Capturing the dynamics of pathogens with many strains

Infection thresholds for two interacting pathogens in a wild animal population

We present a model for the dynamics of two interacting pathogen variants in a wild animal host population. Using the next-generation matrix approach we define the invasion threshold for one pathogen variant when the other is already established and at steady state. We then provide explicit criteria for the special cases where: i) the two pathogen variants exclude each other; ii) one variant excludes the other; iii) the population dynamics of hosts infected with both variants are independent of the order of infection; iv) there is no interaction between the variants; and v) one variant enhances transmission of the other.

Evolutionary Invasion Analysis of Modern Epidemics Highlights the Context-Dependence of Virulence Evolution

Models are often employed to integrate knowledge about epidemics across scales and simulate disease dynamics. While these approaches have played a central role in studying the mechanics underlying epidemics, we lack ways to reliably predict how the relationship between virulence (the harm to hosts caused by an infection) and transmission will evolve in certain virus-host contexts. In this study, we invoke evolutionary invasion analysis-a method used to identify the evolution of uninvadable strategies in dynamical systems-to examine how the virulence-transmission dichotomy can evolve in models of virus infections defined by different natural histories. We reveal peculiar patterns of virulence evolution between epidemics with different disease natural histories (SARS-CoV-2 and hepatitis C virus). We discuss the findings with regards to the public health implications of predicting virus evolution, and in broader theoretical canon involving virulence evolution in host-parasite systems.

How immune dynamics shape multi-season epidemics: a continuous-discrete model in one dimensional antigenic space

We extend a previously published model for the dynamics of a single strain of an influenza-like infection. The model incorporates a waning acquired immunity to infection and punctuated antigenic drift of the virus, employing a set of coupled integral equations within a season and a discrete map between seasons. The long term behaviour of the model is demonstrated by examples where immunity to infection depends on the time since a host was last infected, and where immunity depends on the number of times that a host has been infected. The first scenario leads to complicated dynamics in some regions of parameter space, and to regions of parameter space with more than one attractor. The second scenario leads to a stable fixed point, corresponding to an identical epidemic each season. We also examine the model with both paradigms in combination, almost always but not exclusively observing a stable fixed point or periodic solution. Adding stochastic perturbations to the between season map fails to destroy the model's qualitative dynamics. Our results suggest that if the level of host immunity depends on the elapsed time since the last infection then the epidemiological dynamics may be unpredictable.

Key Challenges for Respiratory Virus Surveillance while Transitioning out of Acute Phase of COVID-19 Pandemic

To support the ongoing management of viral respiratory diseases while transitioning out of the acute phase of the COVID-19 pandemic, many countries are moving toward an integrated model of surveillance for SARS-CoV-2, influenza virus, and other respiratory pathogens. Although many surveillance approaches catalyzed by the COVID-19 pandemic provide novel epidemiologic insight, continuing them as implemented during the pandemic is unlikely to be feasible for nonemergency surveillance, and many have already been scaled back. Furthermore, given anticipated cocirculation of SARS-CoV-2 and influenza virus, surveillance activities in place before the pandemic require review and adjustment to ensure their ongoing value for public health. In this report, we highlight key challenges for the development of integrated models of surveillance. We discuss the relative strengths and limitations of different surveillance practices and studies as well as their contribution to epidemiologic assessment, forecasting, and public health decision-making.

Recombinant transmissible vaccines will be intrinsically contained despite the ability to superinfect

INTRODUCTION

Transmissible vaccines offer a novel approach to suppressing viruses in wildlife populations, with possible applications against viruses that infect humans as zoonoses - Lassa, Ebola, rabies. To ensure safety, current designs propose a recombinant vector platform in which the vector is isolated from the target wildlife population. Because using an endemic vector creates the potential for preexisting immunity to block vaccine transmission, these designs focus on vector viruses capable of superinfection, spreading throughout the host population following vaccination of few individuals.

AREAS COVERED

We present original theoretical arguments that, regardless of its R0 value, a recombinant vaccine using a superinfecting vector is not expected to expand its active infection coverage when released into a wildlife population that already carries the vector. However, if superinfection occurs at a high rate such that individuals are repeatedly infected throughout their lives, the immunity footprint in the population can be high despite a low incidence of active vaccine infections. Yet we provide reasons that the above expectation is optimistic.

EXPERT OPINION

High vaccine coverage will typically require repeated releases or release into a population lacking the vector, but careful attention to vector choice and vaccine engineering should also help improve transmissible vaccine utility.

Characterization of differential susceptibility and differential infectivity epidemic models

Heterogeneity in susceptibility and infectivity is a central issue in epidemiology. Although the latter has received some attention recently, the former is often neglected in modeling of epidemic systems. Moreover, very few studies consider both of these heterogeneities. This paper is concerned with the characterization of epidemic models with differential susceptibility and differential infectivity under a general setup. Specifically, we investigate the global asymptotic behavior of equilibria of these systems when the network configuration of the Susceptible-Infectious interactions is strongly connected. These results prove two conjectures by Bonzi et al. (J Math Biol 62:39-64, 2011) and Hyman and Li (Math Biosci Eng 3:89-100, 2006). Moreover, we consider the scenario in which the strong connectivity hypothesis is dropped. In this case, the model exhibits a wider range of dynamical behavior, including the rise of boundary and interior equilibria, all based on the topology of network connectivity. Finally, a model with multidirectional transitions between infectious classes is presented and completely analyzed.

Quasi-neutral dynamics in a coinfection system with N strains and asymmetries along multiple traits

Understanding the interplay of different traits in a co-infection system with multiple strains has many applications in ecology and epidemiology. Because of high dimensionality and complex feedback between traits manifested in infection and co-infection, the study of such systems remains a challenge. In the case where strains are similar (quasi-neutrality assumption), we can model trait variation as perturbations in parameters, which simplifies analysis. Here, we apply singular perturbation theory to many strain parameters simultaneously and advance analytically to obtain their explicit collective dynamics. We consider and study such a quasi-neutral model of susceptible-infected-susceptible (SIS) dynamics among N strains, which vary in 5 fitness dimensions: transmissibility, clearance rate of single- and co-infection, transmission probability from mixed coinfection, and co-colonization vulnerability factors encompassing cooperation and competition. This quasi-neutral system is analyzed with a singular perturbation method through an appropriate slow-fast decomposition. The fast dynamics correspond to the embedded neutral system, while the slow dynamics are governed by an N-dimensional replicator equation, describing the time evolution of strain frequencies. The coefficients of this replicator system are pairwise invasion fitnesses between strains, which, in our model, are an explicit weighted sum of pairwise asymmetries along all trait dimensions. Remarkably these weights depend only on the parameters of the neutral system. Such model reduction highlights the centrality of the neutral system for dynamics at the edge of neutrality and exposes critical features for the maintenance of diversity.

