DYNAMIC BEHAVIOR OF A DELAY CHOLERA MODEL WITH CONSTANT INFECTIOUS PERIOD

Xue-yong Zhou; Xiang-yun Shi; Jing-an Cui

doi:10.11948/20190006

2020 Volume 10 Issue 2

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Xue-yong Zhou, Xiang-yun Shi, Jing-an Cui. DYNAMIC BEHAVIOR OF A DELAY CHOLERA MODEL WITH CONSTANT INFECTIOUS PERIOD[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 598-623. doi: 10.11948/20190006

Citation:

Xue-yong Zhou, Xiang-yun Shi, Jing-an Cui. DYNAMIC BEHAVIOR OF A DELAY CHOLERA MODEL WITH CONSTANT INFECTIOUS PERIOD[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 598-623. doi: 10.11948/20190006

DYNAMIC BEHAVIOR OF A DELAY CHOLERA MODEL WITH CONSTANT INFECTIOUS PERIOD

1.
School of Mathematics and Statistics, Xinyang Normal University, No. 237 Nanhu Road, 464000 Xinyang, China
2.
School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, China

Corresponding author: Email address:xueyongzhou@xynu.edu.cn(X. Zhou)
Fund Project: This work is supported by the National Natural Science Foundation of China (No. 11701495), Scientific and Technological Key Projects of Henan Province (No. 192102310193) and Nanhu Scholars Program for Young Scholars of XYNU

Abstract

Abstract

In this paper, a delay cholera model with constant infectious period is investigated. By analyzing the characteristic equations, the local stability of a disease-free equilibrium and an endemic equilibrium of the model is established. It is proved that if the basic reproductive number $ \mathcal{R}_0>1 $, the system is permanent. If $ \mathcal{R}_0<1 $, by means of an iteration technique, sufficient conditions are obtained for the global asymptotic stability of the disease-free equilibrium. If $ \mathcal{R}_0>1 $, also by means of an iteration technique, sufficient conditions are obtained for the global asymptotic stability of the endemic equilibrium. Numerical simulations are carried out to illustrate the main theoretical results.
- Cholera model /
- permanence /
- stability /
- delay
MSC: 92B05

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References

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