Global dynamic behavior of a multigroup cholera model with indirect transmission

Abstract

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 0 is identified and global dynamics are completely determined by 0. It shows that 0 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. © 2013 Ming-Tao Li et al.