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Analysis of a dengue disease transmission model. (English) Zbl 0930.92020
Summary: A model for the transmission of dengue fever in a constant human population and variable vector population is discussed. A complete global analysis is given, which uses the results of the theory of competitive systems and stability of periodic orbits, to establish the global stability of the endemic equilibrium. The control measures of the vector population are discussed in terms of the threshold condition, which governs the existence and stability of the endemic equilibrium.

MSC:
92D30 Epidemiology
37N25 Dynamical systems in biology
34D23 Global stability of solutions to ordinary differential equations
37C75 Stability theory for smooth dynamical systems
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