A global mathematical model of malaria transmission dynamics with structured mosquito population and temperature variations. (June 2020) - Traoré, Bakary; Koutou, Ousmane; Sangaré, Boureima
Abstract: In this paper, a mathematical model of malaria transmission which takes into account the four distinct mosquito metamorphic stages is presented. The model is formulated thanks to the coupling of two sub-models, namely the model of mosquito population and the model of malaria parasite transmission due to the interaction between mosquitoes and humans. Moreover, considering that climate factors have a great impact on the mosquito life cycle and parasite survival in mosquitoes, we incorporate seasonality in the model by considering some parameters which are periodic functions. Through a rigorous analysis via theories and methods of dynamical systems, we prove that the global behavior of the model depends strongly on two biological insightful quantities : the vector reproduction ratio R v and the basic reproduction ratio R 0 . Indeed, if R v < 1, mosquitoes and malaria die out; if R v > 1 and R 0 < 1, the disease-free periodic equilibrium is globally attractive; and if R v > 1 and R 0 > 1 the disease remains persistent. Finally, using the reported monthly mean temperature of Burkina Faso, we perform some numerical simulations to illustrate our theoretical results.