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.

In the present research paper, deterministic and the corresponding stochastic mathematical models describing the dynamics of cholera epidemic are presented by incorporating vaccination. The total population size of the model is divided into five compartments namely Susceptible , Vaccinated, Infected, Quarantined for treatment and Recovered class. Initially, the cholera model is developed, and is determined by a deterministic approach. Since this deterministic approach is not considering either environmental factors or the randomness process of the dynamics, a corresponding stochastic approach has been introduced. The model equations of both deterministic and stochastic cases have been proved to be positive and also bounded. Furthermore, for both the models, mathematical formulations of the basic reproduction numbers are developed by employing the next generation matrix method. The analysis shows that the basic reproduction number for determinis-tic approach is much greater than that for the stochastic one. Finally, numerical simulations are also performed. The simulation study has revealed that combination of a decrease in contact between infected and susceptible individuals, increasing vaccination coverage, creating awareness to reduce contact rate, increasing recovery rate with proper treatment, and environmental sanitation are the most basic control strategies so as to eliminate cholera disease from the community.