A Mathematical Modelling of the Effect of Treatment in the Control of Malaria in a Population with Infected Immigrants

Abstract

In this work, we developed a compartmental bio-mathematical model to study the effect of treatment in the control of malaria in a population with infected immigrants. In particular, the vector-host population model consists of eleven variables, for which graphical profiles were provided to depict their individual variations with time. This was possible with the help of MathCAD software which implements the Runge-Kutta numerical algorithm to solve numerically the eleven differential equations representing the vector-host malaria population model. We computed the basic reproduction ratio R 0 following the next generation matrix. This procedure converts a system of ordinary differential equations of a model of infectious disease dynamics to an operator that translates from one generation of infectious individuals to the next. We obtained R 0 = , i.e ., the square root of the product of the basic reproduction ratios for the mosquito and human populations respectively. R 0m explains the number of humans that one mosquito can infect through contact during the life time it survives as infectious. R 0h on the other hand describes the number of mosquitoes that are infected through contacts with the infectious human during infectious period. Sensitivity analysis was performed for the parameters of the model to help us know which parameters in particular have high impact on the disease transmission, in other words on the basic reproduction ratio R 0 .