A global mathematical model of malaria transmission dynamics with structured mosquito population and temperature variations

• Published in: Nonlinear analysis: real world applications Vol. 53; p. 103081
• Main Authors: Traoré, Bakary, Koutou, Ousmane, Sangaré, Boureima
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.06.2020; Elsevier BV; Elsevier
• Subjects: Basic reproduction ratio; Computer simulation; Global stability; Malaria; Malaria transmission; Mathematical models; Mathematics; Mosquito population; Mosquitoes; Periodic functions; Reproduction (biology); Temperature variations; Vector reproduction ratio; Malaria transmission; Global stability; Vector reproduction ratio; Temperature variations; Basic reproduction ratio; Mosquito population
• ISSN: 1468-1218; 1878-5719
• DOI: 10.1016/j.nonrwa.2019.103081

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 Rv and the basic reproduction ratio R0. Indeed, if Rv<1, mosquitoes and malaria die out; if Rv>1 and R0<1, the disease-free periodic equilibrium is globally attractive; and if Rv>1 and R0>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.