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Threshold dynamics of a malaria transmission model in periodic environment. (English) Zbl 1274.92050
Summary: In this paper, we propose a malaria transmission model with periodic environment. The basic reproduction number \(R_{0}\) is computed for the model and it is shown that the disease-free periodic solution of the model is globally asymptotically stable when \(R_{0}<1\), that is, the disease goes extinct when \(R_{0}<1\), while the disease is uniformly persistent and there is at least one positive periodic solution when \(R_{0}>1\). It indicates that \(R_{0}\) is the threshold value determining the extinction and the uniform persistence of the disease. Finally, some examples are given to illustrate the main theoretical results. The numerical simulations show that, when the disease is uniformly persistent, different dynamic behaviors may be found in this model, such as the global attractivity and the chaotic attractor.

MSC:
92D30 Epidemiology
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