Mathematical model of Malaria Transmission with Three Optimal Controls Applied to Democratic Republic of the Congo
In this paper, we studied the effect of the specific incidence function for the appearance of backward bifurcation in malaria transmission model with standard incidence rate. The stability analysis of disease-free equilibrium (DFE) was investigated, the basic reproduction number R0, was obtained using the next generation matrix technique, the existence of the endemic equilibrium was also investigated and the existence of feasible region where the model is well-known shows that the model exhibits the backward bifurcation phenomenon when R0 < 1 and the global stability of the endemic equilibrium has been proved. Furthermore, we applied the model to exiting data of the Democratic Republic of the Congo (DRC) to fit some parameters. In addition to that, we formulated an optimal control problem with an objective function, with three controls, the preventive using Long-Lasting Insecticide Treated Net (LLITN) , the treatment with drug of infected individuals and the insecticide spray on the breeds grounds for the mosquitoes , has been used as control measures for infected individuals. Numerical simulations that were carried out to support our analytic results also suggest that, two control strategies and together are more effective than other controls in controlling the number of infected individuals in the DRC. Reducing the number of infected individuals and increasing the number of recovered humans with reduce the disease transmission.
