Mathematical Approach for Modelling Malaria Disease in the Presence of Drug Therapy and Treatment

Abstract

An S−L−B−I−Q−T epidemic mathematical model incorporating drug therapy and treatment is investigated for malaria disease. We obtained the Disease Free Equilibrium (DFE) points and compute the basic reproduction number (R0). The local and global stability of the Disease Free Equilibrium was analyzed using Jacobian matrix stability techniques and Lyapunov function respectively. The local and global stability was asymptotically stable if R0 < 1 and R0 ≤ 1 respectively. Sensitivity analysis of R0 for drug therapy and treatment showed that R0 is strictly a decreasing function of σ3, θ, ν, τ and p. The numerical simulation of R0 and control parameters of the model were presented graphically. The findings of this study strongly suggest a combination of effective drug therapy and treatment as a crucial strategy to control the malaria disease.