Dynamics in a behavioral-epidemiological model for individual adherence to a nonpharmaceutical intervention.

The SARS-CoV-2 pandemic has highlighted the importance of behavioral drivers in epidemic dynamics. With the relaxation of mandated nonpharmaceutical interventions (NPIs) formerly in place to decrease transmission, such as mask-wearing or social distancing, adherence to an NPI is now the result of individual decision-making. To study these coupled dynamics, we embed a game-theoretic model for individual NPI adherence within an epidemiological model. When the disease is endemic, we find that our model has multiple (but none concurrently stable) equilibria: one each with zero, complete, or partial NPI adherence. Surprisingly, for the equilibrium with partial NPI adherence, the number of infections is independent of the transmission rate. Therefore, in that regime, a change in the rate of pathogen transmission, e.g., due to another (mandated) NPI or a new variant, has no effect on endemic infection levels. On the other hand, we show that vaccination successfully decreases endemic infection levels, and, unexpectedly, also reduces the number of susceptibles at equilibrium when there is partial adherence. From a game-theoretic perspective, we find that highly effective NPIs lead at most to partial adherence. As this effectiveness decreases, partially effective NPIs initially lead to increases in population-level adherence, especially if the risk is high enough. However, a completely ineffective NPI results in no adherence. Furthermore, we identify parameter regions where the individual incentives may not align with those of society as a whole. Overall, our findings illustrate complexities that can arise due to behavioral-epidemiological feedback and suggest appropriate measures to avoid more pessimistic population-level outcomes.

Individual costs and societal benefits of interventions during the COVID-19 pandemic.

Individual and societal reactions to an ongoing pandemic can lead to social dilemmas: In some cases, each individual is tempted to not follow an intervention, but for the whole society, it would be best if they did. Now that in most countries, the extent of regulations to reduce SARS-CoV-2 transmission is very small, interventions are driven by individual decision-making. Assuming that individuals act in their best own interest, we propose a framework in which this situation can be quantified, depending on the protection the intervention provides to a user and to others, the risk of getting infected, and the costs of the intervention. We discuss when a tension between individual and societal benefits arises and which parameter comparisons are important to distinguish between different regimes of intervention use.

Impact of waning immunity against SARS-CoV-2 severity exacerbated by vaccine hesitancy.

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.

Long-term benefits of nonpharmaceutical interventions for endemic infections are shaped by respiratory pathogen dynamics.

COVID-19 nonpharmaceutical interventions (NPIs), including mask wearing, have proved highly effective at reducing the transmission of endemic infections. A key public health question is whether NPIs could continue to be implemented long term to reduce the ongoing burden from endemic pathogens. Here, we use epidemiological models to explore the impact of long-term NPIs on the dynamics of endemic infections. We find that the introduction of NPIs leads to a strong initial reduction in incidence, but this effect is transient: As susceptibility increases, epidemics return while NPIs are in place. For low R0 infections, these return epidemics are of reduced equilibrium incidence and epidemic peak size. For high R0 infections, return epidemics are of similar magnitude to pre-NPI outbreaks. Our results underline that managing ongoing susceptible buildup, e.g., with vaccination, remains an important long-term goal.

Host heterogeneity and epistasis explain punctuated evolution of SARS-CoV-2.

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.

Epidemiological impacts of post-infection mortality.

Infectious diseases may cause some long-term damage to their host, leading to elevated mortality even after recovery. Mortality due to complications from so-called 'long COVID' is a stark illustration of this potential, but the impacts of such post-infection mortality (PIM) on epidemic dynamics are not known. Using an epidemiological model that incorporates PIM, we examine the importance of this effect. We find that in contrast to mortality during infection, PIM can induce epidemic cycling. The effect is due to interference between elevated mortality and reinfection through the previously infected susceptible pool. In particular, robust immunity (via decreased susceptibility to reinfection) reduces the likelihood of cycling; on the other hand, disease-induced mortality can interact with weak PIM to generate periodicity. In the absence of PIM, we prove that the unique endemic equilibrium is stable and therefore our key result is that PIM is an overlooked phenomenon that is likely to be destabilizing. Overall, given potentially widespread effects, our findings highlight the importance of characterizing heterogeneity in susceptibility (via both PIM and robustness of host immunity) for accurate epidemiological predictions. In particular, for diseases without robust immunity, such as SARS-CoV-2, PIM may underlie complex epidemiological dynamics especially in the context of seasonal forcing.

