Dynamical Analysis of Peptic Ulcer Disease Model in Nigeria with the Effect of Vaccination and Treatment Program

Abstract

The study developed a non-linear deterministic mathematical model to investigate the transmission dynamics of peptic ulcer disease in human population by considering both direct and indirect contact transmission with vaccine and treatment as control. In developing the model, the population was compartmentalized into susceptible-vaccinated-exposed-infected-treated-helicobacter pylori concentration in the environment recovered. The model developed is a system of differential equations. The rate of change of the system, existence and uniqueness of solution, region of absolute stability and positivity of the solution was established. Existence of disease-free equilibrium state and basic reproduction number was also established. Mathematical analysis was determined by the basic reproduction number if , the disease-free equilibrium is locally asymptotically stable whereas if then the equilibrium is unstable whereas the numerical analysis for the estimated basic reproduction number of the model is greater than unity in perspective of Nigeria, for which the Herd Immunity Threshold indicated that vaccinating 99.47% of Nigeria population can control spreading of Peptic ulcer disease in the country. The paper recommended amongst other things that if significant changes concerning the issue of threshold target are observed to improve the rate at which peptic ulcer can be minimized from the population where Government and non-governmental organization should encourage the use of peptic ulcer drugs and vaccines among individuals.