Global Dynamic Behavior of a Multigroup Cholera Model with Indirect Transmission

For a multigroup cholera model with indirect transmission, the infection fora susceptible person is almost invariably transmitted by drinking contaminatedwater in which pathogens, V. cholerae, are present. The basic reproductionnumber 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 lessthan one, the disease-free equilibrium is globally asymptotically stable; whereasif it is larger than one, there is a unique endemic equilibrium which is globalasymptotically stable. For the proof of global stability with the disease-freeequilibrium, we use the comparison principle; and for the endemic equilibriumwe use the classical method of Lyapunov function and the graph-theoretic approach