Development and analysis of a malaria transmission mathematical model with seasonal mosquito life-history traits |
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Authors: | Ramsés Djidjou-Demasse Gbenga J. Abiodun Abiodun M. Adeola Joel O. Botai |
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Affiliation: | 1. MIVEGEC, IRD, CNRS, University of Montpellier, Montpellier, France;2. Department of Mathematics, Southern Methodist University, Dallas, Texas, USA;3. South African Weather Service, Pretoria, South Africa Institute for Sustainable Malaria Control, University of Pretoria, Pretoria, South Africa;4. South African Weather Service, Pretoria, South Africa Department of Geography, Geoinformation and Meteorology, University of Pretoria, Hatfield, South Africa |
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Abstract: | In this paper, we develop and analyze a malaria model with seasonality of mosquito life-history traits: periodic-mosquitoes per capita birth rate, -mosquitoes death rate, -probability of mosquito to human disease transmission, -probability of human to mosquito disease transmission, and -mosquitoes biting rate. All these parameters are assumed to be time dependent leading to a nonautonomous differential equation system. We provide a global analysis of the model depending on two threshold parameters and (with ). When , then the disease-free stationary state is locally asymptotically stable. In the presence of the human disease-induced mortality, the global stability of the disease-free stationary state is guarantied when . On the contrary, if , the disease persists in the host population in the long term and the model admits at least one positive periodic solution. Moreover, by a numerical simulation, we show that a sub-critical (backward) bifurcation is possible at . Finally, the simulation results are in accordance with the seasonal variation of the reported cases of a malaria-epidemic region in Mpumalanga province in South Africa. |
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Keywords: | basic reproduction number global stability periodic solution seasonal pattern uniform persistence |
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