Dynamical Analysis on A Model of Cholera Epidemic with Quarantine, Vaccination, and Two Path of Transmissions

Abstract

This research focus on dynamical analysis of a SIQRVB (Susceptible-Infectious-Quarantined-Recovered-Vaccinated-Bacterial) model. It describe the spread of cholerae with quarantine, vaccination and two transmission paths. As is well-known, there mainly exist two transmission paths for cholerae: environment-to-human transmission and human-to-human transmission. This model has two equilibrium points, that is disease-free equilibrium point which always exists and an endemic equilibrium point that exists with some conditions. The local stability of the equilibrium points is investigated by using Routh-Hurwitz criteria. The method of Next Generation Matrix is applied to get the basic reproduction number R0 . It can be shown numerically that disease-free equilibrium point is locally asymptotic stable when R0 < 1, while the endemic equilibrium point exist and locally asymptotic stable when satisfy Routh-Hurwitz criteria. Numerical simulations are given to illustrate the theoretical results.