Mathematical Modeling On The Transmission Dynamics And Control Of Malaria With Treatment Within A Population
Omale David
Department of Mathematical Sciences, Faculty of Natural Science, Kogi State University Anyigba.
Omale Joe Peter
Department of Mathematical Sciences, Faculty of Natural Science, Kogi State University Anyigba.
Atokolo William
Department of Mathematical Sciences, Faculty of Natural Science, Kogi State University Anyigba.
Keywords: Mathematical Modelling, Disease-Free Equilibrium, Basic Reproduction Number, Endemic Equilibrium Point, Sensitivity Analysis
Abstract
This paper investigates the transmission of malaria and attempts to control the disease using mathematical model. In this research, we analyse the dynamics of malaria using a system of nine differential equations. The analysis carried out reveals that if the basic reproduction number Ro<l, the disease free equilibrium point is stable, but if Ro>l, the disease free equilibrium is unstable. We conclude from the analysis that there is no endemic equilibrium and malaria – free society is feasible. Our analysis also reveals that certain control strategies are capable of reducing malaria transmission. These are: sufficient treatment of infected people with drugs; spraying of insecticides and the use of insecticide-treated bed nets; destruction of mosquito breeding sites and campaign strategy for malaria control