Dynamics in a simple evolutionary-epidemiological model for the evolution of an initial asymptomatic infection stage.

Pathogens exhibit a rich variety of life history strategies, shaped by natural selection. An important pathogen life history characteristic is the propensity to induce an asymptomatic yet productive (transmissive) stage at the beginning of an infection. This characteristic is subject to complex trade-offs, ranging from immunological considerations to population-level social processes. We aim to classify the evolutionary dynamics of such asymptomatic behavior of pathogens (hereafter "latency") in order to unify epidemiology and evolution for this life history strategy. We focus on a simple epidemiological model with two infectious stages, where hosts in the first stage can be partially or fully asymptomatic. Immunologically, there is a trade-off between transmission and progression in this first stage. For arbitrary trade-offs, we derive different conditions that guarantee either at least one evolutionarily stable strategy (ESS) at zero, some, or maximal latency of the first stage or, perhaps surprisingly, at least one unstable evolutionarily singular strategy. In this latter case, there is bistability between zero and nonzero (possibly maximal) latency. We then prove the uniqueness of interior evolutionarily singular strategies for power-law and exponential trade-offs: Thus, bistability is always between zero and maximal latency. Overall, previous multistage infection models can be summarized with a single model that includes evolutionary processes acting on latency. Since small changes in parameter values can lead to abrupt transitions in evolutionary dynamics, appropriate disease control strategies could have a substantial impact on the evolution of first-stage latency.

Distributed medium viscosity yields quasi-exponential step-size probability distributions in heterogeneous media.

The analysis of the statistics of random walks undertaken by passive particles in complex media has important implications in a number of areas including pathogen transport and drug delivery. In several systems in which heterogeneity is important, the distribution of particle step-sizes has been found to be exponential in nature, as opposed to the Gaussian distribution associated with Brownian motion. Here, we first develop a theoretical framework to study a simplified version of this problem: the motion of passive tracers in a range of sub-environments with different viscosity. We show that in the limit of a large number of equi-distributed sub-environments spanning a broad viscosity range, an exact analytical expression for the underlying particle step-size distribution can be derived, which approaches an exponential distribution when step sizes are small. We then validate this using a simple experimental system of glycerol-water mixtures, in which the volume fraction of glycerol is systematically varied. Overall, the assumption of exponentially distributed step sizes may substantially over-estimate the incidence of large steps in heterogeneous systems, with important implications in the analysis of various biophysical processes.

Implications of localized charge for human influenza A H1N1 hemagglutinin evolution: Insights from deep mutational scans.

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.

Stochastic Model of Bovine Babesiosis with Juvenile and Adult Cattle.

A stochastic model for Bovine Babesiosis (BB) including ticks, and both juvenile and adult cattle is developed. This model is formulated by a system of continuous-time Markov chains (CTMCs) that is derived based on an extension of the deterministic ordinary differential equation model developed by Saad-Roy et al. (Bull Math Biol 77:514-547, 2015). The nonlinear CTMC model is approximated by a multitype branching process, giving a theoretical estimate of the probability of an outbreak of BB. Unlike the deterministic dynamics where the basic reproduction number is a sharp threshold parameter, the stochastic model indicates that there is always a positive probability of disease extinction within the cattle population. For parameter values from Colombia data, conditional probability distributions are numerically obtained for the time to disease extinction or outbreak, and are found to depend on the host type at the initiation of infection. The models with and without the inclusion of juvenile cattle are compared, and our result highlights that neglecting juvenile bovine in the models may lead to faulty predictions of critical disease statistics: particularly, it may underestimate the risk of infection. Endemic disease prevalence in adult cattle is examined for certain parameter values in the corresponding deterministic model. Notably, with long-lasting immunity, increased tick to juvenile infectivity decreases the proportion of infectious adults.

Dynamic Perspectives on the Search for a Universal Influenza Vaccine.

