Global dynamics of a dengue epidemic mathematical model.

*(English)*Zbl 1198.34075Summary: 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.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

##### 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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\textit{L. Cai} et al., Chaos Solitons Fractals 42, No. 4, 2297--2304 (2009; Zbl 1198.34075)

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