%0 Journal Article
%9 ACL : Articles dans des revues avec comité de lecture répertoriées par l'AERES
%A Djidjou-Demasse, Ramsès
%A Abiodun, G. J.
%A Adeola, A. M.
%A Botai, J. O.
%T Development and analysis of a malaria transmission mathematical model with seasonal mosquito life-history traits
%D 2019
%L fdi:010077771
%G ENG
%J Studies in Applied Mathematics
%@ 0022-2526
%K basic reproduction number ; global stability ; periodic solution ; seasonal ; pattern ; uniform persistence
%M ISI:000504698600001
%P [23 ]
%R 10.1111/sapm.12296
%U https://www.documentation.ird.fr/hor/fdi:010077771
%> https://www.documentation.ird.fr/intranet/publi/2020/01/010077771.pdf
%V [Early Access]
%W Horizon (IRD)
%X 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 R0 and R over bar 0<1 (with R0 <= R over bar 0). When R0<1, 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 R over bar 0<1. On the contrary, if R0>1, 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 R0=1. 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.
%$ 020