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 ($R_{0} $). 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 $R_{0} <1$ and $R_{0} \le 1$ respectively. Sensitivity analysis of $R_{0} $ for drug therapy and treatment showed that $R_{0} $ is strictly a decreasing function of $\sigma _{3} ,\theta ,\nu ,\tau $ and $p$. The numerical simulation of $R_{0} $ 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.