Dynamical Study in Fuzzy Threshold Dynamics of a Cholera Epidemic Model

Abstract

In this paper, a fuzzy mathematical model on cholera disease has been developed in which all parameters related to the disease have been considered as fuzzy numbers. Here, total human population is divided into three subpopulations such as susceptible persons, infected ones and recovered ones. Also, the bacterial population is the Vibrio Cholerae in the environment. Then the existence condition and boundedness of solution to our proposed mathematical model have been discussed. Also, the different equilibrium points and the stability condition of the system around these equilibrium points have been analyzed. The global stability condition of the proposed system around the endemic equilibrium point has been also discussed. Finally, some numerical simulations have been shown to test the theoretical results of the system.