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On the basis of historical influenza and COVID-19 forecasts, we found that more than 3 forecast models are needed to ensure robust ensemble accuracy. Additional models can improve ensemble performance, but with diminishing accuracy returns. This understanding will assist with the design of current and future collaborative infectious disease forecasting efforts.

Cities across China implemented stringent social distancing measures in early 2020 to curb coronavirus disease outbreaks. We estimated the speed with which these measures contained transmission in cities. A 1-day delay in implementing social distancing resulted in a containment delay of 2.41 (95% CI 0.97-3.86) days.

As infectious disease outbreaks emerge, public health agencies often enact vaccination and social distancing measures to slow transmission. Their success depends on not only strategies and resources, but also public adherence. Individual willingness to take precautions may be influenced by global factors, such as news media, or local factors, such as infected family members or friends. Here, we compare three modes of epidemiological decision-making in the midst of a growing outbreak using network-based mathematical models that capture plausible heterogeneity in human contact patterns. Individuals decide whether to adopt a recommended intervention based on overall disease prevalence, the proportion of social contacts infected, or the number of social contacts infected. While all strategies can substantially mitigate transmission, vaccinating (or self isolating) based on the number of infected acquaintances is expected to prevent the most infections while requiring the fewest intervention resources. Unlike the other strategies, it has a substantial herd effect, providing indirect protection to a large fraction of the population., Competing Interests: The authors have declared that no competing interests exist.

In an Essay, Michael Johansson and colleagues advocate the posting of research studies addressing infectious disease outbreaks as preprints.

As infectious disease surveillance systems expand to include digital, crowd-sourced, and social network data, public health agencies are gaining unprecedented access to high-resolution data and have an opportunity to selectively monitor informative individuals. Contact networks, which are the webs of interaction through which diseases spread, determine whether and when individuals become infected, and thus who might serve as early and accurate surveillance sensors. Here, we evaluate three strategies for selecting sensors-sampling the most connected, random, and friends of random individuals-in three complex social networks-a simple scale-free network, an empirical Venezuelan college student network, and an empirical Montreal wireless hotspot usage network. Across five different surveillance goals-early and accurate detection of epidemic emergence and peak, and general situational awareness-we find that the optimal choice of sensors depends on the public health goal, the underlying network and the reproduction number of the disease (R0). For diseases with a low R0, the most connected individuals provide the earliest and most accurate information about both the onset and peak of an outbreak. However, identifying network hubs is often impractical, and they can be misleading if monitored for general situational awareness, if the underlying network has significant community structure, or if R0 is high or unknown. Taking a theoretical approach, we also derive the optimal surveillance system for early outbreak detection but find that real-world identification of such sensors would be nearly impossible. By contrast, the friends-of-random strategy offers a more practical and robust alternative. It can be readily implemented without prior knowledge of the network, and by identifying sensors with higher than average, but not the highest, epidemiological risk, it provides reasonably early and accurate information.

As a devastating Ebola outbreak in West Africa continues, non-pharmaceutical control measures including contact tracing, quarantine, and case isolation are being implemented. In addition, public health agencies are scaling up efforts to test and deploy candidate vaccines. Given the experimental nature and limited initial supplies of vaccines, a mass vaccination campaign might not be feasible. However, ring vaccination of likely case contacts could provide an effective alternative in distributing the vaccine. To evaluate ring vaccination as a strategy for eliminating Ebola, we developed a pair approximation model of Ebola transmission, parameterized by confirmed incidence data from June 2014 to January 2015 in Liberia and Sierra Leone. Our results suggest that if a combined intervention of case isolation and ring vaccination had been initiated in the early fall of 2014, up to an additional 126 cases in Liberia and 560 cases in Sierra Leone could have been averted beyond case isolation alone. The marginal benefit of ring vaccination is predicted to be greatest in settings where there are more contacts per individual, greater clustering among individuals, when contact tracing has low efficacy or vaccination confers post-exposure protection. In such settings, ring vaccination can avert up to an additional 8% of Ebola cases. Accordingly, ring vaccination is predicted to offer a moderately beneficial supplement to ongoing non-pharmaceutical Ebola control efforts.

Using Ebolavirus genomic and epidemiological data, we conducted the first joint analysis in which both data types were used to fit dynamic transmission models for an ongoing outbreak. Our results indicate that transmission is clustered, highlighting a potential bias in medical demand forecasts, and provide the first empirical estimate of underreporting., (© The Author 2014. Published by Oxford University Press on behalf of the Infectious Diseases Society of America. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.)