SIRC epidemic model with cross-immunity and multiple time delays

Multi-strain diseases lead to the development of some degree of cross-immunity among people. In the present paper, we propose a multi-delayed SIRC epidemic model with incubation and immunity time delays. Here we aim to examine and investigate the effects of incubation delay [Formula: see text] and the impact of vaccine which provides partial/cross-immunity with immunity delay parameter ([Formula: see text]) on the disease dynamics. Also, we study the impact of the strength of cross-immunity [Formula: see text] on the disease prevalence. The positivity and boundedness of the solutions of the epidemic model have been established. Two different types of equilibrium points (disease-free and endemic) have been deduced. Expression for basic reproduction number has been derived. The stability conditions and Hopf-bifurcation about both the equilibrium points in the absence and presence of both delays have been discussed. The Lyapunov stability conditions about the endemic equilibrium point have been established. Numerical simulations have been performed to support our analytical results. We quantitatively demonstrate how oscillations and Hopf-bifurcation allow time delays to alter the dynamics of the system. The combined impacts of both the delays on disease prevalence has been studied. Through parameter sensitivity analysis, we observe that the infected population decreases with an increase in vaccination rate and the system starts to stabilize early with the increase in cross-immunity rate. Global sensitivity analysis for the basic reproduction number has been performed using Latin hypercube sampling and partial rank correlation coefficients techniques. The combined effect of vaccination rate with transmission rate and vaccination rate with re-infection probability (i.e. strength of cross-immunity) on [Formula: see text] have been discussed. Our research underlines the need to take cross-immunity and time delays into account in the epidemic model in order to better understand disease dynamics.

Habitat Heterogeneity, Environmental Feedbacks, and Species Coexistence across Timescales

AbstractClassic ecological theory explains species coexistence in variable environments. While spatial variation is often treated as an intrinsic feature of a landscape, it may be shaped and even generated by the resident community. All species modify their local environment to some extent, driving changes that can feed back to affect the composition and coexistence of the community, potentially over timescales very different from population dynamics. We introduce a simple nested modeling framework for community dynamics in heterogeneous environments, including the possible evolution of heterogeneity over time due to community-environment feedbacks. We use this model to derive analytical conditions for species coexistence in environments where heterogeneity is either fixed or shaped by feedbacks. Among other results, our approach reveals how dispersal and environmental specialization interact to shape realized patterns of habitat association and demonstrates that environmental feedbacks can tune landscape conditions to allow the stable coexistence of any number of species. Our flexible modeling framework helps explain feedback dynamics that arise in a wide range of ecosystems and offers a generic platform for exploring the interplay between species and landscape diversity.

Role of error catastrophe in transmission ability of virus

The role played by error catastrophe is explicitly taken into account in a mathematical formulation to analyze COVID-19 data. The idea is to combine the mathematical genetics formalism of the error catastrophe of mutations in virus gene loci with the standard model of epidemics, which lacks the explicit incorporation of the effect of mutation on the spreading of viruses. We apply this formalism to the case of SARS-CoV-2 virus. We assume the universality of the error catastrophe in the process of analyzing the data. This means that some basic parameter to describe the error catastrophe is independent of which group (country or city) we deal with. Concretely, we analyze Omicron variant data from South Africa and then analyze cases from Japan using the same value of the basic parameter derived in the South Africa analysis. The excellent fit between the two sets of data, one from South Africa and the other from Japan, using the common values of genetic parameters, justifies our assumption of the universality of these parameters.

Modelling the impact of the Omicron BA.5 subvariant in New Zealand

New Zealand experienced a wave of the Omicron variant of SARS-CoV-2 in early 2022, which occurred against a backdrop of high two-dose vaccination rates, ongoing roll-out of boosters and paediatric doses, and negligible levels of prior infection. New Omicron subvariants have subsequently emerged with a significant growth advantage over the previously dominant BA.2. We investigated a mathematical model that included waning of vaccine-derived and infection-derived immunity, as well as the impact of the BA.5 subvariant which began spreading in New Zealand in May 2022. The model was used to provide scenarios to the New Zealand Government with differing levels of BA.5 growth advantage, helping to inform policy response and healthcare system preparedness during the winter period. In all scenarios investigated, the projected peak in new infections during the BA.5 wave was smaller than in the first Omicron wave in March 2022. However, results indicated that the peak hospital occupancy was likely to be higher than in March 2022, primarily due to a shift in the age distribution of infections to older groups. We compare model results with subsequent epidemiological data and show that the model provided a good projection of cases, hospitalizations and deaths during the BA.5 wave.

Exploring a COVID-19 Endemic Scenario: High-Resolution Agent-Based Modeling of Multiple Variants

Our efforts as a society to combat the ongoing COVID-19 pandemic are continuously challenged by the emergence of new variants. These variants can be more infectious than existing strains and many of them are also more resistant to available vaccines. The appearance of these new variants cause new surges of infections, exacerbated by infrastructural difficulties, such as shortages of medical personnel or test kits. In this work, a high-resolution computational framework for modeling the simultaneous spread of two COVID-19 variants: a widely spread base variant and a new one, is established. The computational framework consists of a detailed database of a representative U.S. town and a high-resolution agent-based model that uses the Omicron variant as the base variant and offers flexibility in the incorporation of new variants. The results suggest that the spread of new variants can be contained with highly efficacious tests and mild loss of vaccine protection. However, the aggressiveness of the ongoing Omicron variant and the current waning vaccine immunity point to an endemic phase of COVID-19, in which multiple variants will coexist and residents continue to suffer from infections.

Pathogen diversity in meta-population networks

The pathogen diversity means that multiple strains coexist, and widely exist in the biology systems. The new mutation of SARS-CoV-2 leading to worldwide pathogen diversity is a typical example. What are the main factors of inducing the pathogen diversity? Previous studies indicated the pathogen mutation is the most important reason for inducing the pathogen diversity. The traffic network and gene network are crucial in shaping the dynamics of pathogen contagion, while their roles for the pathogen diversity still lacking a theoretical study. To this end, we propose a reaction-diffusion process of pathogens with mutations on meta-population networks, which includes population movement and strain mutation. We extend the Microscopic Markov Chain Approach (MMCA) to describe the model. Traffic networks make pathogen diversity more likely to occur in cities with lower infection densities. The likelihood of pathogen diversity is low in cities with short effective distances in the traffic network. Star-type gene network is more likely to lead to pathogen diversity than lattice-type and chain-type gene networks. When pathogen localization is present, infection is localized to strains that are at the endpoints of the gene network. Both the increased probability of movement and mutation promote pathogen diversity. The results also show that the population tends to move to cities with short effective distances, resulting in the infection density is high.

