Cholera Models with Hyperinfectivity and Temporary Immunity

A mathematical model for cholera is formulated that incorporates hyperinfectivity and temporary immunity using distributed delays. The basic reproduction number \(\mathcal{R}_{0}\) is defined and proved to give a sharp threshold that determines whether or not the disease dies out. The case of constant temporary immunity is further considered with two different infectivity kernels. Numerical simulations are carried out to show that when \(\mathcal{R}_{0}>1\) , the unique endemic equilibrium can lose its stability and oscillations occur. Using cholera data from the literature, the quantitative effects of hyperinfectivity and temporary immunity on oscillations are investigated numerically.