Optimal Control and Cost-Effectiveness Analysis of Cholera with Vaccination

Abstract

Cholera has been a major global public health problem that is caused due to unsafe water and improper sanitation. These causes have been mainly occurring among the developing country. In this paper, a deterministic model for cholera is formulated with the inclusion of drug resistance compartment. Also, vaccination of newly born babies is considered so as to study its effect on the control. The total population in the present model is divided into five compartments, namely, susceptible, vaccinated newborns, infected, drug resistance, and recovered. The model is mathematically formulated resulting in a system of five ordinary differential equations. In order to verify that the model is valid, it is shown that the solution of the system of equations exists and is both positive and bounded. Fundamental properties of the model such as the basic reproduction number are calculated by employing the method of next-generation matrix. Also, the equilibrium points are identified and their stability analysis is checked. Further in this work, Pontryagin's maximum principle is employed so as to determine the optimal control strategies of the epidemic. The simulation study has revealed that the application of prevention methods will play a significant role in controlling or minimizing the spread of the disease. From the simulated graphs, we observed that an increment in vaccinated population leads to the reduction of the number of infectious population. Moreover, it is shown that if all the intervention strategies are employed together, then the disease will get eradicated within a short span of time. Also, the analysis of cost-effectiveness is conducted. Finally, the simulated values of optimal controls show that the combination of prevention, education, and treatment of individuals with drug resistance is the most efficient and less costly so as to eradicate disease from the community.