The transmission mechanism theory of disease dynamics: Its aims, assumptions and limitations

Most of the progress in the development of single scale mathematical and computational models for the study of infectious disease dynamics which now span over a century is build on a body of knowledge that has been developed to address particular single scale descriptions of infectious disease dynamics based on understanding disease transmission process. Although this single scale understanding of infectious disease dynamics is now founded on a body of knowledge with a long history, dating back to over a century now, that knowledge has not yet been formalized into a scientific theory. In this article, we formalize this accumulated body of knowledge into a scientific theory called the transmission mechanism theory of disease dynamics which states that at every scale of organization of an infectious disease system, disease dynamics is determined by transmission as the main dynamic disease process. Therefore, the transmission mechanism theory of disease dynamics can be seen as formalizing knowledge that has been inherent in the study of infectious disease dynamics using single scale mathematical and computational models for over a century now. The objective of this article is to summarize this existing knowledge about single scale modelling of infectious dynamics by means of a scientific theory called the transmission mechanism theory of disease dynamics and highlight its aims, assumptions and limitations.

Predicting elimination of evolving virus variants

As the SARS-CoV-2 virus spreads around the world new variants are appearing regularly. Although some countries have achieved very swift and successful vaccination campaigns, on a global scale the vast majority of the population is unvaccinated and new variants are proving more resistant to the current set of vaccines. We present a simple model of disease spread, which includes the evolution of new variants of a novel virus and varying vaccine effectiveness to these new strains. We show that rapid vaccine updates to target new strains are more effective than slow updates and containing spread through non-pharmaceutical interventions is vital while these vaccines are delivered. Finally, when measuring the key model inputs, e.g. the rate at which new mutations and variants of concern emerge, is difficult we show how an observable model output, the number of new variants that have been seen, is strongly correlated with the probability the virus is eliminated.

Ecological and evolutionary dynamics of multi-strain RNA viruses

Potential interactions among co-circulating viral strains in host populations are often overlooked in the study of virus transmission. However, these interactions probably shape transmission dynamics by influencing host immune responses or altering the relative fitness among co-circulating strains. In this Review, we describe multi-strain dynamics from ecological and evolutionary perspectives, outline scales in which multi-strain dynamics occur and summarize important immunological, phylogenetic and mathematical modelling approaches used to quantify interactions among strains. We also discuss how host-pathogen interactions influence the co-circulation of pathogens. Finally, we highlight outstanding questions and knowledge gaps in the current theory and study of ecological and evolutionary dynamics of multi-strain viruses.

Activity-driven network modeling and control of the spread of two concurrent epidemic strains

The emergency generated by the current COVID-19 pandemic has claimed millions of lives worldwide. There have been multiple waves across the globe that emerged as a result of new variants, due to arising from unavoidable mutations. The existing network toolbox to study epidemic spreading cannot be readily adapted to the study of multiple, coexisting strains. In this context, particularly lacking are models that could elucidate re-infection with the same strain or a different strain-phenomena that we are seeing experiencing more and more with COVID-19. Here, we establish a novel mathematical model to study the simultaneous spreading of two strains over a class of temporal networks. We build on the classical susceptible-exposed-infectious-removed model, by incorporating additional states that account for infections and re-infections with multiple strains. The temporal network is based on the activity-driven network paradigm, which has emerged as a model of choice to study dynamic processes that unfold at a time scale comparable to the network evolution. We draw analytical insight from the dynamics of the stochastic network systems through a mean-field approach, which allows for characterizing the onset of different behavioral phenotypes (non-epidemic, epidemic, and endemic). To demonstrate the practical use of the model, we examine an intermittent stay-at-home containment strategy, in which a fraction of the population is randomly required to isolate for a fixed period of time.

Considering humans as habitat reveals evidence of successional disease ecology among human pathogens

The realization that ecological principles play an important role in infectious disease dynamics has led to a renaissance in epidemiological theory. Ideas from ecological succession theory have begun to inform an understanding of the relationship between the individual microbiome and health but have not yet been applied to investigate broader, population-level epidemiological dynamics. We consider human hosts as habitat and apply ideas from succession to immune memory and multi-pathogen dynamics in populations. We demonstrate that ecologically meaningful life history characteristics of pathogens and parasites, rather than epidemiological features alone, are likely to play a meaningful role in determining the age at which people have the greatest probability of being infected. Our results indicate the potential importance of microbiome succession in determining disease incidence and highlight the need to explore how pathogen life history traits and host ecology influence successional dynamics. We conclude by exploring some of the implications that inclusion of successional theory might have for understanding the ecology of diseases and their hosts.

This study explores the analogy between ecological succession in terrestrial ecosystems and infections in a human-host landscape over time, showing how the ecosystem of long-term multi-pathogen dynamics within and among hosts may be a critical missing consideration in understanding epidemiology.

Immunity-induced criticality of the genotype network of influenza A (H3N2) hemagglutinin

Seasonal influenza kills hundreds of thousands every year, with multiple constantly changing strains in circulation at any given time. A high mutation rate enables the influenza virus to evade recognition by the human immune system, including immunity acquired through past infection and vaccination. Here, we capture the genetic similarity of influenza strains and their evolutionary dynamics with genotype networks. We show that the genotype networks of influenza A (H3N2) hemagglutinin are characterized by heavy-tailed distributions of module sizes and connectivity indicative of critical behavior. We argue that (i) genotype networks are driven by mutation and host immunity to explore a subspace of networks predictable in structure and (ii) genotype networks provide an underlying structure necessary to capture the rich dynamics of multistrain epidemic models. In particular, inclusion of strain-transcending immunity in epidemic models is dependent upon the structure of an underlying genotype network. This interplay is consistent with self-organized criticality where the epidemic dynamics of influenza locates critical regions of its genotype network. We conclude that this interplay between disease dynamics and network structure might be key for future network analysis of pathogen evolution and realistic multistrain epidemic models.

Modelling the effect of within-host dynamics on the diversity of a multi-strain pathogen

Multi-strain pathogens such as Group A Streptococcus, Streptococcus pneumoniae, and Staphylococcus aureus cause millions of infections each year with a substantial health burden. Control of multi-strain pathogens can be complicated by the high strain diversity often observed in endemic settings. It is not well understood how high strain diversity is maintained in populations, given that they compete with each other both directly (within an individual host) and indirectly (via host immunity). Previous modelling studies have investigated how indirect competition affects the prevalence and diversity of strains. However, these studies often make simplifying assumptions about the direct competition that occurs within hosts. Currently, little data is available to validate these assumptions, hence there is a need to clarify how sensitive model outputs are to these assumptions. In this study, we compare the dynamics of multi-strain pathogens under different assumptions about direct competition between strains using an agent-based model. We find that the assumptions made about direct competition can affect the epidemiological dynamics, particularly when there is no long-term immunity following infections and a low rate of importation of non-circulating strains. Our results suggest that while direct and indirect competition can each decrease strain diversity when they act in isolation, they may increase strain diversity when they act together. This finding highlights the importance of examining sensitivity to assumptions about strain competition. In particular, omitting consideration of direct competition can lead to inaccurate estimates of the likely effectiveness of control strategies as changes in strain diversity shift the level of direct strain competition.

