A nanoluciferase-encoded bacteriophage illuminates viral infection dynamics of Pseudomonas aeruginosa cells.

Bacteriophages (phages) are increasingly considered for both treatment and early detection of bacterial pathogens given their specificity and rapid infection kinetics. Here, we exploit an engineered phage expressing nanoluciferase to detect signals associated with Pseudomonas aeruginosa lysis spanning single cells to populations. Using several P. aeruginosa strains we found that the latent period, burst size, fraction of infected cells, and efficiency of plating inferred from fluorescent light intensity signals were consistent with inferences from conventional population assays. Notably, imaging-based traits were obtained in minutes to hours in contrast to the use of overnight plaques, which opens the possibility to study infection dynamics in spatial and/or temporal contexts where plaque development is infeasible. These findings support the use of engineered phages to study infection kinetics of virus-cell interactions in complex environments and potentially accelerate the determination of viral host range in therapeutically relevant contexts.

Multi-strain phage induced clearance of bacterial infections.

Bacteriophage (or 'phage' - viruses that infect and kill bacteria) are increasingly considered as a therapeutic alternative to treat antibiotic-resistant bacterial infections. However, bacteria can evolve resistance to phage, presenting a significant challenge to the near- and long-term success of phage therapeutics. Application of mixtures of multiple phage (i.e., 'cocktails') have been proposed to limit the emergence of phage-resistant bacterial mutants that could lead to therapeutic failure. Here, we combine theory and computational models of in vivo phage therapy to study the efficacy of a phage cocktail, composed of two complementary phages motivated by the example of Pseudomonas aeruginosa facing two phages that exploit different surface receptors, LUZ19v and PAK_P1. As confirmed in a Luria-Delbrück fluctuation test, this motivating example serves as a model for instances where bacteria are extremely unlikely to develop simultaneous resistance mutations against both phages. We then quantify therapeutic outcomes given single- or double-phage treatment models, as a function of phage traits and host immune strength. Building upon prior work showing monophage therapy efficacy in immunocompetent hosts, here we show that phage cocktails comprised of phage targeting independent bacterial receptors can improve treatment outcome in immunocompromised hosts and reduce the chance that pathogens simultaneously evolve resistance against phage combinations. The finding of phage cocktail efficacy is qualitatively robust to differences in virus-bacteria interactions and host immune dynamics. Altogether, the combined use of theory and computational analysis highlights the influence of viral life history traits and receptor complementarity when designing and deploying phage cocktails in immunocompetent and immunocompromised hosts.

Metapopulation model of phage therapy of an acute Pseudomonas aeruginosa lung infection.