A universal influenza vaccine (UIV) could considerably alleviate the public health burden of both seasonal and pandemic influenza. Although significant progress has been achieved in clarifying basic immunology and virology relating to UIV, several important questions relating to the dynamics of infection, immunity, and pathogen evolution remain unsolved. In this study, we review these gaps, which span integrative levels, from cellular to global and timescales from molecular events to decades. We argue that they can be best addressed by a tight integration of empirical (laboratory, epidemiological) research and theory and suggest fruitful areas for this synthesis. In particular, quantifying natural and vaccinal limitations on viral transmission are central to this effort.

Markets as drivers of selection for highly virulent poultry pathogens.

Theoretical models have successfully predicted the evolution of poultry pathogen virulence in industrialized farm contexts of broiler chicken populations. Whether there are ecological factors specific to more traditional rural farming that affect virulence is an open question. Within non-industrialized farming networks, live bird markets are known to be hotspots of transmission, but whether they could shift selection pressures on the evolution of poultry pathogen virulence has not been addressed. Here, we revisit predictions for the evolution of virulence for viral poultry pathogens, such as Newcastle's disease virus, Marek's disease virus, and influenza virus, H5N1, using a compartmental model that represents transmission in rural markets. We show that both the higher turnover rate and higher environmental persistence in markets relative to farms could select for higher optimal virulence strategies. In contrast to theoretical results modeling industrialized poultry farms, we find that cleaning could also select for decreased virulence in the live poultry market setting. Additionally, we predict that more virulent strategies selected in markets could circulate solely within poultry located in markets. Thus, we recommend the close monitoring of markets not only as hotspots of transmission, but as potential sources of more virulent strains of poultry pathogens.

Assessing population-level target product profiles of universal human influenza A vaccines.

Influenza A has two hemagglutinin groups, with stronger cross-immunity to reinfection within than between groups. Here, we explore the implications of this heterogeneity for proposed cross-protective influenza vaccines that may offer broad, but not universal, protection. While the development goal for the breadth of human influenza A vaccine is to provide cross-group protection, vaccines in current development stages may provide better protection against target groups than non-target groups. To evaluate vaccine formulation and strategies, we propose a novel perspective: a vaccine population-level target product profile (PTPP). Under this perspective, we use dynamical models to quantify the epidemiological impacts of future influenza A vaccines as a function of their properties. Our results show that the interplay of natural and vaccine-induced immunity could strongly affect seasonal subtype dynamics. A broadly protective bivalent vaccine could lower the incidence of both groups and achieve elimination with sufficient vaccination coverage. However, a univalent vaccine at low vaccination rates could permit a resurgence of the non-target group when the vaccine provides weaker immunity than natural infection. Moreover, as a proxy for pandemic simulation, we analyze the invasion of a variant that evades natural immunity. We find that a future vaccine providing sufficiently broad and long-lived cross-group protection at a sufficiently high vaccination rate, could prevent pandemic emergence and lower the pandemic burden. This study highlights that as well as effectiveness, breadth and duration should be considered in epidemiologically informed TPPs for future human influenza A vaccines.

Unlock the potential of vaccines in food-producing animals.

Broader coverage can have economic, climate-related, animal welfare, and human health benefits.

Medium-term scenarios of COVID-19 as a function of immune uncertainties and chronic disease.

As the SARS-CoV-2 trajectory continues, the longer-term immuno-epidemiology of COVID-19, the dynamics of Long COVID, and the impact of escape variants are important outstanding questions. We examine these remaining uncertainties with a simple modelling framework that accounts for multiple (antigenic) exposures via infection or vaccination. If immunity (to infection or Long COVID) accumulates rapidly with the valency of exposure, we find that infection levels and the burden of Long COVID are markedly reduced in the medium term. More pessimistic assumptions on host adaptive immune responses illustrate that the longer-term burden of COVID-19 may be elevated for years to come. However, we also find that these outcomes could be mitigated by the eventual introduction of a vaccine eliciting robust (i.e. durable, transmission-blocking and/or 'evolution-proof') immunity. Overall, our work stresses the wide range of future scenarios that still remain, the importance of collecting real-world epidemiological data to identify likely outcomes, and the crucial need for the development of a highly effective transmission-blocking, durable and broadly protective vaccine.

