Global stability of an $SIR$ epidemic model with delay and general nonlinear incidence - C. Connell McCluskey (Mathematical Biosciences and Engineering)
An SIR model with distributed delay and a general incidence function isstudied. Conditions are given under which the system exhibits thresholdbehaviour: the disease-free equilibrium is globally asymptotically stableif R00=1; if R0>1,then the unique endemic equilibrium is globally asymptotically stable.The global stability proofs use a Lyapunov functional and do not requireuniform persistence to be shown a priori. It is shown that thegiven conditions are satisfied by several common forms of the incidencefunction.