Incorporating heterogeneity into the transmission dynamics of a waterborne disease model

We formulate a mathematical model that captures the essential dynamics of waterborne disease transmission to study the effects of heterogeneity on the spread of the disease. The effects of heterogeneity on some important mathematical features of the model such as the basic reproduction number, type reproduction number and final outbreak size are analysed accordingly. We conduct a real-world application of this model by using it to investigate the heterogeneity in transmission in the recent cholera outbreak in Haiti. By evaluating the measure of heterogeneity between the administrative departments in Haiti, we discover a significant difference in the dynamics of the cholera outbreak between the departments.