The influence of independent jumps on the dynamics of a perturbed SIRS epidemic model with altered behavior

In the realm of infectious disease dynamics, stochasticity and behavioral adaptations play pivotal roles in shaping epidemic outcomes. This paper presents a novel stochastic SIRS (susceptible–infectious–recovered–susceptible) epidemic model that incorporates both behavioral changes among susceptible individuals and jump processes. By integrating dual general incidence functions and a Levy measure to accurately represent independent jump events, our model offers a comprehensive framework for understanding epidemic dynamics in real-world scenarios. We validate the model’s robustness through rigorous analysis of its well-posedness and establish a threshold that distinguishes between epidemic eradication and persistence. Numerical simulations, conducted using estimated parameters for herpes simplex virus type 2, verify the accuracy of this threshold and highlight its practical relevance in epidemic management. This work differs from previous research in Nguyen et al. (J Math Anal Appl 538:128361, 2024) , offering a more comprehensive framework and identifying optimal conditions.