Dynamics of a Stochastic COVID-19 Epidemic Model with Jump-Diffusion

TL;DR

This paper analyzes a stochastic COVID-19 epidemic model with jump-diffusion, proving solution properties, identifying thresholds for disease extinction or persistence, and demonstrating how stochastic noises influence outbreak dynamics through numerical simulations.

Contribution

It introduces a stochastic COVID-19 model with jump-diffusion, establishes existence and uniqueness of solutions, and analyzes how noise impacts disease extinction and persistence thresholds.

Findings

Stochastic noises significantly affect COVID-19 outbreak dynamics.

The threshold $\xi$ determines disease extinction or persistence.

Numerical simulations confirm noise can suppress outbreaks.

Abstract

For a stochastic COVID-19 model with jump-diffusion, we prove the existence and uniqueness of the global positive solution. We also investigate some conditions for the extinction and persistence of the disease. We calculate the threshold of the stochastic epidemic system which determines the extinction or permanence of the disease at different intensities of the stochastic noises. This threshold is denoted by $\xi$ which depends on the white and jump noises. The effects of these noises on the dynamics of the model are studied. The numerical experiments show that the random perturbation introduced in the stochastic model suppresses disease outbreaks as compared to its deterministic counterpart. In other words, the impact of the noises on the extinction and persistence is high. When the noise is large or small, our numerical findings show that the COVID-19 vanishes from the population if $\xi <1;$ whereas the epidemic can't go out of control if $\xi >1.$ From this, we observe that white noise and jump noise have a significant effect on the spread of COVID-19 infection, i.e., we can conclude that the stochastic model is more realistic than the deterministic one. Finally, to illustrate this phenomenon, we put some numerical simulations.