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Global dynamics of a Vector‐Borne disease model with two delays and nonlinear transmission rate
Author(s) -
Tian Dan,
Song Haitao
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4464
Subject(s) - mathematics , basic reproduction number , nonlinear system , stability theory , equilibrium point , incubation period , transmission (telecommunications) , dynamics (music) , incubation , control theory (sociology) , mathematical analysis , computer science , biology , demography , control (management) , population , physics , biochemistry , telecommunications , quantum mechanics , artificial intelligence , sociology , acoustics , differential equation
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 R 0 . The disease‐free equilibrium is globally asymptotically stable if R 0 ≤1; when R 0 >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.