Malaria is one of infectious diseases and has become the most public health issue especially in developing countries. Mathematically, the spread of malaria can be modeled to predict the dynamics of the outbreak of the disease. The present research studies the impact of migration of susceptible population on the dynamics of malaria transmission. In this paper an improved mathematical model is constructed based on a set of reasonable assumptions. Validity of the model is proved by verifying positivity of the solution. Mathematical analysis is carried out including equilibrium point analysis. Basic reproduction number of the model is determined so as to study the effect of migration parameter on the malaria outbreak. It has been observed that the migration parameter is directly proportional to the malaria outbreak. Hence, it is suggested that in order to keep the malaria outbreak under control, the migration parameter is required to be minimized. That is, migration of populations is recommended to reduce so as to reduce the impact of malaria outbreak.

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In this study, we propose and analyze a determinastic nonlinear system of ordinary differential equation model for endemic malaria disease transmission and optimal combinations of control strategies with cost effective analysis. Basic properties of the model, existence of disease-free and endemic equilibrium points, and basic reproduction number of the model are derived and analyzed. From this analysis, we conclude that if the basic reproduction number is less than unity, then the disease-free equilibrium point is both locally and globally asymptotically stable. The endemic equilibrium will also exist if the basic reproduction number is greater than unity. Moreover, existence and necessary condition for forward bifurcation is derived and established. Furthermore, optimal combinations of time-dependent control measures are incorporated to the model. By using Pontryagin’s maximum principal theory, we derived the necessary conditions of optimal control. Numerical simulations were conducted to confirm our analytical results. Our findings were that malaria disease may be controlled well with strict application of the combination of prevention of drug resistance, insecticide-treated net (ITN), indoor residual spray (IRS), and active treatment. The use of a combination of insecticide-treated net, indoor residual spray, and active treatment is the most optimal cost-effective and efficacious strategy.

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