MATHEMATICAL MODELLING FOR THE TRANSMISSION DYNAMICS OF LYMPHATIC FILARIASIS AND MALARIA CO-INFECTION

Abstract

ABSTRACT In this research, a mathematical model for the transmission dynamics of Lymphatic Filariasis and Malaria co-infection in the presence of treatment was formulated, using Bed net, insecticide and chemoprevention as control. It was assumed that the susceptible individual and vector can get infected with Malaria, lymphatic filariasis and co-infection when there is an interaction with any of the five infectious classes: acute stage or chronic stage of Lymphatic filariasis, malaria, both Lymphatic filariasis and malaria co-infected individuals and the infected vectors. The basic reproductive number was obtained using the next generation matrix approach. The Jacobian stability technique and CastilloChavez method were used to establish the Local and global stabilities of the Disease free equilibrium state respectively. The stability analysis showed that the Lyphatic filariasis and Malaria co-infection can be eradicated from the entire population when Rc ≤ 1 but will continue to persevere within the population when Rc > 1. The model was solved analytically using Adomian decomposition method, the stability analysis was verified with graphs using Maple 15. The result showed that use of bednet and insecticides have significant impact on the Susceptible, infected malaria and the vector compartments, but treatment have effect on the infected human compartments. It is therefore recommended that every susceptible individual get and make use of bednet and insecticide always. Those who are acutely and chronically infected with Filariasis should get early medical attention.