Wastewater and environmental surveillance (WES) is a promising method of detecting infectious diseases in human and animal populations and offers significant advantages over traditional surveillance methods in the early detection of outbreaks. However, WES involves financial and human resources, and public policy decisions must determine whether the benefits of WES outweigh the costs, particularly in low-resource areas. The selection of surveillance sites, sampling frequency, and test sensitivity and specificity are crucial determinants of WES effectiveness and cost-efficiency. We created an analytical model and numerical simulations of disease arrival, spread, and WES strategies to determine the optimal sampling frequency for two interacting patches, each represented by a different sampling site. We show that it is optimal to test in one patch more frequently than it is to test in both patches less frequently if the patches are sufficiently interactive, surveillance is of sufficient sensitivity and specificity, and setup costs are substantial. In our value of information (VOI) assessment, the net value of surveillance information for both patches is non-monotonic with respect to the degree of patch interaction. Increased mixing between the patches allows for quicker surveillance detection but is worse for overall infection burden. Overall, optimizing the value of surveillance information for all patches being surveilled requires coordination and deliberate selection of surveillance sites and sampling frequencies. This paper provides a VOI assessment of WES to determine the optimal number of sites and sampling frequency at a high level of abstraction, leaving opportunity to adapt the model to specific pathogens and populations as needed. Our findings can inform the cost-efficient implementation of WES for infectious diseases, particularly in resource-constrained settings.

The SARS-CoV-2 pandemic has generated a considerable number of infections and associated morbidity and mortality across the world. Recovery from these infections, combined with the onset of large-scale vaccination, have led to rapidly-changing population-level immunological landscapes. In turn, these complexities have highlighted a number of important unknowns related to the breadth and strength of immunity following recovery or vaccination. Using simple mathematical models, we investigate the medium-term impacts of waning immunity against severe disease on immuno-epidemiological dynamics. We find that uncertainties in the duration of severity-blocking immunity (imparted by either infection or vaccination) can lead to a large range of medium-term population-level outcomes (i.e. infection characteristics and immune landscapes). Furthermore, we show that epidemiological dynamics are sensitive to the strength and duration of underlying host immune responses; this implies that determining infection levels from hospitalizations requires accurate estimates of these immune parameters. More durable vaccines both reduce these uncertainties and alleviate the burden of SARS-CoV-2 in pessimistic outcomes. However, heterogeneity in vaccine uptake drastically changes immune landscapes toward larger fractions of individuals with waned severity-blocking immunity. In particular, if hesitancy is substantial, more robust vaccines have almost no effects on population-level immuno-epidemiology, even if vaccination rates are compensatorily high among vaccine-adopters. This pessimistic scenario for vaccination heterogeneity arises because those few individuals that are vaccine-adopters are so readily re-vaccinated that the duration of vaccinal immunity has no appreciable consequences on their immune status. Furthermore, we find that this effect is heightened if vaccine-hesitants have increased transmissibility (e.g. due to riskier behavior). Overall, our results illustrate the necessity to characterize both transmission-blocking and severity-blocking immune time scales. Our findings also underline the importance of developing robust next-generation vaccines with equitable mass vaccine deployment.

Influenza pandemics typically occur in multiple waves of infection, often associated with initial emergence of a novel virus, followed (in temperate regions) by a resurgence accompanying the onset of the annual influenza season. Here, we examined whether data collected from an initial pandemic wave could be informative, for the need to implement non-pharmaceutical measures in any resurgent wave. Drawing from the 2009 H1N1 pandemic in 10 states in the USA, we calibrated simple mathematical models of influenza transmission dynamics to data for laboratory confirmed hospitalisations during the initial 'spring' wave. We then projected pandemic outcomes (cumulative hospitalisations) during the fall wave, and compared these projections with data. Model results showed reasonable agreement for all states that reported a substantial number of cases in the spring wave. Using this model we propose a probabilistic decision framework that can be used to determine the need for preemptive measures such as postponing school openings, in advance of a fall wave. This work illustrates how model-based evidence synthesis, in real-time during an early pandemic wave, could be used to inform timely decisions for pandemic response.

Identifying drivers of viral diversity is key to understanding the evolutionary as well as epidemiological dynamics of the COVID-19 pandemic. Using rich viral genomic data sets, we show that periods of steadily rising diversity have been punctuated by sudden, enormous increases followed by similarly abrupt collapses of diversity. We introduce a mechanistic model of saltational evolution with epistasis and demonstrate that these features parsimoniously account for the observed temporal dynamics of inter-genomic diversity. Our results provide support for recent proposals that saltational evolution may be a signature feature of SARS-CoV-2, allowing the pathogen to more readily evolve highly transmissible variants. These findings lend theoretical support to a heightened awareness of biological contexts where increased diversification may occur. They also underline the power of pathogen genomics and other surveillance streams in clarifying the phylodynamics of emerging and endemic infections. In public health terms, our results further underline the importance of equitable distribution of up-to-date vaccines.

