Mathematical modeling of the effects of public health education on tungiasis—a neglected disease with many challenges in endemic communities

Abstract

In this paper, we formulate and study a mathematical model for the dynamics of jigger infestation incorporating public health education using systems of ordinary differential equations and computational simulations. The basic reproduction number $R_{E}$ is obtained and used to determine whether the disease breaks out in the population and results in an endemic equilibrium or dies out eventually corresponding to a disease-free equilibrium. We carried out an analysis of the model and established the conditions for the local and global stabilities of the disease-free and endemic equilibria points. Using the Lyapunov stability theory and LaSalle invariant principle, we found out that the disease-endemic equilibrium point is globally asymptotically stable if $R_{E}>1$ and unstable otherwise. Numerical simulations are performed to illustrate our theoretical predictions. Both the analytical and numerical results show public health education is a very effective control measure in eradicating jigger infestation in the endemic communities at large.