A temperature-dependent mathematical model of malaria transmission with stage-structured mosquito population dynamics

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 ℛv and the basic reproduction ratio ℛ0. 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 ℛv is greater than one and ℛ0 is less than one then, the disease-free periodic equilibrium is globally attractive. If ℛv is greater than one and ℛ0 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.

Keywords

• malaria
• basic reproduction ratio
• vector reproduction ratio
• persistence
• global stability
• periodic solution
• 34d20
• 34d23
• 34d45
• 37c75