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J Biol Dyn. 2019 Dec;13(1):69-102. doi: 10.1080/17513758.2019.1570362.

Global dynamics of an age-structured cholera model with multiple transmissions, saturation incidence and imperfect vaccination.

Lin J1, Xu R2,3, Tian X2,3.

Author information

1
a Institute of Applied Mathematics , Army Engineering University , Shijiazhuang , People's Republic of China.
2
b Complex Systems Research Center , Shanxi University , Taiyuan , People's Republic of China.
3
c Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention , Shanxi University , Taiyuan , People's Republic of China.

Abstract

In this paper, an age-structured cholera model with multiple transmissions, saturation incidence and imperfect vaccination is proposed. In the model, we consider both the infection age of infected individuals and the biological age of Vibrio cholerae in the aquatic environment. Asymptotic smoothness is verified as a necessary argument. By analysing the characteristic equations, the local stability of disease-free and endemic steady states is established. By using Lyapunov functionals and LaSalle's invariance principle, it is proved that the global dynamics of the model can be completely determined by basic reproduction number. The study of optimal control helps us seek cost-effective solutions of time-dependent vaccination strategy against cholera outbreaks. Numerical simulations are carried out to illustrate the corresponding theoretical results.

KEYWORDS:

Cholera model; age structure; imperfect vaccination; optimal control; saturation incidence; stability

PMID:
30696390
DOI:
10.1080/17513758.2019.1570362
[Indexed for MEDLINE]

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