Transmission Dynamics of Lymphatic Filariasis: A Mathematical Approach

C P Bhunu,S Mushayabasa

doi:10.5402/2012/930130

Abstract

An epidemiological model for the spread of lymphatic filariasis, a mosquito-borne infection, is developed and analysed. The epidemic thresholds known as the reproduction number and equilibria for the model are determined and stabilities analysed. Results from the analysis of the reproduction number suggest that treatment will somehow contribute to a reduction in lymphatic filariasis cases, but what it does not show is the magnitude of the reduction, a part answered by the numerical simulations. Numerical simulations show that even when all lymphatic filariasis cases displaying elephantiasis symptoms are put on treatment it will not be able to eradicate the disease. This result suggests that effective control of lymphatic filariasis may lie in treatment for those displaying symptoms as well as chemoprophylaxis for the exposed.

Highlights

Lymphatic filariasis, a debilitating disease, is one of the most prevalent and yet one of the most neglected tropical diseases with serious economic and social consequences [1, 2]
Increases in the average number of mosquito bites increase RE suggesting an increase in lymphatic filariasis cases. This further suggests that other mechanisms which reduce mosquito bites like spraying, use of mosquito nets, and wearing clothes which cover much of the body may be necessary to control lymphatic filariasis
A mathematical model for the transmission dynamics of lymphatic filariasis with treatment for those displaying elephantiasis symptoms is presented as a system of differential equations

Summary

Introduction

A debilitating disease, is one of the most prevalent and yet one of the most neglected tropical diseases with serious economic and social consequences [1, 2]. It is a mosquito-borne disease caused by tissuedwelling nematodes of Brugia malayi, Brugia timori, and Wuchereria bancrofti species [1, 3] and is estimated to affect about 120 million people worldwide [4,5,6]. Wuchereria bancrofti is responsible for 90% of the cases and is found throughout the tropical and subtropical areas of the world; Brugia malayi is confined to southeast and eastern Asia; Brugia timori is found only in Timor and its adjacent islands [7]. In countries where lymphatic filariasis is well established, the prevalence of infection continues to increase due to unplanned growth of cities and water resource development such as irrigation, which creates numerous breeding sites for the mosquitoes that transmit the disease [12]. Proportion of elephantiasis cases equations to explore if treatment for those symptoms alone will be able to keep the infection under control

Model Description

Numerical Simulations

Findings

Discussion