Dynamical Behavior of a Malaria relapse Model with Insecticide Treated Nets (ITNs) as Protection Measure

Authors

Reuben I. Gweryina, Federal University of Agriculture
Anande R. Kimbir, Federal University of Agriculture

Abstract

Malaria is a tropical disease which is mainly spread by plasmodium falciparum which has been the principal enemy to the existence of mankind till date. In this paper a version of a malaria model incorporating the use of treated mosquito nets as a disease control strategy is proposed and then transformed into proportions, so as to assess the global impact of ITNs on the prevalence of malaria. Constructing a Lyapunov function using matrix-theoretic approach, a malaria-free equilibrium state is obtained, which is globally asymptotically stable if the control reproduction number, 𝑅_𝑚<1. This means that malaria can be controlled or eradicated under such a threshold quantity, 𝑅𝑚. On the other hand, a malaria-persistence equilibrium state exists which is globally stable when 𝑅_𝑚>1, using geometric theoretic method with Lozoskii measure. Numerical experiments also indicate that prevalence of infection can be driven to zero provided that the proportion of susceptible humans using treated mosquito nets is above a certain threshold value.

Recommended Citation

Gweryina, Reuben I. and Kimbir, Anande R. (2020). Dynamical Behavior of a Malaria relapse Model with Insecticide Treated Nets (ITNs) as Protection Measure, Applications and Applied Mathematics: An International Journal (AAM), Vol. 15, Iss. 1, Article 9.
Available at: https://digitalcommons.pvamu.edu/aam/vol15/iss1/9