A Study of Malaria Epidemic Model Using the Effect of Lost Immunity

The model is developed to apply malaria data for both human population (hosts) and vector (mosquito) population. The hosts are divided into four compartments, susceptible S_h (t), infected I_h (t) infectious Z_h (t) and removed R_h (t) at time t and vectors are divided into three compartments susceptible mosquitoes S_m (t), infected mosquitoes I_m (t) and infectious mosquitoes Z_m (t) at time t. Recovered group for mosquitoes is not considered, because mosquitoes are assumed to remain infectious until death. As the model has two different populations (hosts and vectors), the expected basic reproduction number reflects the infection transmitted from human to vector and vice-versa. In the present study, we have considered the effect of lost immunity and the partially recovered rate as a function of infection dependent. We have studied the application of optimal control theory to the model. Numerical illustration of the model is also given.