Backward bifurcation and sensitivity analysis of a malaria transmission dynamics model taking into account the role of male mosquitoes
Résumé
This paper introduces a malaria transmission model that incorporates the often -overlooked role of male mosquitoes in the dynamics of the infection. Derived from a coupled vector and malaria transmission framework, the model yields a mosquito reproduction threshold noted R m and we demonstrate that the trivial equilibrium is globally asymptotically stable when R m ≤ 1 and the non-trivial equilibrium is globally asymptotically stable if R > 1. Additionally, we derive an expression of the basic reproduction number R 0 and explore the conditions of the existence of endemic equilibria. Our analysis reveals scenarios of backward bifurcation, where a locally stable disease-free equilibrium coexists with an endemic equilibrium. We also establish conditions for the global stability of the disease-free equilibrium and analyze the global stability of the endemic equilibrium when R 0 > 1. A sensitivity analysis and numerical simulations are performed to identify the most influential model parameters and to illustrate the theoretical findings.
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