Journal of Advances in Mathematics and Computer Science

A new dynamic model for the malaria disease has been developed for areas where the whole populace is at risk and exposure to the malaria infection is continuous throughout the year.  In this model, the two vulnerable groups that is, infectious people those under 5years and pregnant women have been given separate compartments. The model has two equilibria, that is, disease-free and endemic equilibrium points. The basic reproduction number ( R₀ )for the model has been derived using the next-generation matrix approach. The local stability of two equilibria is investigated using matrix elementary row operations. However, global stability of disease-free equilibrium is investigated using theorem by Castillo-Chavez et.al (2002) and that of the endemic equilibrium is also investigated using Lyapunov’s function. It is proven that disease-free equilibrium is locally asymptotically stable if R₀ < 1 and the endemic equilibrium exists if R₀ > 1.  The endemic equilibrium is locally asymptotically stable when  and   E₁₇E₁₉ > E₁₆E₂₀.  Sensitivity analysis has proved that malaria can be controlled or eliminated if the following parameters such as biting rates, recruitment rate and density-dependent natural mortality rate for mosquitoes and clinical recovery rates for humans are controlled.