The effects of an imperfect vaccine on cholera control

Abstract

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 R v . If R v < 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 R v > 1, the unique endemic equilibrium is local asymptotically stable. We perform sensitivity analysis of R v 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.