A Mathematical Model for SIS Cholera Epidemic with Quarantine Effect

Abstract

Cholera was prevalent in the U.S. in the 1800s, before modern water and sewage treatment systems eliminated its spread by contaminated water. Cholera is an acute intestinal infectious disease caused by the bacterium vibrio cholerae. We propose and analyse a mathematical model for cholera considering quarantine. Quarantine plays an important role to control the disease. Our goal is to control the disease through the quarantine even if infected population again becomes suscepted. Determine two equilibrium points of the model: disease-free and endemic. Also basic reproduction number R q is obtained. Reproduction number plays as a key role for analyzing stability for disease-free and endemic equilibrium points. Stability has been discussed for both equilibrium points using Ruth-Hurwitz criterian. We concluded that the disease-free and endemic equilibria are locally asymptotically stable if R q <1 and R q >1 respectively. Also, Numerical simulations are carried out for the model. From the graphically representation it is more clearly seen that when the disease becomes dies out and when it persistence.

Can the establishment of national sanitary cities better resist the impact of COVID-19?

“…In order to deal effectively with the potential risks of the COVID-19 epidemic, mandatory short-term intervention measures became the main means adopted by governments before the vaccine became available. Isolation (3,4), curfews (5), the closure of schools and public places (6,7), traffic control (8,9), paid sick leave (10) and a series of other policies were introduced to prevent the spread of the epidemic by restricting the flow of people.…”