Infections caused by multidrug resistant (MDR) pathogenic bacteria are a global health threat. Bacteriophages ("phage") are increasingly used as alternative or last-resort therapeutics to treat patients infected by MDR bacteria. However, the therapeutic outcomes of phage therapy may be limited by the emergence of phage resistance during treatment and/or by physical constraints that impede phage-bacteria interactions in vivo. In this work, we evaluate the role of lung spatial structure on the efficacy of phage therapy for Pseudomonas aeruginosa infections. To do so, we developed a spatially structured metapopulation network model based on the geometry of the bronchial tree, including host innate immune responses and the emergence of phage-resistant bacterial mutants. We model the ecological interactions between bacteria, phage, and the host innate immune system at the airway (node) level. The model predicts the synergistic elimination of a P. aeruginosa infection due to the combined effects of phage and neutrophils, given the sufficient innate immune activity and efficient phage-induced lysis. The metapopulation model simulations also predict that MDR bacteria are cleared faster at distal nodes of the bronchial tree. Notably, image analysis of lung tissue time series from wild-type and lymphocyte-depleted mice revealed a concordant, statistically significant pattern: infection intensity cleared in the bottom before the top of the lungs. Overall, the combined use of simulations and image analysis of in vivo experiments further supports the use of phage therapy for treating acute lung infections caused by P. aeruginosa, while highlighting potential limits to therapy in a spatially structured environment given impaired innate immune responses and/or inefficient phage-induced lysis. IMPORTANCE: Phage therapy is increasingly employed as a compassionate treatment for severe infections caused by multidrug-resistant (MDR) bacteria. However, the mixed outcomes observed in larger clinical studies highlight a gap in understanding when phage therapy succeeds or fails. Previous research from our team, using in vivo experiments and single-compartment mathematical models, demonstrated the synergistic clearance of acute P. aeruginosa pneumonia by phage and neutrophils despite the emergence of phage-resistant bacteria. In fact, the lung environment is highly structured, prompting the question of whether immunophage synergy explains the curative treatment of P. aeruginosa when incorporating realistic physical connectivity. To address this, we developed a metapopulation network model mimicking the lung branching structure to assess phage therapy efficacy for MDR P. aeruginosa pneumonia. The model predicts the synergistic elimination of P. aeruginosa by phage and neutrophils but emphasizes potential challenges in spatially structured environments, suggesting that higher innate immune levels may be required for successful bacterial clearance. Model simulations reveal a spatial pattern in pathogen clearance where P. aeruginosa are cleared faster at distal nodes of the bronchial tree than in primary nodes. Interestingly, image analysis of infected mice reveals a concordant and statistically significant pattern: infection intensity clears in the bottom before the top of the lungs. The combined use of modeling and image analysis supports the application of phage therapy for acute P. aeruginosa pneumonia while emphasizing potential challenges to curative success in spatially structured in vivo environments, including impaired innate immune responses and reduced phage efficacy.

Accounting for cellular-level variation in lysis: implications for virus-host dynamics.

Viral impacts on microbial populations depend on interaction phenotypes-including viral traits spanning the adsorption rate, latent period, and burst size. The latent period is a key viral trait in lytic infections. Defined as the time from viral adsorption to viral progeny release, the latent period of bacteriophage is conventionally inferred via one-step growth curves in which the accumulation of free virus is measured over time in a population of infected cells. Developed more than 80 years ago, one-step growth curves do not account for cellular-level variability in the timing of lysis, potentially biasing inference of viral traits. Here, we use nonlinear dynamical models to understand how individual-level variation of the latent period impacts virus-host dynamics. Our modeling approach shows that inference of the latent period via one-step growth curves is systematically biased-generating estimates of shorter latent periods than the underlying population-level mean. The bias arises because variability in lysis timing at the cellular level leads to a fraction of early burst events, which are interpreted, artefactually, as an earlier mean time of viral release. We develop a computational framework to estimate latent period variability from joint measurements of host and free virus populations. Our computational framework recovers both the mean and variance of the latent period within simulated infections including realistic measurement noise. This work suggests that reframing the latent period as a distribution to account for variability in the population will improve the study of viral traits and their role in shaping microbial populations.IMPORTANCEQuantifying viral traits-including the adsorption rate, burst size, and latent period-is critical to characterize viral infection dynamics and develop predictive models of viral impacts across scales from cells to ecosystems. Here, we revisit the gold standard of viral trait estimation-the one-step growth curve-to assess the extent to which assumptions at the core of viral infection dynamics lead to ongoing and systematic biases in inferences of viral traits. We show that latent period estimates obtained via one-step growth curves systematically underestimate the mean latent period and, in turn, overestimate the rate of viral killing at population scales. By explicitly incorporating trait variability into a dynamical inference framework that leverages both virus and host time series, we provide a practical route to improve estimates of the mean and variance of viral traits across diverse virus-microbe systems.

Scenario-Based Messages on Social Media Motivate COVID-19 Information Seeking.

