Abstract:
This article suggested and analyzed the transmission dynamics of malaria disease in a population using
a nonlinear mathematical model. The deterministic compartmental model was examined using stability theory
of differential equations. The reproduction number was obtained to be asymptotically stable conditions for the
disease-free, and the endemic equilibria were determined. Moreso, the qualitatively evaluated model incorporates
time-dependent variable controls which was aimed at reducing the proliferation of malaria disease. The optimal
control problem was formulated using Pontryagin’s maximum principle, and three control strategies: disease prevention
through bed nets, treatment and insecticides were incorporated. The optimality system was stimulated
using an iterative technique of forward-backward Runge-Kutta fourth order scheme, so that the impacts of the control
strategies on the infected individuals in the population can be determined. The possible influence of exploring
a single control, the combination of two, and the three controls on the spread of the disease was also investigated.
Numerical simulation was carried out and pertinent findings are displayed graphically.
