Stationary distribution and extinction of a stochastic HIV/AIDS model with nonlinear incidence rate

Helong Liu; Xinyu Song; Helong Liu; Xinyu Song

doi:10.3934/mbe.2024072

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 1: 1650-1671. doi: 10.3934/mbe.2024072

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Stationary distribution and extinction of a stochastic HIV/AIDS model with nonlinear incidence rate

Helong Liu ^{1
,
,},
Xinyu Song ²

1.
School of Mathematics and Statistics, Xinyang College, Xinyang 464000, China
2.
School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China

Academic Editor: Shengqiang Zhang

Received: 11 September 2023 Revised: 19 November 2023 Accepted: 03 December 2023 Published: 02 January 2024

This paper studies a stochastic HIV/AIDS model with nonlinear incidence rate. In the model, the infection rate coefficient and the natural death rates are affected by white noise, and infected people are affected by an intervention strategy. We derive the conditions of extinction and permanence for the stochastic HIV/AIDS model, that is, if $ R_0^s < 1, $ HIV/AIDS will die out with probability one and the distribution of the susceptible converges weakly to a boundary distribution; if $ R_0^s > 1 $, HIV/AIDS will be persistent almost surely and there exists a unique stationary distribution. The conclusions are verified by numerical simulation.
- stochastic HIV/AIDS model,
- nonlinear incidence rate,
- ergodicity,
- extinction,
- stationary distribution
Citation: Helong Liu, Xinyu Song. Stationary distribution and extinction of a stochastic HIV/AIDS model with nonlinear incidence rate[J]. Mathematical Biosciences and Engineering, 2024, 21(1): 1650-1671. doi: 10.3934/mbe.2024072

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Abstract

This paper studies a stochastic HIV/AIDS model with nonlinear incidence rate. In the model, the infection rate coefficient and the natural death rates are affected by white noise, and infected people are affected by an intervention strategy. We derive the conditions of extinction and permanence for the stochastic HIV/AIDS model, that is, if $ R_0^s < 1, $ HIV/AIDS will die out with probability one and the distribution of the susceptible converges weakly to a boundary distribution; if $ R_0^s > 1 $, HIV/AIDS will be persistent almost surely and there exists a unique stationary distribution. The conclusions are verified by numerical simulation.

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