Modeling relapse in infectious diseases.
An integro-differential equation is proposed to model a general relapse phenomenon in infectious diseases including herpes. The basic reproduction number R(0) for the model is identified and the threshold property of R(0) established. For the case of a constant relapse period (giving a delay differential equation), this is achieved by conducting a linear stability analysis of the model, and employing the Lyapunov-Razumikhin technique and monotone dynamical systems theory for global results. Numerical simulations, with parameters relevant for herpes, are presented to complement the theoretical results, and no evidence of sustained oscillatory solutions is found.
van den Driessche
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Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3P4. pvdd@math.uvic.ca
Zou
Xingfu
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D003198:Computer Simulation; D006561:Herpes Simplex / Q000453:epidemiology / Q000821:virology*; D018259:Herpesvirus 1, Human / Q000254:growth & development*; D006801:Humans; D008954:Models, Biological; D012008:Recurrence