Optimal Combinations of Control Strategies for Dynamics of Endemic Malaria Disease Transmission

In this study, a non-linear system of ordinary differential equation model that describe the dynamics of malaria disease transmission is derived and analyzed. Conditions are derived from the existence of disease-free and endemic equilibria. Basic reproduction number R0 of the model is obtained, and we investigated that it is the threshold parameter between the extinction and persistence of the disease. If R0 is less than unity, then the disease-free equilibrium point is both locally and globally asymptotically stable resulting in the disease removing out of the host populations. The disease can persist whenever R0 is greater than unity. At R0 is equal to unity, existence conditions are derived from the endemic equilibrium for both forward and backward bifurcations. Furthermore, optimal combinations of time dependent control measures are incorporated to the model, and we derived the necessary conditions of the optimal control using Pontryagins’s maximum principal theory. Numerical simulations were conducted using MATLAB software to confirm our analytical results. Our findings were that malaria disease may be controlled more with strict application of the combination of all control measures that is, the combination of prevention of drug resistance, insecticide treated net ITN, indoor residual spray IRS and active treatment than when the combination of three control measures are used.