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Risk-driven behaviour provides a feedback mechanism through which individuals both shape and are collectively affected by an epidemic. We introduce a general and flexible compartmental model to study the effect of heterogeneity in the population with regard to risk tolerance. The interplay between behaviour and epidemiology leads to a rich set of possible epidemic dynamics. Depending on the behavioural composition of the population, we find that increasing heterogeneity in risk tolerance can either increase or decrease the epidemic size. We find that multiple waves of infection can arise due to the interplay between transmission and behaviour, even without the replenishment of susceptibles. We find that increasing protective mechanisms such as the effectiveness of interventions, the fraction of risk-averse people in the population and the duration of intervention usage reduce the epidemic overshoot. When the protection is pushed past a critical threshold, the epidemic dynamics enter an underdamped regime where the epidemic size exactly equals the herd immunity threshold and overshoot is eliminated. Finally, we can find regimes where epidemic size does not monotonically decrease with a population that becomes increasingly risk-averse. 

COVID-19 infections have underlined that there can be substantial impacts on health after recovery, including elevated mortality. While such post-infection mortality (PIM) is clearly widespread, we do not yet have any understanding of its evolutionary dynamics. To address this gap, we use an eco-evolutionary model to determine conditions where PIM is evolutionarily favoured. Importantly, from a pathogen perspective, there are two potential ‘resources’: never-infected susceptibles and previously infected susceptibles (provided some reinfection is possible), and PIM only occurs in the latter. A key insight is that unlike classic virulence (i.e. during-infection mortality, DIM) PIM is neutral and not selected against in the absence of other trade-offs. However, PIM modulates characteristics of endemicity, and may also vary with other pathogen-specific components. If PIM is only correlated with transmission, recovery or DIM, it simply acts to modulate their impacts on the evolutionary outcome. On the other hand, if PIM trades off with the relative susceptibility to reinfection, there are important evolutionary implications that contrast with DIM. We find settings where a susceptibility–mortality trade-off (i.e. an increase in mortality leads to higher relative susceptibility to reinfection) can select against DIM but favour PIM. This provides a potential explanation for the ubiquity of PIM. Overall, our work illustrates that PIM can readily evolve in certain settings and highlights the importance of considering different sources of mortality. 

The multiple immunity responses exhibited in the population and co-circulating variants documented during pandemics show a high potential to generate diverse long-term epidemiological scenarios. Transmission variability, immune uncertainties and human behaviour are crucial features for the predictability and implementation of effective mitigation strategies. Nonetheless, the effects of individual health incentives on disease dynamics are not well understood. We use a behavioural-immuno-epidemiological model to study the joint evolution of human behaviour and epidemic dynamics for different immunity scenarios. Our results reveal a trade-off between the individuals’ immunity levels and the behavioural responses produced. We find that adaptive human behaviour can avoid dynamical resonance by avoiding large outbreaks, producing subsequent uniform outbreaks. Our forward-looking behaviour model shows an optimal planning horizon that minimizes the epidemic burden by balancing the individual risk–benefit trade-off. We find that adaptive human behaviour can compensate for differential immunity levels, equalizing the epidemic dynamics for scenarios with diverse underlying immunity landscapes. Our model can adequately capture complex empirical behavioural dynamics observed during pandemics. We tested our model for different US states during the COVID-19 pandemic. Finally, we explored extensions of our modelling framework that incorporate the effects of lockdowns, the emergence of a novel variant, prosocial attitudes and pandemic fatigue. 

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

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

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

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

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

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