Many endangered wildlife populations are vulnerable to infectious diseases for which vaccines exist; yet, pragmatic considerations often preclude large-scale vaccination efforts. These barriers could be reduced by focusing on individuals with the highest contact rates. However, the question then becomes whether targeted vaccination is sufficient to prevent large outbreaks. To evaluate the efficacy of targeted wildlife vaccinations, we simulate pathogen transmission and control on monthly association networks informed by behavioural data from a wild chimpanzee community (Kanyawara N = 37, Kibale National Park, Uganda). Despite considerable variation across monthly networks, our simulations indicate that targeting the most connected individuals can prevent large outbreaks with up to 35% fewer vaccines than random vaccination. Transmission heterogeneities might be attributed to biological differences among individuals (e.g. sex, age, dominance and family size). Thus, we also evaluate the effectiveness of a trait-based vaccination strategy, as trait data are often easier to collect than interaction data. Our simulations indicate that a trait-based strategy can prevent large outbreaks with up to 18% fewer vaccines than random vaccination, demonstrating that individual traits can serve as effective estimates of connectivity. Overall, these results suggest that fine-scale behavioural data can help optimize pathogen control efforts for endangered wildlife., (© 2014 The Author(s) Published by the Royal Society. All rights reserved.)

Contact patterns in group-structured populations determine the course of infectious disease outbreaks. Network-based models have revealed important connections between group-level contact patterns and the dynamics of epidemics, but these models typically ignore heterogeneities in within-group composition. Here, we analyse a flexible mathematical model of disease transmission in a hierarchically structured wildlife population, and find that increased variation in group size reduces the epidemic threshold, making social animal populations susceptible to a broader range of pathogens. Variation in group size also increases the likelihood of an epidemic for mildly transmissible diseases, but can reduce the likelihood and expected size of an epidemic for highly transmissible diseases. Further, we introduce the concept of epidemiological effective group size, which we define to be the group size of a hypothetical population containing groups of identical size that has the same epidemic threshold as an observed population. Using data from the Serengeti Lion Project, we find that pride-living Serengeti lions are epidemiologically comparable to a homogeneous population with up to 20 per cent larger prides.

The increasingly complex and rapid transmission dynamics of many infectious diseases necessitates the use of new, more advanced methods for surveillance, early detection, and decision-making. Here, we demonstrate that a new method for optimizing surveillance networks can improve the quality of epidemiological information produced by typical provider-based networks. Using past surveillance and Internet search data, it determines the precise locations where providers should be enrolled. When applied to redesigning the provider-based, influenza-like-illness surveillance network (ILINet) for the state of Texas, the method identifies networks that are expected to significantly outperform the existing network with far fewer providers. This optimized network avoids informational redundancies and is thereby more effective than networks designed by conventional methods and a recently published algorithm based on maximizing population coverage. We show further that Google Flu Trends data, when incorporated into a network as a virtual provider, can enhance but not replace traditional surveillance methods.

Background: As Pandemic (H1N1) 2009 influenza spreads around the globe, it strikes school-age children more often than adults. Although there is some evidence of pre-existing immunity among older adults, this alone may not explain the significant gap in age-specific infection rates., Methods and Findings: Based on a retrospective analysis of pandemic strains of influenza from the last century, we show that school-age children typically experience the highest attack rates in primarily naive populations, with the burden shifting to adults during the subsequent season. Using a parsimonious network-based mathematical model which incorporates the changing distribution of contacts in the susceptible population, we demonstrate that new pandemic strains of influenza are expected to shift the epidemiological landscape in exactly this way., Conclusions: Our analysis provides a simple demographic explanation for the age bias observed for H1N1/09 attack rates, and suggests that this bias may shift in coming months. These results have significant implications for the allocation of public health resources for H1N1/09 and future influenza pandemics.

Serengeti lions frequently experience viral outbreaks. In 1994, one-third of Serengeti lions died from canine distemper virus (CDV). Based on the limited epidemiological data available from this period, it has been unclear whether the 1994 outbreak was propagated by lion-to-lion transmission alone or involved multiple introductions from other sympatric carnivore species. More broadly, we do not know whether contacts between lions allow any pathogen with a relatively short infectious period to percolate through the population (i.e. reach epidemic proportions). We built one of the most realistic contact network models for a wildlife population to date, based on detailed behavioural and movement data from a long-term lion study population. The model allowed us to identify previously unrecognized biases in the sparse data from the 1994 outbreak and develop methods for judiciously inferring disease dynamics from typical wildlife samples. Our analysis of the model in light of the 1994 outbreak data strongly suggest that, although lions are sufficiently well connected to sustain epidemics of CDV-like diseases, the 1994 epidemic was fuelled by multiple spillovers from other carnivore species, such as jackals and hyenas.

The reproductive ratio, R0, is a fundamental quantity in epidemiology, which determines the initial increase in an infectious disease in a susceptible host population. In most epidemic models, there is a specific value of R0, the epidemic threshold, above which epidemics are possible, but below which epidemics cannot occur. As the complexity of an epidemic model increases, so too does the difficulty of calculating epidemic thresholds. Here we derive the reproductive ratio and epidemic thresholds for susceptible-infected-recovered (SIR) epidemics in a simple class of dynamic random networks. As in most epidemiological models, R0 depends on two basic epidemic parameters, the transmission and recovery rates. We find that R0 also depends on social parameters, namely the degree distribution that describes heterogeneity in the numbers of concurrent contacts and the mixing parameter that gives the rate at which contacts are initiated and terminated. We show that social mixing fundamentally changes the epidemiological landscape and, consequently, that static network approximations of dynamic networks can be inadequate.

