Dynamics of a stochastic SICA epidemic model for HIV transmission with higher-order perturbation

Abstract

In this paper, we propose and study a higher order stochastically perturbed SICA epidemic model for HIV transmission. We obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the system by establishing a series of suitable Lyapunov functions. In a biological point of view, the existence of a stationary distribution indicates that the infectious disease will be prevalent and persistent in the population. Moreover, we make up adequate conditions for complete eradication and wiping out of the infectious disease.

Keywords:

• SICA epidemic model
• HIV infection
• Stationary distribution
• Ergodicity
• Extinction

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (No.12001090) and the Fundamental Research Funds for the Central Universities of China (No.2412020QD024).