The rapid replacement of the Delta variant by Omicron (B.1.1.529) in England

The emergence of the B.1.1.529 (Omicron) variant caused international concern due to its rapid spread in Southern Africa. It was unknown whether this variant would replace or co-exist with (either transiently or long-term) the then-dominant Delta variant on its introduction to England. We developed a set of hierarchical logistic growth models to describe changes in the frequency of S gene target failure (SGTF) PCR tests, which was a proxy for Omicron. The doubling time of SGTF cases peaked at 1.56 days (95% CI: 1.49, 1.63) on the 5^th of December, while triple positive cases were halving every 5.82 days (95% CI: 5.11, 6.67) going into Christmas 2021. We were unable to characterize the replacement of Delta by Omicron with a single rate. The replacement rate decreased by 53.56% (95% CrI: 45.38, 61.01) between the 14^th and 15^th of December, meaning the competitive advantage of Omicron approximately halved. Preceding the changepoint, Omicron was replacing Delta 16.24% (95% CrI: 9.72, 23.41) faster in those with two or more vaccine doses, indicative of vaccine escape being a substantial component of the competitive advantage. Despite the slowdown, Delta had almost entirely been replaced in England within a month of the first sequenced domestic case. The synchrony of changepoints across regions at various stages of Omicron epidemics suggests that the growth rate advantage was not attenuated due to biological mechanisms related to strain competition. The step-change in replacement could have resulted from behavioral changes, potentially elicited by public health messaging or policies, that differentially affected Omicron.

Multi-scale modelling reveals that early super-spreader events are a likely contributor to novel variant predominance

The emergence of new SARS-CoV-2 variants of concern (VOC) has hampered international efforts to contain the COVID-19 pandemic. VOCs have been characterized to varying degrees by higher transmissibility, worse infection outcomes and evasion of vaccine and infection-induced immunologic memory. VOCs are hypothesized to have originated from animal reservoirs, communities in regions with low surveillance and/or single individuals with poor immunologic control of the virus. Yet, the factors dictating which variants ultimately predominate remain incompletely characterized. Here we present a multi-scale model of SARS-CoV-2 dynamics that describes population spread through individuals whose viral loads and numbers of contacts (drawn from an over-dispersed distribution) are both time-varying. This framework allows us to explore how super-spreader events (SSE) (defined as greater than five secondary infections per day) contribute to variant emergence. We find stochasticity remains a powerful determinant of predominance. Variants that predominate are more likely to be associated with higher infectiousness, an SSE early after variant emergence and ongoing decline of the current dominant variant. Additionally, our simulations reveal that most new highly infectious variants that infect one or a few individuals do not achieve permanence in the population. Consequently, interventions that reduce super-spreading may delay or mitigate emergence of VOCs.

Evolution during primary HIV infection does not require adaptive immune selection

Modern HIV research depends crucially on both viral sequencing and population measurements. To directly link mechanistic biological processes and evolutionary dynamics during HIV infection, we developed multiple within-host phylodynamic models of HIV primary infection for comparative validation against viral load and evolutionary dynamics data. The optimal model of primary infection required no positive selection, suggesting that the host adaptive immune system reduces viral load but surprisingly does not drive observed viral evolution. Rather, the fitness (infectivity) of mutant variants is drawn from an exponential distribution in which most variants are slightly less infectious than their parents (nearly neutral evolution). This distribution was not largely different from either in vivo fitness distributions recorded beyond primary infection or in vitro distributions that are observed without adaptive immunity, suggesting the intrinsic viral fitness distribution may drive evolution. Simulated phylogenetic trees also agree with independent data and illuminate how phylogenetic inference must consider viral and immune-cell population dynamics to gain accurate mechanistic insights.

Influenza immune escape under heterogeneous host immune histories

In a pattern called immune imprinting, individuals gain the strongest immune protection against the influenza strains encountered earliest in life. In many recent examples, differences in early infection history can explain birth year-associated differences in susceptibility (cohort effects). Susceptibility shapes strain fitness, but without a clear conceptual model linking host susceptibility to the identity and order of past infections general conclusions on the evolutionary and epidemic implications of cohort effects are not possible. Failure to differentiate between cohort effects caused by differences in the set, rather than the order (path), of past infections is a current source of confusion. We review and refine hypotheses for path-dependent cohort effects, which include imprinting. We highlight strategies to measure their underlying causes and emergent consequences.

The Hard Lessons and Shifting Modeling Trends of COVID-19 Dynamics: Multiresolution Modeling Approach

The COVID-19 pandemic has placed epidemiologists, modelers, and policy makers at the forefront of the global discussion of how to control the spread of coronavirus. The main challenges confronting modelling approaches include real-time projections of changes in the numbers of cases, hospitalizations, and fatalities, the consequences of public health policy, the understanding of how best to implement varied non-pharmaceutical interventions and potential vaccination strategies, now that vaccines are available for distribution. Here, we: (i) review carefully selected literature on COVID-19 modeling to identify challenges associated with developing appropriate models along with collecting the fine-tuned data, (ii) use the identified challenges to suggest prospective modeling frameworks through which adaptive interventions such as vaccine strategies and the uses of diagnostic tests can be evaluated, and (iii) provide a novel Multiresolution Modeling Framework which constructs a multi-objective optimization problem by considering relevant stakeholders’ participatory perspective to carry out epidemic nowcasting and future prediction. Consolidating our understanding of model approaches to COVID-19 will assist policy makers in designing interventions that are not only maximally effective but also economically beneficial.

Challenges in modeling the emergence of novel pathogens

The emergence of infectious agents with pandemic potential present scientific challenges from detection to data interpretation to understanding determinants of risk and forecasts. Mathematical models could play an essential role in how we prepare for future emergent pathogens. Here, we describe core directions for expansion of the existing tools and knowledge base, including: using mathematical models to identify critical directions and paths for strengthening data collection to detect and respond to outbreaks of novel pathogens; expanding basic theory to identify infectious agents and contexts that present the greatest risks, over both the short and longer term; by strengthening estimation tools that make the most use of the likely range and uncertainties in existing data; and by ensuring modelling applications are carefully communicated and developed within diverse and equitable collaborations for increased public health benefit.

