GLOBAL DYNAMICS OF A CHOLERA MODEL WITH AGE-OF-IMMUNITY STRUCTURE AND REINFECTION

Liming Cai; Jinliang Liu; Gaoxu Fan; Huidong Chen

doi:10.11948/20180311

2019 Volume 9 Issue 5

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Liming Cai, Jinliang Liu, Gaoxu Fan, Huidong Chen. GLOBAL DYNAMICS OF A CHOLERA MODEL WITH AGE-OF-IMMUNITY STRUCTURE AND REINFECTION[J]. Journal of Applied Analysis & Computation, 2019, 9(5): 1731-1749. doi: 10.11948/20180311

Citation:

Liming Cai, Jinliang Liu, Gaoxu Fan, Huidong Chen. GLOBAL DYNAMICS OF A CHOLERA MODEL WITH AGE-OF-IMMUNITY STRUCTURE AND REINFECTION[J]. Journal of Applied Analysis & Computation, 2019, 9(5): 1731-1749. doi: 10.11948/20180311

GLOBAL DYNAMICS OF A CHOLERA MODEL WITH AGE-OF-IMMUNITY STRUCTURE AND REINFECTION

1.
College of Mathematics and statistics, Xinyang Normal University, Xinyang 464000, China
2.
College of Mathematics and Information Science, Henan Normal University Xinxiang 453007, China
3.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266000, China

Corresponding author: Email address:limingcai@amss.ac.cn(L. Cai)
Fund Project: This research was supported partially the National Nature Science Foundation of China grant (11871415, 11371305) and Nanhu Scholars Program for Young Scholars XYNU

Abstract

Abstract

To understand Vibrio cholerae transmission dynamics, in this paper, a mathematical model for the dynamics of cholera with reinfection is formulated, where we incorporate the duration time of the recovery individuals (age-of-immunity). The basic reproduction number $\Re_0$ for the proposed model is identified and the threshold property of $\Re_0$ is established. By applying the persistence theory for infinite-dimensional systems, we show that the disease is uniformly persistent if the basic reproductive number $\Re_0>1$. By constructing suitable Lyapunov functions, the global stability of the infection-free equilibrium in the system is obtained for $\Re_0<1$; the unique endemic equilibrium of the system is globally asymptotically stable for $\Re_0>1$.
- Cholera model /
- duration time of immunity /
- Lyapunov functional /
- global stability
MSC: 92D30, 35B35, 35Q92

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References

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