Global dynamics of an age-structured cholera model with multiple transmissions, saturation incidence and imperfect vaccination. Issue 1 (1st January 2019)

• Record Type: Journal Article
• Authors: Lin, Jiazhe; Xu, Rui; Tian, Xiaohong
• Is Part Of: Journal of biological dynamics. Volume 13:Issue 1(2019)
• Page Start: 69
• Page End: 102
• Publication Date: 2019-01-01
• Subjects: Cholera model -- age structure -- saturation incidence -- imperfect vaccination -- stability -- optimal control; Biology -- Mathematical models -- Periodicals; 570.15118
• DOI: 10.1080/17513758.2019.1570362
• Languages: English
• ISSNs: 1751-3758

Abstract

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.