Exploring threshold dynamics of a behavioral epidemic model featuring two susceptible classes and second-order jump–diffusion

Understanding and modeling behavioral changes during epidemic outbreaks is crucial for devising effective public health interventions. In this paper, we introduce an enhanced behavioral epidemic model that integrates novel elements to better capture real-world phenomena. Our model incorporates logistic growth as a recruitment rate, reflecting the population’s intrinsic growth constraints. Additionally, we consider two incidence rates to account for varying transmission dynamics. To extend the model’s applicability, we introduce perturbations through second-order jump–diffusion processes, allowing for abrupt changes in population dynamics. We define a threshold parameter based on the properties of an auxiliary system, which distinguishes between the existence of a unique stationary distribution and stochastic extinction. Through numerical simulations, we validate our theoretical findings and demonstrate the impact of nonlinear noise on the model dynamical behavior.