Communicating information about health risks empowers individuals to make informed decisions. To identify effective communication strategies, we manipulated the specificity, self-relevance, and emotional framing of messages designed to motivate information seeking about COVID-19 exposure risk. In Study 1 (N=221,829), we conducted a large-scale social media field study. Using Facebook advertisements, we targeted users by age and political attitudes. Episodic specificity drove engagement: Advertisements that contextualized risk in specific scenarios produced the highest click-through rates, across all demographic groups. In Study 2, we replicated and extended our findings in an online experiment (N=4,233). Message specificity (but not self-relevance or emotional valence) drove interest in learning about COVID-19 risks. Across both studies, we found that older adults and liberals were more interested in learning about COVID-19 risks. However, message specificity increased engagement across demographic groups. Overall, evoking specific scenarios motivated information seeking about COVID-19, facilitating risk communication to a broad audience.

Design, optimization, and inference of biphasic decay of infectious virus particles.

Virus population dynamics are driven by counter-balancing forces of production and loss. Whereas viral production arises from complex interactions with susceptible hosts, the loss of infectious virus particles is often approximated as a first-order kinetic process. As such, experimental protocols to measure infectious virus loss are not typically designed to identify non-exponential decay processes. Here, we propose methods to evaluate if an experimental design is adequate to identify multiphasic virus particle decay and to optimize the sampling times of decay experiments, accounting for uncertainties in viral kinetics. First, we evaluate synthetic scenarios of biphasic decays, with varying decay rates and initial proportions of subpopulations. We show that robust inference of multiphasic decay is more likely when the faster decaying subpopulation predominates insofar as early samples are taken to resolve the faster decay rate. Moreover, design optimization involving non-equal spacing between observations increases the precision of estimation while reducing the number of samples. We then apply these methods to infer multiple decay rates associated with the decay of bacteriophage ('phage') Φ D 9 , an evolved isolate derived from phage Φ 21 . A pilot experiment confirmed that Φ D 9 decay is multiphasic, but was unable to resolve the rate or proportion of the fast decaying subpopulation(s). We then applied a Fisher information matrix-based design optimization method to propose non-equally spaced sampling times. Using this strategy, we were able to robustly estimate multiple decay rates and the size of the respective subpopulations. Notably, we conclude that the vast majority (94%) of the phage Φ D 9 population decays at a rate 16-fold higher than the slow decaying population. Altogether, these results provide both a rationale and a practical approach to quantitatively estimate heterogeneity in viral decay.

Disentangling top-down drivers of mortality underlying diel population dynamics of Prochlorococcus in the North Pacific Subtropical Gyre.

Photosynthesis fuels primary production at the base of marine food webs. Yet, in many surface ocean ecosystems, diel-driven primary production is tightly coupled to daily loss. This tight coupling raises the question: which top-down drivers predominate in maintaining persistently stable picocyanobacterial populations over longer time scales? Motivated by high-frequency surface water measurements taken in the North Pacific Subtropical Gyre (NPSG), we developed multitrophic models to investigate bottom-up and top-down mechanisms underlying the balanced control of Prochlorococcus populations. We find that incorporating photosynthetic growth with viral- and predator-induced mortality is sufficient to recapitulate daily oscillations of Prochlorococcus abundances with baseline community abundances. In doing so, we infer that grazers in this environment function as the predominant top-down factor despite high standing viral particle densities. The model-data fits also reveal the ecological relevance of light-dependent viral traits and non-canonical factors to cellular loss. Finally, we leverage sensitivity analyses to demonstrate how variation in life history traits across distinct oceanic contexts, including variation in viral adsorption and grazer clearance rates, can transform the quantitative and even qualitative importance of top-down controls in shaping Prochlorococcus population dynamics.

Emergence and maintenance of stable coexistence during a long-term multicellular evolution experiment.

