Research ArticleNo Access

Ergodic stationary distribution of two stochastic tuberculosis models with imperfect vaccination and early and late latency

Qian Jiang

School of Mathematics and Statistics, Hubei Minzu University, Enshi, Hubei, 445000, P. R. China

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Zhijun Liu

https://orcid.org/0000-0003-3383-5621

School of Mathematics and Statistics, Hubei Minzu University, Enshi, Hubei, 445000, P. R. China

E-mail Address: zjliu@hbmzu.edu.cn

E-mail Address: zhijun_liu47@hotmail.com

Corresponding author.

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https://doi.org/10.1142/S1793524522501121Cited by:0 (Source: Crossref)

Abstract

This contribution probes into ergodic stationary distribution for two stochastic SVELIT (susceptible-vaccinated-early latent-late latent-infective-treated) tuberculosis (TB) models to observe the impact of white noises and color noises on TB control in random environments. We first investigate the existence and uniqueness of ergodic stationary distribution (EUESD) for the autonomous SVELIT model subject to white noises via the proper Lyapunov functions, and sufficient conditions on the extinction of disease are acquired. Next, sufficient conditions for the EUESD and the extinction of disease for the SVELIT model with Markov switching are also established. Eventually, some numerical examples validate the theoretical findings. What’s more, it has been observed that higher amplitude noises may lead to the eradication of TB, which is conducive to TB control.

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