Stochastic dual epidemic hypothesis model with Ornstein-Uhlenbeck process: Analysis and numerical simulations with SARS-CoV-2 variants

Abstract

As it is widely known, the spread of infectious diseases can result in significant socioeconomic consequences and pose a threat to public health. However, biologically plausible models that incorporate stochastic interference and dual epidemic hypotheses have received limited attention. This paper aims to bridge this gap by examining a stochastic dual epidemic hypothesis model that incorporates Ornstein-Uhlenbeck processes to perturb the nonlinear incidence rate. We provide a rigorous analysis of the model, first proving the existence and uniqueness of global solution. We also analyze sufficient conditions for the extinction or persistence of each disease. Additionally, we establish the existence of an ergodic stationary distribution and derive expressions for the normal distribution followed by the global solution around the endemic equilibrium. Finally, using several numerical experimental examples, we validate our theoretical results with the case of dual variants of SARS-CoV-2 that can simultaneously infect humans. This paper contributes to the understanding of stochastic dual epidemic hypotheses and provides a foundation for future research in this field.