TRANSMISSION DYNAMICS OF CHOLERA MODEL WITH CONTROL MEASURES

Abstract

Cholera is an infectious intestinal disease that occurs as a result of poor sanitation and lack of basic education in its transmission. It is characterized by profuse vomiting and severe diarrhea when an individual eats food or drinks water contaminated with the Vibrio cholerae. In this present work, a dynamic mathematical model that explicitly simulates the transmission mechanism of cholera by considering the role of control measures and the environment in transmitting the disease is developed. The model comprises two populations: the human population and the bacteria population and the number of awareness programs driven by disease prevalence and media coverage. The nextgeneration method is used to compute the basic reproduction number, 0 . Moreover, the sensitivity indices of each parameter with respect to 0 of the model are computed. To show the impact of the model parameters, the model equations were solved over a specific time period using the Homotopy Perturbation Method. Necessary conditions of the optimal control problem were analysed using Pontryagin’s maximum principle with control measures such as awareness campaigns, vaccination of susceptible individuals, treatment of infected individuals and treatment of water bodies used to optimize the objective function. The results revealed that both the Disease-Free and Endemic Equilibria are shown to be locally and globally stable for values less than unity and unstable otherwise. The model simulations confirm the significant role played by control measures (education, vaccination, therapeutic treatment and treatment of water bodies) and the bacteria in the environment in the transmission dynamics as well as reducing the spread of cholera. The optimal control results revealed that the best strategy for controlling cholera is the application of all control measures and this is attained when 0.08. The research also affirmed that the worst-case scenario occurs when there is no any control strategy for the epidemic. This research revealed that the effective reproduction number c 0

0

c 0 tends to zero