Global dynamics of an age-structured cholera model with saturation incidence and multiple transmission pathways

Cholera is an acute diarrheal disease caused by the bacterium Vibrio cholerae. With the consideration of the transmission mechanism and heterogeneity of population, an age-structured cholera epidemic model is proposed, involving saturation incidence rates that describe direct and indirect transmission pathways and all class-ages with the susceptible age of susceptible individuals, infection age of infected individuals and biological age of Vibrio cholerae. The focus is to investigate the global dynamics of the model by using the basic reproduction number $R_0$ . After establishing the well-posedness of the initial-boundary value problem of the model, we study the existence of endemic steady state and local stability of the disease-free steady state in terms of $R_0$ . Next asymptotic smoothness of the semi-flow is discussed in order to obtain the existence of a global attractor. Finally, global stability of the disease-free and endemic steady states is obtained by combining Volterra-type Lyapunov functionals and existence of global attractors. Numerical simulations are given to demonstrate the effect of age structures and to illustrate the theoretical results.