A note on fractional-order model for cholera disease transmission with control strategies

Abstract

In this paper, we formulated and analyzed a fractional-order model for cholera disease transmission that consists of human population and surrounding environment. Three control strategies namely: health education campaigns, hygiene practices, and treatment of infected individuals are investigated. We divided the human population into three sub-classes namely: Susceptible, infected and recovered classes. The main assumptions on the disease transmission were that susceptible humans acquire the disease through contact with either infected humans or directly from environment. Mathematical analysis of the model was carried out and the threshold quantity R0 which determine the existence of the disease in the population was determined. The model analysis showed that the disease exist in the population whenever R₀ > 1 and dies wherever R₀ ≤ 1. It was also noted that both the disease-free and endemic equilibria are globally stable. Further more, we performed the numerical simulations of the model and the results showed that the order of derivatives have the influence on spread of cholera disease in the population. It was also noted that both the aforementioned control strategies have the potential to minimize the spread of cholera in the community.