. These previous models assumed that populations mix homogeneously. However, for some diseases, such as HIV and smallpox, individuals are more likely to get the disease from certain social contacts. Here we show that using a network model that captures this social structure can reconcile the previous theories to the empirical fact that diseases can be eradicated under voluntary vaccination. When infection is transmitted only through close contacts in the network, then an outbreak can be quickly contained using only voluntary vaccination. However, when infection can potentially be transmitted to almost everyone in the network (such as for measles), a disease outbreak can never be contained using voluntary vaccination. This latter observation may have some relevance to the Measles–Mumps–Rubella autism “vaccine scare.”

Large-scale vaccination campaigns (SIAs) and improved routine immunization (RI) have greatly reduced measles incidence in low-income countries. However, the interval between SIAs required to maintain these gains over the long term is not clear. We developed a dynamic model of measles transmission to assess measles vaccination strategies in Cambodia, Ghana, India, Morocco, Nigeria, and Uganda. We projected measles cases from 2008 to 2050 under (a) holding SIAs every 2, 4, 6, or 8 years, (b) improvements in first dose routine measles vaccine (MCV1) coverage of 0%, 1%, 3% annually, and (c) introducing MCV2 once MCV1 coverage reaches 70%, 80%, 90%. If MCV1 continues improving, then India and Nigeria could hold SIAs every 4 years without significant probability of large outbreaks, and the other countries every 6-8 years. If RI remains stagnant, India and Nigeria should hold SIAs every 2 years, and the other countries every 4-6 years.