Modeling Pediculosis Transmission with Infection Awareness for Control
A. S. Wunuji *
Department of Mathematics and Statistics, Federal University, Wukari, Taraba State, Nigeria.
D. A. Amayindi
Department of Mathematical Science, Taraba State University, Jalingo, Nigeria.
Joseph Navokhi
Department of Mathematics and Statistics, Taraba State Polytechnic, Jalingo, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this paper, a mathematical model for pediculosis infection was developed and analysed. The model was designed by dividing the system into six compactments leading to a system of ordinary differential equations. The model is built on the assumption that some of those with pediculosis infection are aware of the disease while others are not. Conditions are derived for the positivity of the solution, and the existence of disease free and endemic equilibria. It shows that the disease can be eliminated under certain conditions. The model equation was solved using the homotopy perturbation method and numerical simulation were carried out to investigate the effects of some of the transmission parameters on the dynamics of the infection. The results showed that with effective treatment, pediculosis can be eradicated from a human population.
Keywords: Pediculosis disease, mathematical model, awareness infection, transmission dynamics and homotopy pertbation method (HPM)