The evolution of multicellular life spurred evolutionary radiations, fundamentally changing many of Earth's ecosystems. Yet little is known about how early steps in the evolution of multicellularity affect eco-evolutionary dynamics. Through long-term experimental evolution, we observed niche partitioning and the adaptive divergence of two specialized lineages from a single multicellular ancestor. Over 715 daily transfers, snowflake yeast were subjected to selection for rapid growth, followed by selection favouring larger group size. Small and large cluster-forming lineages evolved from a monomorphic ancestor, coexisting for over ~4,300 generations, specializing on divergent aspects of a trade-off between growth rate and survival. Through modelling and experimentation, we demonstrate that coexistence is maintained by a trade-off between organismal size and competitiveness for dissolved oxygen. Taken together, this work shows how the evolution of a new level of biological individuality can rapidly drive adaptive diversification and the expansion of a nascent multicellular niche, one of the most historically impactful emergent properties of this evolutionary transition.

Metapopulation model of phage therapy of an acute Pseudomonas aeruginosa lung infection.

Infections caused by multi-drug resistant (MDR) pathogenic bacteria are a global health threat. Phage therapy, which uses phage to kill bacterial pathogens, is increasingly used to treat patients infected by MDR bacteria. However, the therapeutic outcome of phage therapy may be limited by the emergence of phage resistance during treatment and/or by physical constraints that impede phage-bacteria interactions in vivo. In this work, we evaluate the role of lung spatial structure on the efficacy of phage therapy for Pseudomonas aeruginosa infection. To do so, we developed a spatially structured metapopulation network model based on the geometry of the bronchial tree, and included the emergence of phage-resistant bacterial mutants and host innate immune responses. We model the ecological interactions between bacteria, phage, and the host innate immune system at the airway (node) level. The model predicts the synergistic elimination of a P. aeruginosa infection due to the combined effects of phage and neutrophils given sufficiently active immune states and suitable phage life history traits. Moreover, the metapopulation model simulations predict that local MDR pathogens are cleared faster at distal nodes of the bronchial tree. Notably, image analysis of lung tissue time series from wild-type and lymphocyte-depleted mice (n=13) revealed a concordant, statistically significant pattern: infection intensity cleared in the bottom before the top of the lungs. Overall, the combined use of simulations and image analysis of in vivo experiments further supports the use of phage therapy for treating acute lung infections caused by P. aeruginosa while highlighting potential limits to therapy given a spatially structured environment, such as impaired innate immune responses and low phage efficacy.

Inferring strain-level mutational drivers of phage-bacteria interaction phenotypes.

The enormous diversity of bacteriophages and their bacterial hosts presents a significant challenge to predict which phages infect a focal set of bacteria. Infection is largely determined by complementary -and largely uncharacterized- genetics of adsorption, injection, and cell take-over. Here we present a machine learning (ML) approach to predict phage-bacteria interactions trained on genome sequences of and phenotypic interactions amongst 51 Escherichia coli strains and 45 phage λ strains that coevolved in laboratory conditions for 37 days. Leveraging multiple inference strategies and without a priori knowledge of driver mutations, this framework predicts both who infects whom and the quantitative levels of infections across a suite of 2,295 potential interactions. The most effective ML approach inferred interaction phenotypes from independent contributions from phage and bacteria mutations, predicting phage host range with 86% mean classification accuracy while reducing the relative error in the estimated strength of the infection phenotype by 40%. Further, transparent feature selection in the predictive model revealed 18 of 176 phage λ and 6 of 18 E. coli mutations that have a significant influence on the outcome of phage-bacteria interactions, corroborating sites previously known to affect phage λ infections, as well as identifying mutations in genes of unknown function not previously shown to influence bacterial resistance. While the genetic variation studied was limited to a focal, coevolved phage-bacteria system, the method's success at recapitulating strain-level infection outcomes provides a path forward towards developing strategies for inferring interactions in non-model systems, including those of therapeutic significance.

Macrophage-induced reduction of bacteriophage density limits the efficacy of in vivo pulmonary phage therapy.

