Effect of behavior change pattern on disease transmission dynamics

A general modeling framework is proposed to investigate the effect of behavior change on disease transmission dynamics. Specifically, based on the classic SIS model, we considered two different behavioral patterns: the first pattern (Model I) characterizes behavior change through an imitation process, where individuals exclusively adopt the behavior associated with higher payoff, while the second one (Model II) assumes that the switching pattern of behavior change only relies on the fraction of individuals currently intending to change their decisions, leading to a non-smooth co-evolution model. We initially investigated the global dynamics of the first model in terms of the basic reproduction number R0 and demonstrated that the unique disease-free equilibrium is globally asymptotically stable if R0<1 and two endemic equilibria are globally asymptotically stable under different conditions, respectively. Then for the non-smooth model, the dynamics of two subsystems, the nature of equilibria and the global properties were examined. Furthermore, we numerically explored the effectiveness of human behavior change on the disease transmission. Compared to the classic SIS model, we observed that a lower prevalence threshold or a faster rate of behavior change leads to a more pronounced reduction in both daily infections and peak prevalence, with earlier epidemic peak. Interestingly, Model II exhibits a lower daily infection fraction and a reduced epidemic peak compared to Model I. Our results reveal that adopting the second behavioral pattern is more effective in reducing disease prevalence, thereby explaining the free-rider effect. Also, behavior change does not necessarily lead to oscillations, which is related to the modeling approach of epidemics.