Abstract
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 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 ℛ v is greater than one and ℛ0 is less than one then, the disease-free periodic equilibrium is globally attractive. If ℛ v 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.
Highlights
Malaria is a potentially deadly disease caused by protozoan parasites known as Plasmodium, that infect and replicate within human blood cells
The rst subsystem governs the dynamics of vector population and the second subsystem describes the dynamics of malaria virus transmission due to the interaction between vector and human hosts
The model has taken into account the temperature e ects in the vector population dynamics and the intrinsic incubation period in mosquitoes and human hosts is incorporated
Summary
Malaria is a potentially deadly disease caused by protozoan parasites known as Plasmodium, that infect and replicate within human blood cells. It is spread between humans via the bite of the infectious female adult Anopheles mosquito and is one of the greatest infectious diseases to beset mankind. There are ve (previously four) Plasmodium species that commonly infect humans, namely P. falciparum, P. vivax, P. ovale, P. malariae, and very recently, P. knowlesi. In 2019, the World Health Organization’s report revealed that an estimated 200 million people and more than , deaths due to malaria occured worldwide in 2018. Over 90% of all malarial mortality in sub-Saharan Africa is attributable to P. falciparum, where children under ve, pregnant women and non-immune adults are most at risk. Asia, Latin America and to a lesser extent the Middle East of Europe are infected [10, 18, 48]
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