A Lyapunov functional for a SIRI model with nonlinear incidence of infection and relapse

We analyze the dynamics of a disease propagation model with relapse under the assumption that the incidence of infection is given in an abstract, possibly bi-nonlinear form. Sufficient conditions for the local stability of equilibria are obtained by means of Lyapunov’s second method and it is shown that global stability can be attained under suitable monotonicity conditions. The persistence of the system is then investigated and it is established that the basic reproduction number R0R0 is a threshold parameter for the stability of the system. Alternate Lyapunov functionals are also introduced, being observed that the originating functional template generalizes both quadratic and Volterra functionals.