Global Dynamic Behavior of a Multigroup Cholera Model with Indirect Transmission - Ming-Tao Li; Gui-Quan Sun; Juan Zhang; Zhen Jin (Discrete Dynamics in Nature and Society)
For a multigroup cholera model with indirect transmission, the infection for a susceptible person is almost invariably transmitted by drinking contaminated water in which pathogens, V. cholerae, are present. The basic reproduction number ℛ0 is identified and global dynamics are completely determined by ℛ0. It shows that ℛ0 is a globally threshold parameter in the sense that if it is less than one, the disease-free equilibrium is globally asymptotically stable; whereas if it is larger than one, there is a unique endemic equilibrium which is global asymptotically stable. For the proof of global stability with the disease-free equilibrium, we use the comparison principle; and for the endemic equilibrium we use the classical method of Lyapunov function and the graph-theoretic approach.