Global dynamics of a Vector‐Borne disease model with two delays and nonlinear transmission rate |
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| Authors: | Dan Tian Haitao Song |
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| Institution: | 1. Complex Systems Research Center, Shanxi University, Taiyuan, China;2. School of Mathematical Sciences, Shanxi University, Taiyuan, China;3. Laboratory of Mathematical Parallel Systems (LAMPS), Department of Mathematics and Statistics, York University, Toronto, Canada |
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| Abstract: | In this paper, we investigate a Vector‐Borne disease model with nonlinear incidence rate and 2 delays: One is the incubation period in the vectors and the other is the incubation period in the host. Under the biologically motivated assumptions, we show that the global dynamics are completely determined by the basic reproduction number R0. The disease‐free equilibrium is globally asymptotically stable if R0≤1; when R0>1, the system is uniformly persistent, and there exists a unique endemic equilibrium that is globally asymptotically. Numerical simulations are conducted to illustrate the theoretical results. |
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| Keywords: | global stability Lyapunov functional nonlinear transmission rate two delays vector‐host epidemic model |
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