Abstract
<jats:title>ABSTRACT</jats:title> <jats:p>In the face of an epidemic where a population behaviour both influences disease transmission and reacts to it, social processes can generate norms to support socially beneficial behaviour. Most mathematical models of coupled behaviour–disease dynamics treat norms as pre-existing rather than explaining how they are maintained. Here, we investigate whether altruistic punishment can sustain a social distancing norm when individuals may defect, cooperate without punishing, or cooperate while paying a cost to punish defectors. We couple a transmission model to an imitation model for these three strategies. Disease prevalence affects behavioural payoffs, while the behavioural composition modifies transmission. We also compare this coupled system with a control where behavioural decisions respond to a fixed prevalence. We find a wide parameter regime corresponding to the establishment of an injunctive social norm in support of social distancing, where the punisher strategy is widespread. Persistence may occur through stable states where punishers or dominant. Disease–behaviour feedback can also create oscillations (where the three strategies succeed one another in response to epidemic waves) or tipping points (sharp transitions between all-defector and cooperative states). These effects do not occur in the uncoupled model, although there are still broad parameter regimes where a social norm persists. Our findings show that costly peer punishment can support persistence of social norms that mitigate disease transmission. More broadly, endogenous epidemic feedback can qualitatively change the conditions under which cooperation and punishment are sustained, producing tipping points and long-term behavioural–epidemiological cycles that fixed-payoff models cannot capture.</jats:p> <jats:sec> <jats:title>Significance Statement</jats:title> <jats:p>Populations both shape disease transmission and respond to prevalence, allowing social processes to sustain norms. We examine whether altruistic punishment can maintain social distancing where individuals may defect, cooperate, or cooperate while also paying to punish defectors. A transmission model is coupled to imitation dynamics, so disease prevalence and behaviour influence one another. We compare this system with a control based on fixed perceived prevalence. Across broad parameter ranges, punishers persist and support a social distancing norm. Coupled feedback can also generate oscillations, as strategies rise and fall with epidemic waves, and tipping points between defection and cooperation. These features are absent from the uncoupled model. Thus, epidemic feedback can alter how cooperation, punishment, and disease control norms persist.</jats:p> </jats:sec>