Possible future waves of SARS-CoV-2 infection generated by variants of concern with a range of characteristics

Viral reproduction of SARS-CoV-2 provides opportunities for the acquisition of advantageous mutations, altering viral transmissibility, disease severity, and/or allowing escape from natural or vaccine-derived immunity. We use three mathematical models: a parsimonious deterministic model with homogeneous mixing; an age-structured model; and a stochastic importation model to investigate the effect of potential variants of concern (VOCs). Calibrating to the situation in England in May 2021, we find epidemiological trajectories for putative VOCs are wide-ranging and dependent on their transmissibility, immune escape capability, and the introduction timing of a postulated VOC-targeted vaccine. We demonstrate that a VOC with a substantial transmission advantage over resident variants, or with immune escape properties, can generate a wave of infections and hospitalisations comparable to the winter 2020-2021 wave. Moreover, a variant that is less transmissible, but shows partial immune-escape could provoke a wave of infection that would not be revealed until control measures are further relaxed.

Temporal lineage dynamics of the ORF5 gene of porcine reproductive and respiratory syndrome virus in Korea in 2014-2019

Porcine reproductive and respiratory syndrome virus (PRRSV) is the most important pathogen in the Korean swine industry. Despite efforts including improved biosecurity and vaccination protocols, the virus continues to circulate and evolve. Based on phylogenetic analysis of open reading frame 5 (ORF5), Korean PRRSVs are known to form not only globally circulating lineages but also country-specific lineages (Lin Kor A, B, and C). To understand the recent epidemiological status of PRRSV in Korea, a total of 1349 ORF5 sequences of Korean PRRSV isolates from 2014 to 2019 were analyzed. Phylogenetic analysis was conducted using the maximum-likelihood method, and temporal changes in the relative prevalence of lineages were investigated. The analysis showed that PRRSV1 and PRRSV2 were both highly prevalent throughout the years examined. Among the PRRSV1 isolates, subgroup A (90.1%) and vaccine-like subgroup C (9.0%) composed most of the population. For PRRSV2 isolates, vaccine-like lineage 5 (36.3%) was dominant, followed by Lin Kor B (25.9%), Kor C (16.6%), lineage 1 (11.6%), and Kor A (9.1%). The PRRSV2 lineage 1 population increased from 2014 (1.8%) to 2019 (29.6%) in Korea due to the continual spread of sublineage 1.8 (NADC30-like) and introduction of sublineage 1.6 into the country. Additional genetic analysis, including analysis of non synonymous and synonymous mutations, revealed evidence of diversification and positive selection in immunologically important regions of the genome, suggesting that current vaccination is failing and promoting immune-mediated selection. Overall, these findings provide insights into the epidemiological and evolutionary dynamics of cocirculating viral lineages, and constant surveillance of PRRSV occurrence is needed.

Modeling neutral viral mutations in the spread of SARS-CoV-2 epidemics

Although traditional models of epidemic spreading focus on the number of infected, susceptible and recovered individuals, a lot of attention has been devoted to integrate epidemic models with population genetics. Here we develop an individual-based model for epidemic spreading on networks in which viruses are explicitly represented by finite chains of nucleotides that can mutate inside the host. Under the hypothesis of neutral evolution we compute analytically the average pairwise genetic distance between all infecting viruses over time. We also derive a mean-field version of this equation that can be added directly to compartmental models such as SIR or SEIR to estimate the genetic evolution. We compare our results with the inferred genetic evolution of SARS-CoV-2 at the beginning of the epidemic in China and found good agreement with the analytical solution of our model. Finally, using genetic distance as a proxy for different strains, we use numerical simulations to show that the lower the connectivity between communities, e.g., cities, the higher the probability of reinfection.

Covasim: An agent-based model of COVID-19 dynamics and interventions

The COVID-19 pandemic has created an urgent need for models that can project epidemic trends, explore intervention scenarios, and estimate resource needs. Here we describe the methodology of Covasim (COVID-19 Agent-based Simulator), an open-source model developed to help address these questions. Covasim includes country-specific demographic information on age structure and population size; realistic transmission networks in different social layers, including households, schools, workplaces, long-term care facilities, and communities; age-specific disease outcomes; and intrahost viral dynamics, including viral-load-based transmissibility. Covasim also supports an extensive set of interventions, including non-pharmaceutical interventions, such as physical distancing and protective equipment; pharmaceutical interventions, including vaccination; and testing interventions, such as symptomatic and asymptomatic testing, isolation, contact tracing, and quarantine. These interventions can incorporate the effects of delays, loss-to-follow-up, micro-targeting, and other factors. Implemented in pure Python, Covasim has been designed with equal emphasis on performance, ease of use, and flexibility: realistic and highly customized scenarios can be run on a standard laptop in under a minute. In collaboration with local health agencies and policymakers, Covasim has already been applied to examine epidemic dynamics and inform policy decisions in more than a dozen countries in Africa, Asia-Pacific, Europe, and North America.

Covasim: An agent-based model of COVID-19 dynamics and interventions

The COVID-19 pandemic has created an urgent need for models that can project epidemic trends, explore intervention scenarios, and estimate resource needs. Here we describe the methodology of Covasim (COVID-19 Agent-based Simulator), an open-source model developed to help address these questions. Covasim includes country-specific demographic information on age structure and population size; realistic transmission networks in different social layers, including households, schools, workplaces, long-term care facilities, and communities; age-specific disease outcomes; and intrahost viral dynamics, including viral-load-based transmissibility. Covasim also supports an extensive set of interventions, including non-pharmaceutical interventions, such as physical distancing and protective equipment; pharmaceutical interventions, including vaccination; and testing interventions, such as symptomatic and asymptomatic testing, isolation, contact tracing, and quarantine. These interventions can incorporate the effects of delays, loss-to-follow-up, micro-targeting, and other factors. Implemented in pure Python, Covasim has been designed with equal emphasis on performance, ease of use, and flexibility: realistic and highly customized scenarios can be run on a standard laptop in under a minute. In collaboration with local health agencies and policymakers, Covasim has already been applied to examine epidemic dynamics and inform policy decisions in more than a dozen countries in Africa, Asia-Pacific, Europe, and North America.

The confounding effect of multi-type human papillomavirus infections on type-specific natural history parameter identification

The natural history of human papillomavirus (HPV) from infection to cervical cancer differs between HPV types. Accordingly, type-specific natural history parameters are crucial for the mathematical models used to optimize the nearly life-long series of disease prevention measures. These parameters are estimated from genotyped data from trials and population level screening programs, typically one type at a time, which requires projecting the multiple-type data to the single type. To analyze impacts of such projection methods on the estimates, we compared estimating one type at a time using different projection methods with estimating all types together. We simulated genotyped data with chosen parameter values for two HPV types and analyzed the identifiability of the chosen values using the different estimation methods. We found the success of estimating one type at a time to be excessively sensitive to the data projection method, with potential to falsely identify the parameters at wrong values. Estimating all types together identified the parameters well. Our results were consistent both when trial and population level data were used. In conclusion, the potential confounding by multi-type infections has to be considered when choosing an estimation method for type-specific natural history parameters.