The rise of antimicrobial resistance has led to renewed interest in evaluating phage therapy. In murine models highly effective treatment of acute pneumonia caused by Pseudomonas aeruginosa relies on the synergistic antibacterial activity of bacteriophages with neutrophils. Here, we show that depletion of alveolar macrophages (AM) shortens the survival of mice without boosting the P. aeruginosa load in the lungs. Unexpectedly, upon bacteriophage treatment, pulmonary levels of P. aeruginosa were significantly lower in AM-depleted than in immunocompetent mice. To explore potential mechanisms underlying the benefit of AM-depletion in treated mice, we developed a mathematical model of phage, bacteria, and innate immune system dynamics. Simulations from the model fitted to data suggest that AM reduce bacteriophage density in the lungs. We experimentally confirmed that the in vivo decay of bacteriophage is faster in immunocompetent compared to AM-depleted animals. These findings demonstrate the involvement of feedback between bacteriophage, bacteria, and the immune system in shaping the outcomes of phage therapy in clinical settings.

Rapid bacteria-phage coevolution drives the emergence of multiscale networks.

Interactions between species catalyze the evolution of multiscale ecological networks, including both nested and modular elements that regulate the function of diverse communities. One common assumption is that such complex pattern formation requires spatial isolation or long evolutionary timescales. We show that multiscale network structure can evolve rapidly under simple ecological conditions without spatial structure. In just 21 days of laboratory coevolution, Escherichia coli and bacteriophage Φ21 coevolve and diversify to form elaborate cross-infection networks. By measuring ~10,000 phage-bacteria infections and testing the genetic basis of interactions, we identify the mechanisms that create each component of the multiscale pattern. Our results demonstrate how multiscale networks evolve in parasite-host systems, illustrating Darwin's idea that simple adaptive processes can generate entangled banks of ecological interactions.

Communicating COVID-19 exposure risk with an interactive website counteracts risk misestimation.

During the COVID-19 pandemic, individuals depended on risk information to make decisions about everyday behaviors and public policy. Here, we assessed whether an interactive website influenced individuals' risk tolerance to support public health goals. We collected data from 11,169 unique users who engaged with the online COVID-19 Event Risk Tool (https://covid19risk.biosci.gatech.edu/) between 9/22/21 and 1/22/22. The website featured interactive elements, including a dynamic risk map, survey questions, and a risk quiz with accuracy feedback. After learning about the risk of COVID-19 exposure, participants reported being less willing to participate in events that could spread COVID-19, especially for high-risk large events. We also uncovered a bias in risk estimation: Participants tended to overestimate the risk of small events but underestimate the risk of large events. Importantly, even participants who voluntarily sought information about COVID risks tended to misestimate exposure risk, demonstrating the need for intervention. Participants from liberal-leaning counties were more likely to use the website tools and more responsive to feedback about risk misestimation, indicating that political partisanship influences how individuals seek and engage with COVID-19 information. Lastly, we explored temporal dynamics and found that user engagement and risk estimation fluctuated over the course of the Omicron variant outbreak. Overall, we report an effective large-scale method for communicating viral exposure risk; our findings are relevant to broader research on risk communication, epidemiological modeling, and risky decision-making.

Metacommunity structure preserves genome diversity in the presence of gene-specific selective sweeps under moderate rates of horizontal gene transfer.

The horizontal transfer of genes is fundamental for the eco-evolutionary dynamics of microbial communities, such as oceanic plankton, soil, and the human microbiome. In the case of an acquired beneficial gene, classic population genetics would predict a genome-wide selective sweep, whereby the genome spreads clonally within the community and together with the beneficial gene, removing genome diversity. Instead, several sources of metagenomic data show the existence of "gene-specific sweeps", whereby a beneficial gene spreads across a bacterial community, maintaining genome diversity. Several hypotheses have been proposed to explain this process, including the decreasing gene flow between ecologically distant populations, frequency-dependent selection from linked deleterious allelles, and very high rates of horizontal gene transfer. Here, we propose an additional possible scenario grounded in eco-evolutionary principles. Specifically, we show by a mathematical model and simulations that a metacommunity where species can occupy multiple patches, acting together with a realistic (moderate) HGT rate, helps maintain genome diversity. Assuming a scenario of patches dominated by single species, our model predicts that diversity only decreases moderately upon the arrival of a new beneficial gene, and that losses in diversity can be quickly restored. We explore the generic behaviour of diversity as a function of three key parameters, frequency of insertion of new beneficial genes, migration rates and horizontal transfer rates.Our results provides a testable explanation for how diversity can be maintained by gene-specific sweeps even in the absence of high horizontal gene transfer rates.

