An age-structured vector-borne disease model with horizontal transmission in the host

Xia Wang; Yuming Chen; Xia Wang; Yuming Chen

doi:10.3934/mbe.2018049

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 5: 1099-1116. doi: 10.3934/mbe.2018049

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An age-structured vector-borne disease model with horizontal transmission in the host

Xia Wang ^{1
,
,},
Yuming Chen ²

1.
College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, Henan, China
2.
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada

Received: 04 April 2017 Accepted: 22 March 2018 Published: 01 October 2018
MSC : Primary: 34K20, 92D25; Secondary: 35A24

We concern with a vector-borne disease model with horizontal transmission and infection age in the host population. With the approach of Lyapunov functionals, we establish a threshold dynamics, which is completely determined by the basic reproduction number. Roughly speaking, if the basic reproduction number is less than one then the infection-free equilibrium is globally asymptotically stable while if the basic reproduction number is larger than one then the infected equilibrium attracts all solutions with initial infection. These theoretical results are illustrated with numerical simulations.

Keywords:

Citation: Xia Wang, Yuming Chen. An age-structured vector-borne disease model with horizontal transmission in the host[J]. Mathematical Biosciences and Engineering, 2018, 15(5): 1099-1116. doi: 10.3934/mbe.2018049

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Abstract

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