Contact patterns in populations fundamentally influence the spread of infectious diseases. Current mathematical methods for epidemiological forecasting on networks largely assume that contacts between individuals are fixed, at least for the duration of an outbreak. In reality, contact patterns may be quite fluid, with individuals frequently making and breaking social or sexual relationships. Here, we develop a mathematical approach to predicting disease transmission on dynamic networks in which each individual has a characteristic behaviour (typical contact number), but the identities of their contacts change in time. We show that dynamic contact patterns shape epidemiological dynamics in ways that cannot be adequately captured in static network models or mass-action models. Our new model interpolates smoothly between static network models and mass-action models using a mixing parameter, thereby providing a bridge between disparate classes of epidemiological models. Using epidemiological and sexual contact data from an Atlanta high school, we demonstrate the application of this method for forecasting and controlling sexually transmitted disease outbreaks.

Contact network epidemiology is an approach to modeling the spread of infectious diseases that explicitly considers patterns of person-to-person contacts within a community. Contacts can be asymmetric, with a person more likely to infect one of their contacts than to become infected by that contact. This is true for some sexually transmitted diseases that are more easily caught by women than men during heterosexual encounters; and for severe infectious diseases that cause an average person to seek medical attention and thereby potentially infect health care workers (HCWs) who would not, in turn, have an opportunity to infect that average person. Here we use methods from percolation theory to develop a mathematical framework for predicting disease transmission through semi-directed contact networks in which some contacts are undirected-the probability of transmission is symmetric between individuals-and others are directed-transmission is possible only in one direction. We find that the probability of an epidemic and the expected fraction of a population infected during an epidemic can be different in semi-directed networks, in contrast to the routine assumption that these two quantities are equal. We furthermore demonstrate that these methods more accurately predict the vulnerability of HCWs and the efficacy of various hospital-based containment strategies during outbreaks of severe respiratory diseases.

Effectively controlling infectious diseases requires quantitative comparisons of quarantine, infection control precautions, case identification and isolation, and immunization interventions. We used contact network epidemiology to predict the effect of various control policies for a mildly contagious disease, such as severe acute respiratory syndrome, and a moderately contagious disease, such as smallpox. The success of an intervention depends on the transmissibility of the disease and the contact pattern between persons within a community. The model predicts that use of face masks and general vaccination will only moderately affect the spread of mildly contagious diseases. In contrast, quarantine and ring vaccination can prevent the spread of a wide spectrum of diseases. Contact network epidemiology can provide valuable quantitative input to public health decisionmaking, even before a pathogen is well characterized.

Many infectious diseases spread through populations via the networks formed by physical contacts among individuals. The patterns of these contacts tend to be highly heterogeneous. Traditional "compartmental" modeling in epidemiology, however, assumes that population groups are fully mixed, that is, every individual has an equal chance of spreading the disease to every other. Applications of compartmental models to Severe Acute Respiratory Syndrome (SARS) resulted in estimates of the fundamental quantity called the basic reproductive number R0--the number of new cases of SARS resulting from a single initial case--above one, implying that, without public health intervention, most outbreaks should spark large-scale epidemics. Here we compare these predictions to the early epidemiology of SARS. We apply the methods of contact network epidemiology to illustrate that for a single value of R0, any two outbreaks, even in the same setting, may have very different epidemiological outcomes. We offer quantitative insight into the heterogeneity of SARS outbreaks worldwide, and illustrate the utility of this approach for assessing public health strategies.

Policymakers must make management decisions despite incomplete knowledge and conflicting model projections. Little guidance exists for the rapid, representative, and unbiased collection of policy-relevant scientific input from independent modeling teams. Integrating approaches from decision analysis, expert judgment, and model aggregation, we convened multiple modeling teams to evaluate COVID-19 reopening strategies for a mid-sized United States county early in the pandemic. Projections from seventeen distinct models were inconsistent in magnitude but highly consistent in ranking interventions. The 6-mo-ahead aggregate projections were well in line with observed outbreaks in mid-sized US counties. The aggregate results showed that up to half the population could be infected with full workplace reopening, while workplace restrictions reduced median cumulative infections by 82%. Rankings of interventions were consistent across public health objectives, but there was a strong trade-off between public health outcomes and duration of workplace closures, and no win-win intermediate reopening strategies were identified. Between-model variation was high; the aggregate results thus provide valuable risk quantification for decision making. This approach can be applied to the evaluation of management interventions in any setting where models are used to inform decision making. This case study demonstrated the utility of our approach and was one of several multimodel efforts that laid the groundwork for the COVID-19 Scenario Modeling Hub, which has provided multiple rounds of real-time scenario projections for situational awareness and decision making to the Centers for Disease Control and Prevention since December 2020.