On the Transmission Dynamics of Malaria with Three Control Strategies

Abstract

In this paper, we proposed a non-linear model with three strategies for the control of malaria transmission between the human and the vectors. The model incorporated insecticide treated bed nets, treatment of infected human and the indoor residual spray as the control strategies. The disease-free equilibrium of the model and stability conditions were obtained. We derived the basic
reproduction number for the model using next generation matrix approach. The Routh Hurwitz criterion has been applied where we carried out the local and global stabilities of the disease-free equilibrium. However, the results show that the disease-free equilibrium is locally and globally asymptotically stable when R_o< 1 and unstable when R_o>1. We carried out numerical simulations using Runge-Kutta of order four and the results revealed that the disease could be curtailed when the three control strategies are adequately implemented