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| Threshold Dynamics of a Time-periodic Reaction-Diffusion Malaria Model with Distributed Latencies |
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| KeyWord:Incubation period the basic reproduction number periodic solution distributed latency uniform persistence |
| Author Name | Affiliation | | Haoyu Wang | School of Information Science & Engineering, Lanzhou University, Lanzhou, Gansu 730000, China | | A-yun Zhang | School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China
Department of Basic Teaching and Research, Qinghai University, Xining, Qinghai 810000, China | | Zhicheng Wang | School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China |
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| Abstract: |
| It is well-known that the transmission of malaria is caused by the bites of mosquitoes. Since the life habit of mosquitoes is influenced by seasonal factors such as temperature, humidity and rainfall, the transmission of malaria presents clear seasonable changes. In this paper, in order to take into account the incubation periods in humans and mosquitoes, we study the threshold dynamics of two periodic reaction-diffusion malaria models with distributed delay in terms of the basic reproduction number. Firstly, the basic reproduction number R0 is introduced by virtue of the next generation operator method and the Poincar ́e mapping of a linear system. Secondly, the threshold dynamics is established in terms of R0. It is proved that if R0 < 1, then the disease-free periodic solution of the model is globally asymptotically stable; and if R0 > 1, then the disease is persistent. |
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