The effects of an imperfect vaccine on cholera control

In this paper, we consider a SVIR-B cholera model with imperfect vaccination. By analyzing the corresponding characteristic equations, the local asymptotically stability of a disease-free equilibrium and an endemic equilibrium is established. We calculate the certain threshold known as the basic reproduction number Rv. If Rv < 1, we obtain sufficient conditions for the global asymptotically stability of the disease- free equilibrium, the diseases will be eliminated from the community. By comparison arguments, it is proved that if Rv > 1, the unique endemic equilibrium is local asymptotically stable. We perform sensitivity analysis of Rv on the parameters in order to determine their relative importance to disease control and show that an imperfect vaccine is always beneficial in reducing disease spread within the community.