Global stability of an age-structure epidemic model with imperfect vaccination and relapse

Bin Cao, Hai-Feng Huo and Hong Xiang

Physica A: Statistical Mechanics and its Applications, 2017, vol. 486, issue C, 638-655

Abstract: A new age-structured epidemic model with imperfect vaccination and relapse is proposed. The total population of our model is partitioned into five subclasses: susceptible class S, vaccinated class V, exposed class E, infectious class I and removed class R. Age-structures are equipped with in exposed and recovered classes. Furthermore, imperfect vaccination is also introduced in our model. The basic reproduction number R0 is defined and proved as a threshold parameter of the model. Asymptotic smoothness of solutions and uniform persistence of the system are showed via reformulating the system as a system of Volterra integral equation. Furthermore, by constructing proper Volterra-type Lyapunov functional we get when R0<1, the disease-free equilibrium is globally asymptotically stable. When R0>1, the endemic equilibrium is globally stable. Our results show that to increase the efficiency of vaccination and reduce influence of relapse are vital essential for controlling epidemic.

Keywords: Epidemic; Age-structure; Stability; Vaccination; Relapse (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:486:y:2017:i:c:p:638-655

DOI: 10.1016/j.physa.2017.05.056

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