Analysis of a stochastic HIV-1 infection model with degenerate diffusion

Tao Feng, Zhipeng Qiu, Xinzhu Meng and Libin Rong

Applied Mathematics and Computation, 2019, vol. 348, issue C, 437-455

Abstract: This paper studies a stochastic HIV-1 infection model with degenerate diffusion. The asymptotic dynamics of the stochastic model are shown to be governed by a threshold parameter. When the parameter is negative, the infection is predicted to go extinct exponentially while the level of healthy cells converges weakly to a unique invariant measure. When the threshold parameter is positive, the solution of the stochastic model converges polynomially to a unique invariant probability measure, indicating that the system admits a unique ergodic stationary distribution. Numerical simulations are conducted to show the analytical results. These results highlight the role of environmental noise in the spread of HIV-1. The method can also be applied to the non-degenerate systems.

Keywords: Stochastic stability; HIV-1 infection model; Ergodicity; Polynomial convergence rate; Cell-to-cell spread; Invariant measure (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:348:y:2019:i:c:p:437-455

DOI: 10.1016/j.amc.2018.12.007

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