Measles is one the best-documented and most-mechanistically-studied non-linear infectious disease dynamical systems. However, systematic investigation into the comparative performance of traditional mechanistic models and machine learning approaches in forecasting the transmission dynamics of this pathogen are still rare. Here, we compare one of the most widely used semi-mechanistic models for measles (TSIR) with a commonly used machine learning approach (LASSO), comparing performance and limits in predicting short to long term outbreak trajectories and seasonality for both regular and less regular measles outbreaks in England and Wales (E&W) and the United States. First, our results indicate that the proposed LASSO model can efficiently use data from multiple major cities and achieve similar short-to-medium term forecasting performance to semi-mechanistic models for E&W epidemics. Second, interestingly, the LASSO model also captures annual to biennial bifurcation of measles epidemics in E&W caused by susceptible response to the late 1940s baby boom. LASSO may also outperform TSIR for predicting less-regular dynamics such as those observed in major cities in US between 1932-45. Although both approaches capture short-term forecasts, accuracy suffers for both methods as we attempt longer-term predictions in highly irregular, post-vaccination outbreaks in E&W. Finally, we illustrate that the LASSO model can both qualitatively and quantitatively reconstruct mechanistic assumptions, notably susceptible dynamics, in the TSIR model. Our results characterize the limits of predictability of infectious disease dynamics for strongly immunizing pathogens with both mechanistic and machine learning models, and identify connections between these two approaches.

Human travel is one of the primary drivers of infectious disease spread. Models of travel are often used that assume the amount of travel to a specific destination decreases as cost of travel increases with higher travel volumes to more populated destinations. Trip duration, the length of time spent in a destination, can also impact travel patterns. We investigated the spatial patterns of travel conditioned on trip duration and find distinct differences between short and long duration trips. In short-trip duration travel networks, trips are skewed towards urban destinations, compared with long-trip duration networks where travel is more evenly spread among locations. Using gravity models to inform connectivity patterns in simulations of disease transmission, we show that pathogens with shorter generation times exhibit initial patterns of spatial propagation that are more predictable among urban locations. Further, pathogens with a longer generation time have more diffusive patterns of spatial spread reflecting more unpredictable disease dynamics.

Seasonal influenza A viruses of humans evolve rapidly due to strong selection pressures from host immune responses, principally on the hemagglutinin (HA) viral surface protein. Based on mouse transmission experiments, a proposed mechanism for immune evasion consists of increased avidity to host cellular receptors, mediated by electrostatic charge interactions with negatively charged cell surfaces. In support of this, the HA charge of the globally circulating H3N2 has increased over time since its pandemic. However, the same trend was not seen in H1N1 HA sequences. This is counter-intuitive, since immune escape due to increased avidity (due itself to an increase in charge) was determined experimentally. Here, we explore whether patterns of local charge of H1N1 HA can explain this discrepancy and thus further associate electrostatic charge with immune escape and viral evolutionary dynamics. Measures of site-wise functional selection and expected charge computed from deep mutational scan data on an early H1N1 HA yield a striking division of residues into three groups, separated by charge. We then explored evolutionary dynamics of these groups from 1918 to 2008. In particular, one group increases in net charge over time and consists of sites that are evolving the fastest, that are closest to the receptor binding site (RBS), and that are exposed to solvent (i.e., on the surface). By contrast, another group decreases in net charge and consists of sites that are further away from the RBS and evolving slower, but also exposed to solvent. The last group consists of those sites in the HA core, with no change in net charge and that evolve very slowly. Thus, there is a group of residues that follows the same trend as seen for the entire H3N2 HA. It is possible that the H1N1 HA is under other biophysical constraints that result in compensatory decreases in charge elsewhere on the protein. Our results implicate localized charge in HA interactions with host cells, and highlight how deep mutational scan data can inform evolutionary hypotheses.

A key question in ecology is the relative impact of internal nonlinear dynamics and external perturbations on the long-term trajectories of natural systems. Measles has been analyzed extensively as a paradigm for consumer-resource dynamics due to the oscillatory nature of the host-pathogen life cycle, the abundance of rich data to test theory, and public health relevance. The dynamics of measles in London, in particular, has acted as a prototypical test bed for such analysis using incidence data from the pre-vaccination era (1944-1967). However, during this timeframe there were few external large-scale perturbations, limiting an assessment of the relative impact of internal and extra demographic perturbations to the host population. Here, we extended the previous London analyses to include nearly a century of data that also contains four major demographic changes: the First and Second World Wars, the 1918 influenza pandemic, and the start of a measles mass vaccination program. By combining mortality and incidence data using particle filtering methods, we show that a simple stochastic epidemic model, with minimal historical specifications, can capture the nearly 100 years of dynamics including changes caused by each of the major perturbations. We show that the majority of dynamic changes are explainable by the internal nonlinear dynamics of the system, tuned by demographic changes. In addition, the 1918 influenza pandemic and World War II acted as extra perturbations to this basic epidemic oscillator. Our analysis underlines that long-term ecological and epidemiological dynamics can follow very simple rules, even in a non-stationary population subject to significant perturbations and major secular changes.

