Mathematical Modelling of the Transmission Dynamics of Malaria Infection with Optimal Control

Abstract

In this study, we formed a mathematical model for the transmission of malaria infection in other to explore the transmission dynamics and optimal control. We considered the S_h , E_h , I_h , R_h , S_v , E_v , I_v  model with optimal control considering the effect of two optimal controls (Use of bed net and Treatment). The positivity and boundedness, reproduction number, stability and optimal control analysis were carried out accordingly. Numerical simulations were done. We further discovered the conditions necessary for the stability of both disease-free equilibrium (DFE) and endemic equilibrium. The DFE is asymptotically stable. Also, the endemic equilibrium is stable. The numerical simulation also shows the effective use of bed net and Treatment on the curve. Finally, we deduce that the use of bed nets and treatment over a long period can eventually help to flatten the curve of infection. However, this control intervention has no significant impact on the mosquito population.