Stability analysis of a Malaria epidemic model transmission dynamics

Résumé

Malaria is a vector-borne disease that has been haunting mankind and still remains a major public health issue. It is caused by the parasites, from the genus Plasmodium, which spread to people through the bite of infected adult female mosquitoes of the Anopheles species. In 2017, an estimated 219 million cases occurred worldwide with children accounting for 61% of deaths.
In this paper, we formulate a mathematical model that reduces malaria transmission dynamics and investigate the basic properties of the model; the disease Free Equilibrium and the basic reproduction number of the model were obtained. The Jacobian matrix stability technique was used to analysed the stability of the disease free equilibrium. The analysis shows that the disease free equilibrium is locally asymptotically stable that is R0 < 1.This discovery indicates that, malaria transmission can
be reduced or eliminated from the population.