GLOBAL STABILITY OF AN SIR EPIDEMIC MODEL WITH DELAY AND GENERAL NONLINEAR INCIDENCE

An SIR model with distributed delay and a general incidence function is studied. Conditions are given under which the system exhibits threshold behaviour: the disease-free equilibrium is globally asymptotically stable if R(0) < 1 and globally attracting if R(0) = 1; if R(0) > 1, then the unique endemic equilibrium is globally asymptotically stable. The global stability proofs use a Lyapunov functional and do not require uniform persistence to be shown a priori. It is shown that the given conditions are satisfied by several common forms of the incidence function.