Transmission model of endemic human malaria in a partially immune population

A new transmission model of human malaria in a partially immune population with three discrete delays is formulated for variable host and vector populations. These are latent period in the host population, latent period in the vector population and duration of partial immunity. The results of our mathematical analysis indicate that a threshold parameter R0R0 exists. For R0>1R0>1, the expected number of mosquitoes infected from humans RhmRhm should be greater than a certain critical value Rhm∗ or should be less than Rhm∗ when Rhm∗>1, for a stable endemic equilibrium to exist. We deduce from model analysis that an increase in the period within which partial immunity is lost increases the spread of the disease. Numerically we deduce that treatment of the partially immune humans assists in reducing the severity of the disease and that transmission blocking vaccines would be effective in a partially immune population. Numerical simulations support our analytical conclusions and illustrate possible behaviour scenarios of the model.