Development and analysis of a malaria transmission mathematical model with seasonal mosquito life‐history traits

• Published in: Studies in applied mathematics (Cambridge) Vol. 144; no. 4; pp. 389 - 411
• Main Authors: Djidjou‐Demasse, Ramsés, Abiodun, Gbenga J., Adeola, Abiodun M., Botai, Joel O.
• Format: Journal Article
• Language: English
• Published: Cambridge Blackwell Publishing Ltd 01.05.2020; Wiley-Blackwell
• Subjects: basic reproduction number; Bifurcations; Computer simulation; Differential equations; Disease control; Disease transmission; Dynamical Systems; Functional Analysis; global stability; Malaria; Mathematical models; Mathematics; Mosquitoes; Parameters; periodic solution; seasonal pattern; Seasonal variations; Time dependence; uniform persistence; periodic solution; uniform persistence; global stability; seasonal pattern; basic reproduction number
• ISSN: 0022-2526; 1467-9590
• DOI: 10.1111/sapm.12296

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¯0<1 (with R0≤R¯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¯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.