Host Specialisation, Immune Cross-Reaction and the Composition of Communities of Co-circulating Borrelia Strains

We use mathematical modelling to examine how microbial strain communities are structured by the host specialisation traits and antigenic relationships of their members. The model is quite general and broadly applicable, but we focus on Borrelia burgdorferi, the Lyme disease bacterium, transmitted by ticks to mice and birds. In this system, host specialisation driven by the evasion of innate immunity has been linked to multiple niche polymorphism, while antigenic differentiation driven by the evasion of adaptive immunity has been linked to negative frequency dependence. Our model is composed of two host species, one vector, and multiple co-circulating pathogen strains that vary in their host specificity and their antigenic distances from one another. We explore the conditions required to maintain pathogen diversity. We show that the combination of host specificity and antigenic differentiation creates an intricate niche structure. Unequivocal rules that relate the stability of a strain community directly to the trait composition of its members are elusive. However, broad patterns are evident. When antigenic differentiation is weak, stable communities are typically composed entirely of generalists that can exploit either host species equally well. As antigenic differentiation increases, more diverse stable communities emerge, typically around trait compositions of generalists, generalists and very similar specialists, and specialists roughly balanced between the two host species.

Competition between RSV and influenza: Limits of modelling inference from surveillance data

Respiratory Syncytial Virus (RSV) and Influenza cause a large burden of disease. Evidence of their interaction via temporary cross-protection implies that prevention of one could inadvertently lead to an increase in the burden of the other. However, evidence for the public health impact of such interaction is sparse and largely derives from ecological analyses of peak shifts in surveillance data. To test the robustness of estimates of interaction parameters between RSV and Influenza from surveillance data we conducted a simulation and back-inference study. We developed a two-pathogen interaction model, parameterised to simulate RSV and Influenza epidemiology in the UK. Using the infection model in combination with a surveillance-like stochastic observation process we generated a range of possible RSV and Influenza trajectories and then used Markov Chain Monte Carlo (MCMC) methods to back-infer parameters including those describing competition. We find that in most scenarios both the strength and duration of RSV and Influenza interaction could be estimated from the simulated surveillance data reasonably well. However, the robustness of inference declined towards the extremes of the plausible parameter ranges, with misleading results. It was for instance not possible to tell the difference between low/moderate interaction and no interaction. In conclusion, our results illustrate that in a plausible parameter range, the strength of RSV and Influenza interaction can be estimated from a single season of high-quality surveillance data but also highlights the importance to test parameter identifiability a priori in such situations.

Localization, epidemic transitions, and unpredictability of multistrain epidemics with an underlying genotype network

Mathematical disease modelling has long operated under the assumption that any one infectious disease is caused by one transmissible pathogen spreading among a population. This paradigm has been useful in simplifying the biological reality of epidemics and has allowed the modelling community to focus on the complexity of other factors such as population structure and interventions. However, there is an increasing amount of evidence that the strain diversity of pathogens, and their interplay with the host immune system, can play a large role in shaping the dynamics of epidemics. Here, we introduce a disease model with an underlying genotype network to account for two important mechanisms. One, the disease can mutate along network pathways as it spreads in a host population. Two, the genotype network allows us to define a genetic distance between strains and therefore to model the transcendence of immunity often observed in real world pathogens. We study the emergence of epidemics in this model, through its epidemic phase transitions, and highlight the role of the genotype network in driving cyclicity of diseases, large scale fluctuations, sequential epidemic transitions, as well as localization around specific strains of the associated pathogen. More generally, our model illustrates the richness of behaviours that are possible even in well-mixed host populations once we consider strain diversity and go beyond the “one disease equals one pathogen” paradigm.

Epidemics rarely involve a single unique pathogen but are often modelled as such. Rather, most pathogens circulate under a family of strains which can interact differently with the host immune system and undergo further mutations. Here we extend a classic epidemiological model to consider the genetic structure connecting these strains—i.e., the genotype network mapping possible mutation pathways—and investigate the dynamics and emergence of epidemics beyond the “one disease equals one pathogen” paradigm. This simple model allows us to consider the impacts of (i) mutation, (ii) cross-immunity between strains, (iii) competition between strains, and (iv) the structure of the genotype network. We find that, altogether, these features do not affect the classic epidemic threshold but localize outbreaks around key strains and yield a second immune invasion threshold below which the epidemics follow almost cyclical and chaos-like dynamics. Our results illustrate how little biological realism is needed to introduce key features of real epidemics in even the simplest disease models: epidemic cycles, unpredictability, and heterogeneous strain prevalence.

Dynamic network connectivity influences the spread of a sub-lineage of porcine reproductive and respiratory syndrome virus

Swine production in the United States is characterized by dynamic farm contacts through animal movements; such movements shape the risk of disease occurrence on farms. Pig movements have been linked to the spread of a virulent porcine reproductive and respiratory syndrome virus (PRRSV), RFLP type 1-7-4, herein denoted as phylogenetic sub-lineage 1A [L1A]. This study aimed to quantify the contribution of pig movements to the risk of L1A occurrence on farms in the United States. Farms were defined as L1A-positive in a given 6-month period if at least one L1A sequence was recovered from the farm. Temporal network autocorrelation modelling was performed using data on animal movements and 1,761 PRRSV ORF5 sequences linked to 494 farms from a dense pig production area in the United States between 2014 and 2017. A farm's current and past exposure to L1A and other PRRSV variants was assessed through its primary and secondary contacts in the animal movement network. Primary and secondary contacts with an L1A-positive farm increased the likelihood of L1A occurrence on a farm by 19% (p = .04) and 23% (p = .03), respectively. While the risk posed by primary contacts with PRRS-positive farms is unsurprising, the observation that secondary contacts also increase the likelihood of infection is novel. Risk of L1A occurrence on a farm also increased by 3.0% (p = .01) for every additional outgoing shipment, possibly due to biosecurity breaches during loading and transporting pigs from the farm. Finally, use of vaccines or field virus inoculation on sow farms one year prior reduced the risk of L1A occurrence in downstream farms by 36% (p = .04), suggesting that control measures that reduce viral circulation and enhance immunological protection in sow farms have a carry-over effect on L1A occurrence in downstream farms. Therefore, coordinated disease management interventions between farms connected via animal movements may be more effective than individual farm-based interventions.