Bacteria-phage coevolution with a seed bank.

Dormancy is an adaptation to living in fluctuating environments. It allows individuals to enter a reversible state of reduced metabolic activity when challenged by unfavorable conditions. Dormancy can also influence species interactions by providing organisms with a refuge from predators and parasites. Here we test the hypothesis that, by generating a seed bank of protected individuals, dormancy can modify the patterns and processes of antagonistic coevolution. We conducted a factorially designed experiment where we passaged a bacterial host (Bacillus subtilis) and its phage (SPO1) in the presence versus absence of a seed bank consisting of dormant endospores. Owing in part to the inability of phages to attach to spores, seed banks stabilized population dynamics and resulted in minimum host densities that were 30-fold higher compared to bacteria that were unable to engage in dormancy. By supplying a refuge to phage-sensitive strains, we show that seed banks retained phenotypic diversity that was otherwise lost to selection. Dormancy also stored genetic diversity. After characterizing allelic variation with pooled population sequencing, we found that seed banks retained twice as many host genes with mutations, whether phages were present or not. Based on mutational trajectories over the course of the experiment, we demonstrate that seed banks can dampen bacteria-phage coevolution. Not only does dormancy create structure and memory that buffers populations against environmental fluctuations, it also modifies species interactions in ways that can feed back onto the eco-evolutionary dynamics of microbial communities.

Inferring the differences in incubation-period and generation-interval distributions of the Delta and Omicron variants of SARS-CoV-2.

Estimating the differences in the incubation-period, serial-interval, and generation-interval distributions of SARS-CoV-2 variants is critical to understanding their transmission. However, the impact of epidemic dynamics is often neglected in estimating the timing of infection-for example, when an epidemic is growing exponentially, a cohort of infected individuals who developed symptoms at the same time are more likely to have been infected recently. Here, we reanalyze incubation-period and serial-interval data describing transmissions of the Delta and Omicron variants from the Netherlands at the end of December 2021. Previous analysis of the same dataset reported shorter mean observed incubation period (3.2 d vs. 4.4 d) and serial interval (3.5 d vs. 4.1 d) for the Omicron variant, but the number of infections caused by the Delta variant decreased during this period as the number of Omicron infections increased. When we account for growth-rate differences of two variants during the study period, we estimate similar mean incubation periods (3.8 to 4.5 d) for both variants but a shorter mean generation interval for the Omicron variant (3.0 d; 95% CI: 2.7 to 3.2 d) than for the Delta variant (3.8 d; 95% CI: 3.7 to 4.0 d). The differences in estimated generation intervals may be driven by the "network effect"-higher effective transmissibility of the Omicron variant can cause faster susceptible depletion among contact networks, which in turn prevents late transmission (therefore shortening realized generation intervals). Using up-to-date generation-interval distributions is critical to accurately estimating the reproduction advantage of the Omicron variant.

Attitudes towards booster, testing and isolation, and their impact on COVID-19 response in winter 2022/2023 in France, Belgium, and Italy: a cross-sectional survey and modelling study.

