Abstract
We derived and analyzed rigorously a mathematical model that describes the dynamics of malaria infection with the recruitment of infected immigrants, treatment of infectives and spray of insecticides against mosquitoes in the population. Both qualitative and quantitative analysis of the deterministic model are performed with respect to stability of the disease free and endemic equilibria. It is found that in the absence of infected immigrants disease-free equilibrium is achievable and is locally asymptotically stable. Using Pontryagin's Maximum Principle, the optimal strategies for disease control are established. Finally, numerical simulations are performed to illustrate the analytical results.
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