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Global dynamics of a dengue epidemic mathematical model. (English) Zbl 1198.34075
Summary: The paper investigates the global stability of a dengue epidemic model with saturation and bilinear incidence. The constant human recruitment rate and exponential natural death, as well as vector population with asymptotically constant population, are incorporated into the model. The model exhibits two equilibria, namely, the disease-free equilibrium and the endemic equilibrium. The stability of these two equilibria is controlled by the threshold number $$\mathfrak R_0$$. It is shown that if $$\mathfrak R_0$$ is less than one, the disease-free equilibrium is globally asymptotically stable and in such a case the endemic equilibrium does not exist; if $$\mathfrak R_0$$ is greater than one, then the disease persists and the unique endemic equilibrium is globally asymptotically stable.
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##### MSC:
 34C60 Qualitative investigation and simulation of ordinary differential equation models 92D30 Epidemiology 34D23 Global stability of solutions to ordinary differential equations
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##### References:
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