Modeling of control strategies for cholera epidemic

Abstract

The SIRB model for the dynamics of cholera epidemic introduced by Codeco is modified by incorporating some control strategies: vaccination is introduced to susceptible class, therapeutic treatment is applied to infected class, and water sanitation leads to the death of vibrios. The resulting system is solved numerically using the Runge-Kutta integration scheme with a modified version of Newton-Raphson shooting method with β, λ, σ, and υ as prescribed parameters. It is found out that with strong control measures, the concentration of toxigenic 𝑉.cholerae in water, 𝐵(𝑡), would be zero so that the disease-free equilibrium is globally asymptotically stable. With weak controls, instead, a unique and globally stable endemic equilibrium would still occur, though at a lower infection level.