Epidemic dynamics of cholera with impulsive sanitation

In this work, we develop an ordinary differential equation (ODE) model with impulsive sanitation of cholera. The sanitation interventions are classified into three types in this article. The first two types are human sanitation, with type-1 sanitation focused on the prevention of direct and indirect transmissions and type-2 focused on prevention of bacterial shedding. The third type refers to pathogen sanitation where interventions are performed in contaminated water environment via disinfection. For the developed impulsive model, we introduce the basic production number $R_0$ and show that $R_0$ remains a sharp disease threshold parameter despite the incorporation of impulsive sanitation. We numerically investigate the impact of impulsive sanitation on the prevention and control of the disease. Our numerical results indicate that type-1 sanitation tends to bear the longest time window between subsequent interventions among all the three types of sanitation provided the same level of sanitation efficacy. Particularly, when the sanitation efficacy is 50% under 90% compliance, type-1 sanitation can be implemented about every 7 months for the purpose of disease control, whereas type-2 and type-3 sanitation will have be performed on a daily basis and every three weeks or so, respectively.