Phylodynamic modelling, which studies the joint dynamics of epidemiological and evolutionary processes, has made significant progress in recent years due to increasingly available genomic data and advances in statistical modelling. These advances have greatly improved our understanding of transmission dynamics of many important pathogens. Nevertheless, there remains a lack of effective, targetted diagnostic tools for systematically detecting model mis-specification. Development of such tools is essential for model criticism, refinement, and calibration. The idea of utilising latent residuals for model assessment has already been exploited in general spatio-temporal epidemiological settings. Specifically, by proposing appropriately designed non-centered, re-parameterizations of a given epidemiological process, one can construct latent residuals with known sampling distributions which can be used to quantify evidence of model mis-specification. In this paper, we extend this idea to formulate a novel model-diagnostic framework for phylodynamic models. Using simulated examples, we show that our framework may effectively detect a particular form of mis-specification in a phylodynamic model, particularly in the event of superspreading. We also exemplify our approach by applying the framework to a dataset describing a local foot-and-mouth (FMD) outbreak in the UK, eliciting strong evidence against the assumption of no within-host-diversity in the outbreak. We further demonstrate that our framework can facilitate model calibration in real-life scenarios, by proposing a within-host-diversity model which appears to offer a better fit to data than one that assumes no within-host-diversity of FMD virus.

The surveillance of influenza activity is critical to early detection of epidemics and pandemics and the design of disease control strategies. Case reporting through a voluntary network of sentinel physicians is a commonly used method of passive surveillance for monitoring rates of influenza-like illness (ILI) worldwide. Despite its ubiquity, little attention has been given to the processes underlying the observation, collection, and spatial aggregation of sentinel surveillance data, and its subsequent effects on epidemiological understanding. We harnessed the high specificity of diagnosis codes in medical claims from a database that represented 2.5 billion visits from upwards of 120,000 United States healthcare providers each year. Among influenza seasons from 2002-2009 and the 2009 pandemic, we simulated limitations of sentinel surveillance systems such as low coverage and coarse spatial resolution, and performed Bayesian inference to probe the robustness of ecological inference and spatial prediction of disease burden. Our models suggest that a number of socio-environmental factors, in addition to local population interactions, state-specific health policies, as well as sampling effort may be responsible for the spatial patterns in U.S. sentinel ILI surveillance. In addition, we find that biases related to spatial aggregation were accentuated among areas with more heterogeneous disease risk, and sentinel systems designed with fixed reporting locations across seasons provided robust inference and prediction. With the growing availability of health-associated big data worldwide, our results suggest mechanisms for optimizing digital data streams to complement traditional surveillance in developed settings and enhance surveillance opportunities in developing countries.

Seasonal influenza epidemics offer unique opportunities to study the invasion and re-invasion waves of a pathogen in a partially immune population. Detailed patterns of spread remain elusive, however, due to lack of granular disease data. Here we model high-volume city-level medical claims data and human mobility proxies to explore the drivers of influenza spread in the US during 2002-2010. Although the speed and pathways of spread varied across seasons, seven of eight epidemics likely originated in the Southern US. Each epidemic was associated with 1-5 early long-range transmission events, half of which sparked onward transmission. Gravity model estimates indicate a sharp decay in influenza transmission with the distance between infectious and susceptible cities, consistent with spread dominated by work commutes rather than air traffic. Two early-onset seasons associated with antigenic novelty had particularly localized modes of spread, suggesting that novel strains may spread in a more localized fashion than previously anticipated.

In recent years there has been growing availability of individual-level spatio-temporal disease data, particularly due to the use of modern communicating devices with GPS tracking functionality. These detailed data have been proven useful for inferring disease transmission to a more refined level than previously. However, there remains a lack of statistically sound frameworks to model the underlying transmission dynamic in a mechanistic manner. Such a development is particularly crucial for enabling a general epidemic predictive framework at the individual level. In this paper we propose a new statistical framework for mechanistically modelling individual-to-individual disease transmission in a landscape with heterogeneous population density. Our methodology is first tested using simulated datasets, validating our inferential machinery. The methodology is subsequently applied to data that describes a regional Ebola outbreak in Western Africa (2014-2015). Our results show that the methods are able to obtain estimates of key epidemiological parameters that are broadly consistent with the literature, while revealing a significantly shorter distance of transmission. More importantly, in contrast to existing approaches, we are able to perform a more general model prediction that takes into account the susceptible population. Finally, our results show that, given reasonable scenarios, the framework can be an effective surrogate for susceptible-explicit individual models which are often computationally challenging.