Predicting N-Strain Coexistence from Co-colonization Interactions: Epidemiology Meets Ecology and the Replicator Equation

Multi-type infection processes are ubiquitous in ecology, epidemiology and social systems, but remain hard to analyze and to understand on a fundamental level. Here, we study a multi-strain susceptible-infected-susceptible model with coinfection. A host already colonized by one strain can become more or less vulnerable to co-colonization by a second strain, as a result of facilitating or competitive interactions between the two. Fitness differences between N strains are mediated through \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N^2$$\end{document}N2 altered susceptibilities to secondary infection that depend on colonizer-cocolonizer identities (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K_{ij}$$\end{document}Kij). By assuming strain similarity in such pairwise traits, we derive a model reduction for the endemic system using separation of timescales. This ‘quasi-neutrality’ in trait space sets a fast timescale where all strains interact neutrally, and a slow timescale where selective dynamics unfold. We find that these slow dynamics are governed by the replicator equation for N strains. Our framework allows to build the community dynamics bottom-up from only pairwise invasion fitnesses between members. We highlight that mean fitness of the multi-strain network, changes with their individual dynamics, acts equally upon each type, and is a key indicator of system resistance to invasion. By uncovering the link between N-strain epidemiological coexistence and the replicator equation, we show that the ecology of co-colonization relates to Fisher’s fundamental theorem and to Lotka-Volterra systems. Besides efficient computation and complexity reduction for any system size, these results open new perspectives into high-dimensional community ecology, detection of species interactions, and evolution of biodiversity.

Within-Host Phenotypic Evolution and the Population-Level Control of Chronic Viral Infections by Treatment and Prophylaxis

Chronic viral infections can persist for decades spanning thousands of viral generations, leading to a highly diverse population of viruses with its own complex evolutionary history. We propose an expandable mathematical framework for understanding how the emergence of genetic and phenotypic diversity affects the population-level control of those infections by both non-curative treatment and chemo-prophylactic measures. Our frameworks allows both neutral and phenotypic evolution, and we consider the specific evolution of contagiousness, resistance to therapy, and efficacy of prophylaxis. We compute both the controlled and uncontrolled, population-level basic reproduction number accounting for the within-host evolutionary process where new phenotypes emerge and are lost in infected persons, which we also extend to include both treatment and prophylactic control efforts. We used these results to discuss the conditions under which the relative efficacy of prophylactic versus therapeutic methods of control are superior. Finally, we give expressions for the endemic equilibrium of these models for certain constrained versions of the within-host evolutionary model providing a potential method for estimating within-host evolutionary parameters from population-level genetic sequence data.

The impact of climate and antigenic evolution on seasonal influenza virus epidemics in Australia

Although seasonal influenza viruses circulate globally, prevention and treatment occur at the level of regions, cities, and communities. At these scales, the timing, duration and magnitude of epidemics vary substantially, but the underlying causes of this variation are poorly understood. Here, based on analyses of a 15-year city-level dataset of 18,250 laboratory-confirmed and antigenically-characterised influenza virus infections from Australia, we investigate the effects of previously hypothesised environmental and virological drivers of influenza epidemics. We find that anomalous fluctuations in temperature and humidity do not predict local epidemic onset timings. We also find that virus antigenic change has no consistent effect on epidemic size. In contrast, epidemic onset time and heterosubtypic competition have substantial effects on epidemic size and composition. Our findings suggest that the relationship between influenza population immunity and epidemiology is more complex than previously supposed and that the strong influence of short-term processes may hinder long-term epidemiological forecasts.

Coinfections by noninteracting pathogens are not independent and require new tests of interaction

If pathogen species, strains, or clones do not interact, intuition suggests the proportion of coinfected hosts should be the product of the individual prevalences. Independence consequently underpins the wide range of methods for detecting pathogen interactions from cross-sectional survey data. However, the very simplest of epidemiological models challenge the underlying assumption of statistical independence. Even if pathogens do not interact, death of coinfected hosts causes net prevalences of individual pathogens to decrease simultaneously. The induced positive correlation between prevalences means the proportion of coinfected hosts is expected to be higher than multiplication would suggest. By modelling the dynamics of multiple noninteracting pathogens causing chronic infections, we develop a pair of novel tests of interaction that properly account for nonindependence between pathogens causing lifelong infection. Our tests allow us to reinterpret data from previous studies including pathogens of humans, plants, and animals. Our work demonstrates how methods to identify interactions between pathogens can be updated using simple epidemic models.

If pathogen species, strains, or clones do not interact, intuition suggests the proportion of coinfected hosts can be obtained by simply multiplying the individual prevalences. However, even simple epidemiological models show this to be untrue. This study develops new tests for interaction between pathogens that account for this surprising lack of statistical independence.

Temporal Dynamics of Co-circulating Lineages of Porcine Reproductive and Respiratory Syndrome Virus

Porcine Reproductive and Respiratory Syndrome Virus (PRRSV) is the most important endemic pathogen in the U.S. swine industry. Despite control efforts involving improved biosecurity and different vaccination protocols, the virus continues to circulate and evolve. One of the foremost challenges in its control is high levels of genetic and antigenic diversity. Here, we quantify the co-circulation, emergence and sequential turnover of multiple PRRSV lineages in a single swine-producing region in the United States over a span of 9 years (2009-2017). By classifying over 4,000 PRRSV sequences (open-reading frame 5) into phylogenetic lineages and sub-lineages, we document the ongoing diversification and temporal dynamics of the PRRSV population, including the rapid emergence of a novel sub-lineage that appeared to be absent globally pre-2008. In addition, lineage 9 was the most prevalent lineage from 2009 to 2010, but its occurrence fell to 0.5% of all sequences identified per year after 2014, coinciding with the emergence or re-emergence of lineage 1 as the dominant lineage. The sequential dominance of different lineages, as well as three different sub-lineages within lineage 1, is consistent with the immune-mediated selection hypothesis for the sequential turnover in the dominant lineage. As host populations build immunity through natural infection or vaccination toward the most common variant, this dominant (sub-) lineage may be replaced by an emerging variant to which the population is more susceptible. An analysis of patterns of non- synonymous and synonymous mutations revealed evidence of positive selection on immunologically important regions of the genome, further supporting the potential that immune-mediated selection shapes the evolutionary and epidemiological dynamics for this virus. This has important implications for patterns of emergence and re-emergence of genetic variants of PRRSV that have negative impacts on the swine industry. Constant surveillance on PRRSV occurrence is crucial to a better understanding of the epidemiological and evolutionary dynamics of co-circulating viral lineages. Further studies utilizing whole genome sequencing and exploring the extent of cross-immunity between heterologous PRRS viruses could shed further light on PRRSV immunological response and aid in developing strategies that might be able to diminish disease impact.

