Stationary distribution and extinction of a stochastic staged progression AIDS model with staged treatment and second-order perturbation

Bingtao Han, Daqing Jiang, Tasawar Hayat, Ahmed Alsaedi and Bashir Ahmad

Chaos, Solitons & Fractals, 2020, vol. 140, issue C

Abstract: Focusing on deterministic AIDS model proposed by Hyman (2000) and the detailed data from the World Health Organization (WHO), there are three stages of AIDS process which are described as Acute infection period, Asymptomatic phase and AIDS stage. Our paper is therefore concerned with a stochastic staged progression AIDS model with staged treatment. In view of the complexity of random disturbances, we reasonably take second-order perturbation into consideration for realistic sense. By means of our creative transformation technique and stochastic Lyapunov method, a critical value R0H>1 is firstly obtained for the existence and uniqueness of ergodic stationary distribution to the stochastic system. Not only does it respectively reveal the corresponding dynamical effects of the linear and second-order perturbations to the model, but the unified form of second-order and linear fluctuations is derived. Next, some sufficient conditions about extinction of stochastic system are established in view of the basic reproduction number R0. Finally, some examples and numerical simulations are introduced to illustrate our analytical results. In addition, some advantages of our new method and theory are highlighted by comparison with other existing results at the end of this paper.

Keywords: Stochastic staged progression AIDS model; Staged treatment; Second-order perturbation; Ergodic stationary distribution; Extinction (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920306342

DOI: 10.1016/j.chaos.2020.110238

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