Optimal Control with Treatment and Water Sanitation for Cholera Epidemic Model

Abstract

This paper proposes a mathematical model for cholera using optimal control of treatment through quarantine and water sanitation. Cholera is acute diarrhoea caused by Vibrio cholera bacteria infecting the intestinal tract. The analysis related to the spread of this disease is carried out through a mathematical approach. The constructed mathematical model is demonstrated epidemiologically. The proposed optimal control is the treatment of infected individuals during the quarantine period and sanitation, namely environmental hygiene, especially water. This strategy aims to suppress the number of infected individuals and reduce the concentration of bacteria due to cholera disease. To solve the optimal control problem, we employ the 4th-order forward-backward Runge-Kutta method. Based on the simulation results, the number of individuals infected by cholera and the concentration of bacteria decreased significantly. Moreover, the proposed method can transfer infected to recovered individuals faster than an optimal control treatment.