Stochastic modeling and analysis of SIRS epidemic model with a general incidence: case study on COVID-19

We consider a general-incidence SIRS epidemic model with stochastic dynamics in this paper. The general incidence function, as opposed to traditional methods, takes a more global picture of the dynamics that occur in the real world, such as the change in behavior and the saturation effect during transmission.

On the one hand, through Lyapunov analysis, we determine the existence and uniqueness of a global positive solution, that is, the consistency in the behavior of the system over time. On the other hand, we also obtain a stochastic threshold, an extension of the basic reproduction number, which provides a good condition at which the infection will be expected to fade away.

In order to supplement the theory, we perform numerical simulations. These not only confirm our findings in the analysis but also enable us to answer the question of how the model reacts to variations in important variables such as vaccination rates, incidence functions and noise levels. This assists in determining the real cause of disease dynamics. This flexibility allows the model to readily adjust to a variety of situations and be adjusted using actual data. In the end, this work provides a feasible and versatile instrument for predicting the trends in epidemics and analyzing the effectiveness of control measures in an unpredictable world.