Applied Mathematics & Information Sciences

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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 the deterministic approach is much greater than that for the stochastic one. Finally, numerical simulations are also performed. The simulation study has revealed that a 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.

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