Global Stability of a Cholera Carrier Epidemic Model with Nonlinear Incidence Functions

A new deterministic susceptible-carrier-infectious-removed-pathogen (SCIRP) cholera epidemic model with combined mass action incidence and saturated incidence rates is proposed. The threshold behavior of the model system is analyzed and establishes that cholera dies out whenever basic reproduction number is less than unity, and the disease would persist in the populations whenever the model basic reproduction number exceeds unity. The global stabilities of the model system are investigated using Lyapunov functional approach and were found to be globally asymptotically stable at both equilibrium states. Numerical simulations and graphical illustrations are presented to support the analytical results found in the study.