Mathematical model for the control of lymphatic filariasis transmission dynamics

Festus Abiodun Oguntolu, Gbolahan Bolarin, Olumuyiwa James Peter, Abdullah Idris Enagi, Kayode Oshinubi

Abstract


In this paper, a mathematical model for the transmission dynamics of lymphatic filariasis is presented by incorporating the infected without symptom, the infected with symptom and treatment compartments. The model is shown to have two equilibrium states: the disease-free equilibrium (DFE) and the endemic equilibrium states. An explicit formula for the effective reproduction number was obtained in terms of the demographic and epidemiological parameters of the model. Using the method of linearization, the disease-free equilibrium state was found to be locally asymptotically stable if the basic reproduction number is less than unity.  By constructing a suitable Lyapunov function, the disease-free equilibrium state was found to be globally asymptotically stable. This means that lymphatic filariasis could be put under control in a population when the effective reproduction number is less than one. The endemic equilibrium state was found to be locally asymptotically stable. By constructing yet another Lyapunov function, the endemic equilibrium state was found to be globally asymptotically stable under certain conditions. Sensitivity analysis was carried out on the effective reproduction number, the most sensitive parameters were the treatment rate of human population and the infected rate of human population. Results from the simulation carried out showed that treatment level coverage of human population should target a success rate of 75% for LF to be under control in the population.


Full Text: PDF

Published: 2021-02-23

How to Cite this Article:

Festus Abiodun Oguntolu, Gbolahan Bolarin, Olumuyiwa James Peter, Abdullah Idris Enagi, Kayode Oshinubi, Mathematical model for the control of lymphatic filariasis transmission dynamics, Commun. Math. Biol. Neurosci., 2021 (2021), Article ID 17

Copyright © 2021 Festus Abiodun Oguntolu, Gbolahan Bolarin, Olumuyiwa James Peter, Abdullah Idris Enagi, Kayode Oshinubi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Commun. Math. Biol. Neurosci.

ISSN 2052-2541

Editorial Office: office@scik.org

 

Copyright ©2021 CMBN