We study the interplay between epidemic dynamics and human decision making for epidemics that involve reinfection risk; in particular, the susceptible-infected-susceptible (SIS) and the susceptible-infected-recovered-infected (SIRI) epidemic models. In the proposed game-theoretic setting, individuals choose whether to adopt protection or not based on the trade-off between the cost of adopting protection and the risk of infection; the latter depends on the current prevalence of the epidemic and the fraction of individuals who adopt protection in the entire population. We define the coupled epidemic-behavioral dynamics by modeling the evolution of individual protection adoption behavior according to the replicator dynamics. For the SIS epidemic, we fully characterize the equilibria and their stability properties. We further analyze the coupled dynamics under timescale separation when individual behavior evolves faster than the epidemic, and characterize the equilibria of the resulting discontinuous hybrid dynamical system for both SIS and SIRI models. Numerical results illustrate how the coupled dynamics exhibits oscillatory behavior and convergence to sliding mode solutions under suitable parameter regimes.

翻译：我们研究了涉及再感染风险的流行病动力学与人类决策之间的相互作用；具体而言，考虑了易感-感染-易感（SIS）和易感-感染-康复-感染（SIRI）流行病模型。在所提出的博弈论框架中，个体根据采取防护措施的成本与感染风险之间的权衡，选择是否采取防护；后者取决于当前疫情的流行程度以及整个种群中采取防护措施的个体比例。我们通过根据复制动力学建模个体防护采纳行为的演化，定义了耦合的流行病-行为动力学。对于SIS流行病，我们完整刻画了其均衡点及稳定性性质。我们进一步分析了在个体行为演化快于流行病演化（时间尺度分离）情况下的耦合动力学，并刻画了SIS和SIRI模型下所得不连续混合动力系统的均衡点。数值结果展示了在适当参数条件下，耦合动力学如何表现出振荡行为并收敛至滑模解。