Mathematical modeling and optimal control strategy for a discrete-time cholera model

Abstract

This paper aims to develop and investigate the optimal combination of control interventions for a discrete mathematical cholera model. The population is divided into four compartments: susceptible individuals, symptomatic infected individuals, individuals undergoing treatment, and recovered individuals. The objective is to identify the most effective strategy for minimizing the incidence of cholera cases, susceptible individuals, and symptomatic infected individuals. Three specific control strategies are being considered: the implementation of awareness programs through media and educational channels, the prevention of contact through security campaigns, and the implementation of specific interventions such as sanitation and water treatment. The environmental control strategy aims to reduce the environmental burden of cholera bacteria and minimize the risk of infection through specific interventions. Pontryagin’s maximum principle in discrete time characterizes the optimal control strategy. Numerical simulations using MATLAB are conducted to demonstrate the effectiveness of the optimization strategy.