An Enhanced Mathematical Model Of The Effect Of Treatment In the Control Of Malaria In A Population With Infected Immigrants

ABSTRACT

In this work we modified a mathematical model to study the dynamics of the vector-host disease. In the enhanced model, we obtained seven classes from human population which includes the susceptible, infected, exposed, treated, non-treated, recovered, and protected classes. For the mosquito population, we have four classes, namely; class of mosquito larva, susceptible mosquitoes, infected mosquitoes and exposed mosquitoes. We assume free interaction between the vector and host populations. The mathematical analysis of the compartmental models leads us to eleven coupled systems of nonlinear ordinary differential equations. We calculated the basic reproduction  of the model. We discussed the equilibrium analysis of the model including stability analysis. We also conducted sensitivity analysis of the parameters of the model using the method of next generation matrix. From the result, we discovered that some parameters have negative values example k₁=-0.25 k₂-0.15 while some have positive values. For instance =+0.5 and =+0.5, this means that increasing or decreasing any of them by 10%increases or decreases  by 10%

We also provided a graphical profile of each of the variables involved in the compartmental model.