Nonlinear Dynamical Systems for Malaria Transmission andControl: Ross-Macdonald Model

Abstract

Malaria was declared an emergency in Nigeria and strategies for the control of Malaria in Nigeria were adopted to reduce its prevalence to a level at which the disease will no longer constitute public health problems. In this work, we presented a deterministic (Ross–Macdonald model susceptible, expose/ infected, infectious and recovered) model incorporating the method of control adopted by national Malaria and leprosy control program. We established the disease free and the endemic equilibrium states and carried out the stability analysis of the disease. Free and the equilibrium state. We also carried out numerical simulation of the model to have an insight into the dynamics of the model. We found out that the disease free equilibrium state is stable. The feedback dynamics from mosquito to human and back to mosquito involve considerable time due to the incubation periods of the parasites. In this paper, taking explicit account of the incubation periods of parasites within the human and the mosquito, we first propose a Ross–Macdonald model. The Jacobiant results showed that it would be very difficult to completely eradicate Malaria from Nigeria using the method adopted by national Malaria and leprosy control program.