Background: European countries are focusing on testing, isolation, and boosting strategies to counter the 2022/2023 winter surge due to SARS-CoV-2 Omicron subvariants. However, widespread pandemic fatigue and limited compliance potentially undermine mitigation efforts. Methods: To establish a baseline for interventions, we ran a multicountry survey to assess respondents' willingness to receive booster vaccination and comply with testing and isolation mandates. Integrating survey and estimated immunity data in a branching process epidemic spreading model, we evaluated the effectiveness and costs of current protocols in France, Belgium, and Italy to manage the winter wave. Findings: The vast majority of survey participants (N = 4594) was willing to adhere to testing (>91%) and rapid isolation (>88%) across the three countries. Pronounced differences emerged in the declared senior adherence to booster vaccination (73% in France, 94% in Belgium, 86% in Italy). Epidemic model results estimate that testing and isolation protocols would confer significant benefit in reducing transmission (17-24% reduction, from R = 1.6 to R = 1.3 in France and Belgium, to R = 1.2 in Italy) with declared adherence. Achieving a mitigating level similar to the French protocol, the Belgian protocol would require 35% fewer tests (from 1 test to 0.65 test per infected person) and avoid the long isolation periods of the Italian protocol (average of 6 days vs. 11). A cost barrier to test would significantly decrease adherence in France and Belgium, undermining protocols' effectiveness. Interpretation: Simpler mandates for isolation may increase awareness and actual compliance, reducing testing costs, without compromising mitigation. High booster vaccination uptake remains key for the control of the winter wave. Funding: The European Commission, ANRS-Maladies Infectieuses Émergentes, the Agence Nationale de la Recherche, the Chaires Blaise Pascal Program of the Île-de-France region.

Intermediate levels of asymptomatic transmission can lead to the highest epidemic fatalities.

Asymptomatic infections have hampered the ability to characterize and prevent the transmission of SARS-CoV-2 throughout the pandemic. Although asymptomatic infections reduce severity at the individual level, they can make population-level outcomes worse if asymptomatic individuals-unaware they are infected-transmit more than symptomatic individuals. Using an epidemic model, we show that intermediate levels of asymptomatic infection lead to the highest levels of epidemic fatalities when the decrease in symptomatic transmission, due either to individual behavior or mitigation efforts, is strong. We generalize this result to include presymptomatic transmission, showing that intermediate levels of nonsymptomatic transmission lead to the highest levels of fatalities. Finally, we extend our framework to illustrate how the intersection of asymptomatic spread and immunity profiles determine epidemic trajectories, including population-level severity, of future variants. In particular, when immunity provides protection against symptoms, but not against infections or deaths, epidemic trajectories can have faster growth rates and higher peaks, leading to more total deaths. Conversely, even modest levels of protection against infection can mitigate the population-level effects of asymptomatic spread.

Epidemic modeling with heterogeneity and social diffusion.

We propose and analyze a family of epidemiological models that extend the classic Susceptible-Infectious-Recovered/Removed (SIR)-like framework to account for dynamic heterogeneity in infection risk. The family of models takes the form of a system of reaction-diffusion equations given populations structured by heterogeneous susceptibility to infection. These models describe the evolution of population-level macroscopic quantities S, I, R as in the classical case coupled with a microscopic variable f, giving the distribution of individual behavior in terms of exposure to contagion in the population of susceptibles. The reaction terms represent the impact of sculpting the distribution of susceptibles by the infection process. The diffusion and drift terms that appear in a Fokker-Planck type equation represent the impact of behavior change both during and in the absence of an epidemic. We first study the mathematical foundations of this system of reaction-diffusion equations and prove a number of its properties. In particular, we show that the system will converge back to the unique equilibrium distribution after an epidemic outbreak. We then derive a simpler system by seeking self-similar solutions to the reaction-diffusion equations in the case of Gaussian profiles. Notably, these self-similar solutions lead to a system of ordinary differential equations including classic SIR-like compartments and a new feature: the average risk level in the remaining susceptible population. We show that the simplified system exhibits a rich dynamical structure during epidemics, including plateaus, shoulders, rebounds and oscillations. Finally, we offer perspectives and caveats on ways that this family of models can help interpret the non-canonical dynamics of emerging infectious diseases, including COVID-19.