The Collaborative Cross mouse model for dissecting genetic susceptibility to infectious diseases

Infectious diseases, also known as communicable diseases, refer to a full range of maladies caused by pathogen invasion to the host body. Host response towards an infectious pathogen varies between individuals, and can be defined by responses from asymptomatic to lethal. Host response to infectious pathogens is considered as a complex trait controlled by gene-gene (host-pathogen) and gene-environment interactions, leading to the extensive phenotypic variations between individuals. With the advancement of the human genome mapping approaches and tools, various genome-wide association studies (GWAS) were performed, aimed at mapping the genetic basis underlying host susceptibility towards infectious pathogens. In parallel, immense efforts were invested in enhancing the genetic mapping resolution and gene-cloning efficacy, using advanced mouse models including advanced intercross lines; outbred populations; consomic, congenic; and recombinant inbred lines. Notwithstanding the evident advances achieved using these mouse models, the genetic diversity was low and quantitative trait loci (QTL) mapping resolution was inadequate. Consequently, the Collaborative Cross (CC) mouse model was established by full-reciprocal mating of eight divergent founder strains of mice (A/J, C57BL/6J, 129S1/SvImJ, NOD/LtJ, NZO/HiLtJ, CAST/Ei, PWK/PhJ, and WSB/EiJ) generating a next-generation mouse genetic reference population (CC lines). Presently, the CC mouse model population comprises a set of about 200 recombinant inbred CC lines exhibiting a unique high genetic diversity and which are accessible for multidisciplinary studies. The CC mouse model efficacy was validated by various studies in our lab and others, accomplishing high-resolution (< 1 MB) QTL genomic mapping for a variety of complex traits, using about 50 CC lines (3-4 mice per line). Herein, we present a number of studies demonstrating the power of the CC mouse model, which has been utilized in our lab for mapping the genetic basis of host susceptibility to various infectious pathogens. These include Aspergillus fumigatus, Klebsiella pneumoniae, Porphyromonas gingivalis and Fusobacterium nucleatum (causing oral mixed infection), Pseudomonas aeruginosa, and the bacterial toxins Lipopolysaccharide and Lipoteichoic acid.

Influenza interaction with cocirculating pathogens and its impact on surveillance, pathogenesis, and epidemic profile: A key role for mathematical modelling

Evidence is mounting that influenza virus interacts with other pathogens colonising or infecting the human respiratory tract. Taking into account interactions with other pathogens may be critical to determining the real influenza burden and the full impact of public health policies targeting influenza. This is particularly true for mathematical modelling studies, which have become critical in public health decision-making. Yet models usually focus on influenza virus acquisition and infection alone, thereby making broad oversimplifications of pathogen ecology. Herein, we report evidence of influenza virus interactions with bacteria and viruses and systematically review the modelling studies that have incorporated interactions. Despite the many studies examining possible associations between influenza and Streptococcus pneumoniae, Staphylococcus aureus, Haemophilus influenzae, Neisseria meningitidis, respiratory syncytial virus (RSV), human rhinoviruses, human parainfluenza viruses, etc., very few mathematical models have integrated other pathogens alongside influenza. The notable exception is the pneumococcus-influenza interaction, for which several recent modelling studies demonstrate the power of dynamic modelling as an approach to test biological hypotheses on interaction mechanisms and estimate the strength of those interactions. We explore how different interference mechanisms may lead to unexpected incidence trends and possible misinterpretation, and we illustrate the impact of interactions on public health surveillance using simple transmission models. We demonstrate that the development of multipathogen models is essential to assessing the true public health burden of influenza and that it is needed to help improve planning and evaluation of control measures. Finally, we identify the public health, surveillance, modelling, and biological challenges and propose avenues of research for the coming years.

Coupled, multi-strain epidemic models of mutating pathogens

We introduce and analyze coupled, multi-strain epidemic models designed to simulate the emergence and dissemination of mutant (e.g. drug-resistant) pathogen strains. In particular, we investigate the mathematical and biological properties of a general class of multi-strain epidemic models in which the infectious compartments of each strain are coupled together in a general manner. We derive explicit expressions for the basic reproduction number of each strain and highlight their importance in regulating the system dynamics (e.g. the potential for an epidemic outbreak) and the existence of nonnegative endemic solutions. Importantly, we find that the basic reproduction number of each strain is independent of the mutation rates between the strains - even under quite general assumptions for the form of the infectious compartment coupling. Moreover, we verify that the coupling term promotes strain coexistence (as an extension of the competitive exclusion principle) and demonstrate that the strain with the greatest reproductive capacity is not necessarily the most prevalent. Finally, we briefly discuss the implications of our results for public health policy and planning.

Chimera states in multi-strain epidemic models with temporary immunity

We investigate a time-delayed epidemic model for multi-strain diseases with temporary immunity. In the absence of cross-immunity between strains, dynamics of each individual strain exhibit emergence and annihilation of limit cycles due to a Hopf bifurcation of the endemic equilibrium, and a saddle-node bifurcation of limit cycles depending on the time delay associated with duration of temporary immunity. Effects of all-to-all and non-local coupling topologies are systematically investigated by means of numerical simulations, and they suggest that cross-immunity is able to induce a diverse range of complex dynamical behaviors and synchronization patterns, including discrete traveling waves, solitary states, and amplitude chimeras. Interestingly, chimera states are observed for narrower cross-immunity kernels, which can have profound implications for understanding the dynamics of multi-strain diseases.

Seasonality in risk of pandemic influenza emergence

Influenza pandemics can emerge unexpectedly and wreak global devastation. However, each of the six pandemics since 1889 emerged in the Northern Hemisphere just after the flu season, suggesting that pandemic timing may be predictable. Using a stochastic model fit to seasonal flu surveillance data from the United States, we find that seasonal flu leaves a transient wake of heterosubtypic immunity that impedes the emergence of novel flu viruses. This refractory period provides a simple explanation for not only the spring-summer timing of historical pandemics, but also early increases in pandemic severity and multiple waves of transmission. Thus, pandemic risk may be seasonal and predictable, with the accuracy of pre-pandemic and real-time risk assessments hinging on reliable seasonal influenza surveillance and precise estimates of the breadth and duration of heterosubtypic immunity.

Forecasting Epidemiological and Evolutionary Dynamics of Infectious Diseases

Mathematical models have been powerful tools in developing mechanistic understanding of infectious diseases. Furthermore, they have allowed detailed forecasting of epidemiological phenomena such as outbreak size, which is of considerable public-health relevance. The short generation time of pathogens and the strong selection they are subjected to (by host immunity, vaccines, chemotherapy, etc.) mean that evolution is also a key driver of infectious disease dynamics. Accurate forecasting of pathogen dynamics therefore calls for the integration of epidemiological and evolutionary processes, yet this integration remains relatively rare. We review previous attempts to model and predict infectious disease dynamics with or without evolution and discuss major challenges facing the development of the emerging science of epidemic forecasting.