Global analysis of a stochastic TB model with vaccination and treatment

Tao Feng; Zhipeng Qiu

doi:10.3934/dcdsb.2018292

Article Contents

2019, Volume 24, Issue 6: 2923-2939. Doi: 10.3934/dcdsb.2018292

This issue Previous Article Dynamical behaviors of stochastic type K monotone Lotka-Volterra systems Next Article Polynomial maps with hidden complex dynamics

Global analysis of a stochastic TB model with vaccination and treatment

Tao Feng and
Zhipeng Qiu^,

School of Science, Nanjing University of Science and Technology, Nanjing 210094, China

* Corresponding author: Zhipeng Qiu
* Corresponding author: Zhipeng Qiu

Received: August 31, 2017

Revised: January 31, 2018

Early access: October 2018

Published: June 2019

Z. Qiu is supported by the National Natural Science Foundation of China (NSFC) grant No. 11671206, T. Feng is supported by the Scholarship Foundation of China Scholarship Council grant No. 201806840120, the Postgraduate Research & Practice Innovation Program of Jiangsu Province grant No. KYCX18 0370 and the Fundamental Research Funds for the Central Universities grant No. 30918011339

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Abstract

In this paper, a stochastic model is formulated to describe the transmission dynamics of tuberculosis. The model incorporates vaccination and treatment in the intervention strategies. Firstly, sufficient conditions for persistence in mean and extinction of tuberculosis are provided. In addition, sufficient conditions are obtained for the existence of stationary distribution and ergodicity. Moreover, numerical simulations are given to illustrate these analytical results. The theoretical and numerical results show that large environmental disturbances can suppress the spread of tuberculosis.

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Mathematics Subject Classification: Primary: 92B05, 92D30; Secondary: 60H10.

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Figure 1. Transfer diagram of the ODE TB model

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Figure 2. Trajectory of the solution of system (2) and its corresponding deterministic model (1)

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Figure 3. Trajectory of the solution of system (2) and its corresponding deterministic model (1)

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Figure 4. The pictures on the left are trajectories of the solution of system (2). The pictures on the right are the distribution density functions of system (2)

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