Immuno-epidemiology and the predictability of viral evolution.

Understanding viral evolution depends on a synthesis of evolutionary biology and immuno-epidemiology.

A global system for the next generation of vaccines.

COVID-19 has shown that hurdles can be overcome.

Trajectory of individual immunity and vaccination required for SARS-CoV-2 community immunity: a conceptual investigation.

SARS-CoV-2 is an international public health emergency; high transmissibility and morbidity and mortality can result in the virus overwhelming health systems. Combinations of social distancing, and test, trace, and isolate strategies can reduce the number of new infections per infected individual below 1, thus driving declines in case numbers, but may be both challenging and costly. These interventions must also be maintained until development and (now likely) mass deployment of a vaccine (or therapeutics), since otherwise, many susceptible individuals are still at risk of infection. We use a simple analytical model to explore how low levels of infection, combined with vaccination, determine the trajectory to community immunity. Understanding the repercussions of the biological characteristics of the viral life cycle in this scenario is of considerable importance. We provide a simple description of this process by modelling the scenario where the effective reproduction number [Formula: see text] is maintained at 1. Since the additional complexity imposed by the strength and duration of transmission-blocking immunity is not yet clear, we use our framework to probe the impact of these uncertainties. Through intuitive analytical relations, we explore how the necessary magnitude of vaccination rates and mitigation efforts depends crucially on the durations of natural and vaccinal immunity. We also show that our framework can encompass seasonality or preexisting immunity due to epidemic dynamics prior to strong mitigation measures. Taken together, our simple conceptual model illustrates the importance of individual and vaccinal immunity for community immunity, and that the quantification of individuals immunized against SARS-CoV-2 is paramount.

Evolution of an asymptomatic first stage of infection in a heterogeneous population.

Pathogens evolve different life-history strategies, which depend in part on differences in their host populations. A central feature of hosts is their population structure (e.g. spatial). Additionally, hosts themselves can exhibit different degrees of symptoms when newly infected; this latency is a key life-history property of pathogens. With an evolutionary-epidemiological model, we examine the role of population structure on the evolutionary dynamics of latency. We focus on specific power-law-like formulations for transmission and progression from the first infectious stage as a function of latency, assuming that the across-group to within-group transmission ratio increases if hosts are less symptomatic. We find that simple population heterogeneity can lead to local evolutionarily stable strategies (ESSs) at zero and infinite latency in situations where a unique ESS exists in the corresponding homogeneous case. Furthermore, there can exist more than one interior evolutionarily singular strategy. We find that this diversity of outcomes is due to the (possibly slight) advantage of across-group transmission for pathogens that produce fewer symptoms in a first infectious stage. Thus, our work reveals that allowing individuals without symptoms to travel can have important unintended evolutionary effects and is thus fundamentally problematic in view of the evolutionary dynamics of latency.

Superinfection and the evolution of an initial asymptomatic stage.

Pathogens have evolved a variety of life-history strategies. An important strategy consists of successful transmission by an infected host before the appearance of symptoms, that is, while the host is still partially or fully asymptomatic. During this initial stage of infection, it is possible for another pathogen to superinfect an already infected host and replace the previously infecting pathogen. Here, we study the effect of superinfection during the first stage of an infection on the evolutionary dynamics of the degree to which the host is asymptomatic (host latency) in that same stage. We find that superinfection can lead to major differences in evolutionary behaviour. Most strikingly, the duration of immunity following infection can significantly influence pathogen evolutionary dynamics, whereas without superinfection the outcomes are independent of host immunity. For example, changes in host immunity can drive evolutionary transitions from a fully symptomatic to a fully asymptomatic first infection stage. Additionally, if superinfection relative to susceptible infection is strong enough, evolution can lead to a unique strategy of latency that corresponds to a local fitness minimum, and is therefore invasible by nearby mutants. Thus, this strategy is a branching point, and can lead to coexistence of pathogens with different latencies. Furthermore, in this new framework with superinfection, we also find that there can exist two interior singular strategies. Overall, new evolutionary outcomes can cascade from superinfection.