Epidemics of infectious diseases often occur in predictable limit cycles. Theory suggests these cycles can be disrupted by high amplitude seasonal fluctuations in transmission rates, resulting in deterministic chaos. However, persistent deterministic chaos has never been observed, in part because sufficiently large oscillations in transmission rates are uncommon. Where they do occur, the resulting deep epidemic troughs break the chain of transmission, leading to epidemic extinction, even in large cities. Here we demonstrate a new path to locally persistent chaotic epidemics via subtle shifts in seasonal patterns of transmission, rather than through high-amplitude fluctuations in transmission rates. We base our analysis on a comparison of measles incidence in 80 major cities in the prevaccination era United States and United Kingdom. Unlike the regular limit cycles seen in the UK, measles cycles in US cities consistently exhibit spontaneous shifts in epidemic periodicity resulting in chaotic patterns. We show that these patterns were driven by small systematic differences between countries in the duration of the summer period of low transmission. This example demonstrates empirically that small perturbations in disease transmission patterns can fundamentally alter the regularity and spatiotemporal coherence of epidemics.

Despite the availability of vaccines, influenza remains a major public health challenge. A key reason is the virus capacity for immune escape: ongoing evolution allows the continual circulation of seasonal influenza, while novel influenza viruses invade the human population to cause a pandemic every few decades. Current vaccines have to be updated continually to keep up to date with this antigenic change, but emerging 'universal' vaccines-targeting more conserved components of the influenza virus-offer the potential to act across all influenza A strains and subtypes. Influenza vaccination programmes around the world are steadily increasing in their population coverage. In future, how might intensive, routine immunization with novel vaccines compare against similar mass programmes utilizing conventional vaccines? Specifically, how might novel and conventional vaccines compare, in terms of cumulative incidence and rates of antigenic evolution of seasonal influenza? What are their potential implications for the impact of pandemic emergence? Here we present a new mathematical model, capturing both transmission dynamics and antigenic evolution of influenza in a simple framework, to explore these questions. We find that, even when matched by per-dose efficacy, universal vaccines could dampen population-level transmission over several seasons to a greater extent than conventional vaccines. Moreover, by lowering opportunities for cross-protective immunity in the population, conventional vaccines could allow the increased spread of a novel pandemic strain. Conversely, universal vaccines could mitigate both seasonal and pandemic spread. However, where it is not possible to maintain annual, intensive vaccination coverage, the duration and breadth of immunity raised by universal vaccines are critical determinants of their performance relative to conventional vaccines. In future, conventional and novel vaccines are likely to play complementary roles in vaccination strategies against influenza: in this context, our results suggest important characteristics to monitor during the clinical development of emerging vaccine technologies.

The 2009 H1N1 influenza pandemic provides a unique opportunity for detailed examination of the spatial dynamics of an emerging pathogen. In the US, the pandemic was characterized by substantial geographical heterogeneity: the 2009 spring wave was limited mainly to northeastern cities while the larger fall wave affected the whole country. Here we use finely resolved spatial and temporal influenza disease data based on electronic medical claims to explore the spread of the fall pandemic wave across 271 US cities and associated suburban areas. We document a clear spatial pattern in the timing of onset of the fall wave, starting in southeastern cities and spreading outwards over a period of three months. We use mechanistic models to tease apart the external factors associated with the timing of the fall wave arrival: differential seeding events linked to demographic factors, school opening dates, absolute humidity, prior immunity from the spring wave, spatial diffusion, and their interactions. Although the onset of the fall wave was correlated with school openings as previously reported, models including spatial spread alone resulted in better fit. The best model had a combination of the two. Absolute humidity or prior exposure during the spring wave did not improve the fit and population size only played a weak role. In conclusion, the protracted spread of pandemic influenza in fall 2009 in the US was dominated by short-distance spatial spread partially catalysed by school openings rather than long-distance transmission events. This is in contrast to the rapid hierarchical transmission patterns previously described for seasonal influenza. The findings underline the critical role that school-age children play in facilitating the geographic spread of pandemic influenza and highlight the need for further information on the movement and mixing patterns of this age group.

1 Center for Infectious Disease Dynamics, Department of Biology, The Pennsylvania State University, Mueller Laboratory, University Park, Pennsylvania, United States of America, 2 Fogarty International Center, National Institutes of Health, Bethesda, Maryland, United States of America, 3 Department of Ecology and Evolutionary Biology and Woodrow Wilson School, Princeton University, Princeton, New Jersey, United States of America