A temperature-dependent mathematical model of malaria transmission with stage-structured mosquito population dynamics
- Nonautonomous Dynamical Systems , 8 : 267-296
Résumé
Abstract In this paper, we formulate a temperature-dependent model for malaria transmission dynamics which includes immature stages of mosquitoes. The model is constructed by using ordinary differential equations with some parameters which are periodic functions. Two thresholds dynamics associated to the model have been derived: the vector reproduction ratio ℛ v and the basic reproduction ratio ℛ 0 . Through a rigorous analysis via theories and methods of dynamical systems, we prove that the global behavior of the model depends strongly on these two parameters. More precisely, we show that if ℛ v is greater than one and ℛ 0 is less than one then, the disease-free periodic equilibrium is globally attractive. If ℛ v is greater than one and ℛ 0 is greater than one, the disease remains persistent and the system admits at least one positive periodic solution. Finally, using the reported monthly mean temperature for Burkina Faso, numerical simulations are carried out to illustrate our mathematical results.
Mots-clés
malaria transmission, mosquito population dynamics, stage-structured population model, temperature dependence, periodic coefficients, basic reproduction number, disease-free equilibrium, global attractivity, disease persistence, positive periodic solutions, ordinary differential equations, Malaria basic reproduction ratio vector reproduction ratio persistence global stability periodic solution MSC 34D20 34D23 34D45 37C75, Malaria, Basic reproduction ratio, Vector reproduction ratio, Persistence, Global stability, Periodic solution MSC 34D20, 34D23, 34D45, 37C75