Mathematical model of cholera spread based on SIR: Optimal control

The bacterium Vibrio cholerae is the cause of cholera. Cholera spread through feces an infected individual in a population. From mathematical point view, this problem can be brought into model form Susceptible-Infected-Recovered (SIR), which considers birth rate. Because outbreaks that occur easily if not treated immediately, it necessary to control susceptible population by vaccination. vaccine used Oral For reason, purposes study were establish for cholera without vaccination, analyze stability around equili­brium point, with vaccination control, and describe simulation results numerical completion. Based on analysis equilibrium model, indicates contact rate smaller than sum recovery rate, will disappear over time. If grea­ter then still present, or other words, disease spread. endemic, optimal popu­lation individuals needed, case, so becomes minimum recovered indivi­duals increases.