A mathematical model to describe the transmission of malaria has been formulated to better understand the behaviour of the disease. We constructed a system of nonlinear ordinary differential equations for both the human host and mosquito vector. In the beginning, susceptible humans acquire the disease when they are bitten by an infectious mosquito. Thus, they move into the exposed class and then the infectious, and followed by the recovered class. The model takes into account two possibilities: one is where some infectious humans do not gain any immunity and the other, who have temporary immunity and will return to being susceptible after the immunity fades off. Susceptible mosquitoes are infected when they bite infectious or recovered humans. After which, they will move into the exposed class and then the infectious class. However, mosquitoes do not recover as they remain infectious their whole lifetime. Both host and vector populations follow a logistic population model to avoid the increase of population without bound.  Numerical simulations of this model are presented and it is found that if the average duration of recovery from infectious to susceptible is small enough then the disease can be eradicated from the population. Our analytical theory supports this finding. Steady state equilibrium points allow the Basic Reproduction Number, R0 , to be procured. There are two equilibrium points which are without disease, namely the mosquito-free equilibrium and the disease-free equilibrium. When the Basic Reproduction Number, R0 < 1, the disease-free equilibrium is locally asymptotically stable and otherwise when R0 > 1. Equilibrium points from numerical results are checked with equilibrium equations theoretically and found to be in good agreement.