Dynamical behavior, extinction and persistence in a stochastic delayed two-strain epidemic model with a generalized Crowley-Martin incidence rate

Source abstract

This paper develops and analyzes a novel delayed stochastic SIR epidemic model with two interacting strains and general incidence functions. By establishing the existence and uniqueness of a positive global solution, the well-posedness of the model under stochastic perturbations is ensured. Extinction occurs when the stochastic reproduction number falls below unity, as demonstrated through Itô calculus and martingale convergence theorems, while persistence is guaranteed under the Crowley–Martin incidence when it exceeds one. Numerical experiments based on the Positive Preserving Truncated Euler–Maruyama (PPTEM) scheme confirm the analytical predictions and highlight the influence of time delay and noise intensity on the long-term behavior of the epidemic. The proposed framework extends classical stochastic epidemic theory by integrating multi-strain interactions, delay effects, and general incidence mechanisms within a unified stochastic setting.