SIS epidemics coupled with evolutionary social distancing dynamics

Keith Paarporn, Ceyhun Eksin

Abstract: A major factor contributing to the difficulties in epidemic forecasting is the unpredictable nature of the population behavior that can either mitigate or exacerbate the spread of a disease. In this paper, we consider a game-theoretic framework for modeling the disease prevalence dependent response of the population behavior in a susceptible-infected-susceptible (SIS) epidemiological model. Our behavioral response model is based on replicator dynamics, where the individuals’ underlying payoffs dynamically change in response to the prevalence of the disease. The coupled dynamics highlight the interplay between the epidemic state and distancing behaviors. We establish a critical threshold on the incentive parameters for which below the threshold, the state in which the disease is endemic and the population does not cooperate with the recommended public health measures is globally asymptotically stable (GAS). Above the threshold, we find through extensive numerical simulations that a variety of dynamical outcomes emerge. For some parameters, an interior equilibrium in which the endemic state is mitigated and a fraction of the population socially distancing is stable. For other parameters, a stable limit cycle about this interior state emerges. The arising rich set of dynamics demonstrate the potential of the modeling framework for epidemic forecasting.

External IDs:dblp:conf/amcc/PaarpornE23