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A new intra-host model of malaria that describes the dynamics of the blood stages of the parasite and its interaction with red blood cells and immune effectors is proposed. Local and global stability of the disease free equilibrium are investigated. Conditions for existence and uniqueness of the endemic equilibrium are derived. An intra-host basic reproductive number is identified. We deduce that drugs based on inhibiting parasite production are more effective than those based on inhibiting merozoite invasion of erythrocytes. We extend the model to incorporate, in addition to immune response, drug therapy, following treatment with antimalarial drugs. Using stability analysis of the model, it is shown that infection can be eradicated within the host if the drug efficacy level exceeds a certain threshold value. It will persist if the efficacy is below this threshold. Numerical simulations are done to verify the analytic results and illustrate possible behaviour of the models.