A Lyapunov functional for vaccination model on the dynamics of cholera epidemic with non-linear incidence of infection

Abstract

A new deterministic susceptible-exposed-infectious-vaccinated-removed-pathogen (SEIVRB) cholera epidemic model with combined mass action incidence and saturated incidence rates is proposed and analyzed. A threshold level of vaccine coverage necessary for controlling or eradicating cholera has been determined and analyzed using the next generation matrix approach. It is shown that the higher values of vaccine coverage that are lower than the threshold value significantly reduces the number of infected individuals whenever basic reproduction number is less than unity, and the cholera would persist in the populations whenever the model basic reproduction number exceeds unity. The global stability for cholera free equilibrium state and cholera endemic equilibrium state of the model system is investigated using Lyapunov functional approach and Lasalle invariance principle, which are found to be globally asymptotically stable at both equilibrium states. Numerical simulations and graphical illustrations is presented to support the analytical results found in the study.