Dynamics of a stochastic multigroup S-DI-A model for the transmission of HIV

ABSTRACT

This paper is concerned with a stochastic multigroup S-DI-A model for the transmission of HIV with general incidence rate. We obtain sufficient criteria for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model by constructing a proper stochastic Lyapunov function. The stationary distribution implies that the diseases will be persistent in the long term. Some numerical simulations are introduced to illustrate our theoretical result.

Keywords:

• Multigroup HIV model
• general incidence rate
• stationary distribution
• ergodicity

2010 Mathematics Subject Classifications:

• 60H10
• 92B05

Acknowledgments

This work is supported by the National Natural Science Foundation of China (No.11871473) and Shandong Provincial Natural Science Foundation (No.ZR2019MA010).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 11871473] and Shandong Provincial Natural Science Foundation [grant number ZR2019MA010].