Mathematical analysis of a cholera model with vaccination

We consider a svr-b cholera model with imperfect vaccination. by analyzing the corresponding characteristic equations,the local stability of a disease-free equilibrium and an endemic equilibrium is established. we calculate the certain threshold known as the control reproduction number v. if v < 1,we obtain sufficient conditions for the global asymptotic stability of the disease-free equilibrium; the diseases will be eliminated from the community. by comparison of arguments,it is proved that if v > 1,the disease persists and the unique endemic equilibrium is globally asymptotically stable,which is obtained by the second compound matrix techniques and autonomous convergence theorems. we perform sensitivity analysis of v on the parameters in order to determine their relative importance to disease transmission and show that an imperfect vaccine is always beneficial in reducing disease spread within the community. © 2014 jing'an cui et al.