Transmission dynamics of cholera with hyperinfectious and hypoinfectious vibrios: mathematical modelling and control...

Cholera is a common infectious disease caused by Vibrio cholerae, which has different infectivity. In this paper, we propose a cholera model with hyperinfectious and hypoinfectious vibrios, in which both human-to-human and environment-to-human transmissions are considered. By analyzing the characteristic equations, the local stability of disease-free and endemic equilibria is established. By using Lyapunov functionals and LaSalle's invariance principle, it is verified that the global threshold dynamics of the model can be completely determined by the basic reproduction number. Numerical simulations are carried out to illustrate the corresponding theoretical results and describe the cholera outbreak in Haiti. The study of optimal control helps us seek cost-effective solutions of time-dependent control strategies against cholera outbreaks, which shows that control strategies, such as vaccination and sanitation, should be taken at the very beginning of the outbreak and become less necessary after a certain period.