Dynamics of cholera transmission model with imperfect vaccination and demographics on complex networks

Cholera is a waterborne infectious disease that continually emerges and remains an important global health burden. We formulate and investigate a cholera model with imperfect vaccination and demographics on complex networks, in which two transmission pathways, indirect environment-to-human and direct human-to-human transmissions, are incorporated simultaneously. The contacts among humans are treated as a heterogeneous network and the contacts between environment and humans as homogenous mixing. Using the spectral analysis method, the basic reproduction number is defined and verified to be a sharp threshold which completely determines global dynamical properties of model. Numerical simulations are performed to confirm the theoretical results. The results demonstrate that demographics and the degree distribution of the network are of great importance in cholera propagation, and that the degree distribution is time-dependent until the stationary state is reached. Furthermore, demographics have a significant influence on the basic reproduction number. By increasing the vaccination rate and decreasing the rate at which the vaccine wears off, cholera infection can be effectively controlled.