
Mathematical Biosciences and Engineering, 2018, 15(5): 10991116. doi: 10.3934/mbe.2018049.
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An agestructured vectorborne disease model with horizontal transmission in the host
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: , Accepted: , Published:
We concern with a vectorborne 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 infectionfree 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: Vectorborne disease; infection age; global stability; global attractor; Lyapunov functional
Citation: Xia Wang, Yuming Chen. An agestructured vectorborne disease model with horizontal transmission in the host. Mathematical Biosciences and Engineering, 2018, 15(5): 10991116. doi: 10.3934/mbe.2018049
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