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


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Authors

  • E. Azuaba Department of Mathematics, Bingham University Karu, Nassarawa State, Nigeria
  • J. M. Orverem Department of Mathematical Sciences, Federal University Dutsinma, Katsina State, Nigeria
  • Y. M. Kura Department of Mathematics, Federal Polytechnic Nassarawa, Nassaraw State, Nigeria
  • U. Jnr. Dahiru Department of Mathematics, Federal Polytechnic Nassarawa, Nassaraw State, Nigeria

Keywords:

Malaria disease, Drug therapy, Treatment, Sensitivity, Stability

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.

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Published

15-03-2020

How to Cite

E. Azuaba, J. M. Orverem, Y. M. Kura, & U. Jnr. Dahiru. (2020). Mathematical Approach for Modelling Malaria Disease in the Presence of Drug Therapy and Treatment. International Journal of Mathematics And Its Applications, 8(1), 77–88. Retrieved from http://ijmaa.in/index.php/ijmaa/article/view/177

Issue

Section

Research Article