A general uniqueness result of an endemic state for an epidemic model with external force of infection
Commun. Korean Math. Soc. 2007 Vol. 22, No. 4, 597-608
Printed December 1, 2007
Youngjoon Cha
Sejong University
Abstract : We present a general uniqueness result of an endemic state for an S-I-R model with external force of infection. We reduce the problem of finding non-trivial steady state solutions to that of finding zeros of a real function of one variable so that we can easily prove the uniqueness of an endemic state. We introduce an assumption which was usually used to show stability of a non-trivial steady state. It turns out that such an assumption adopted from a stability analysis is crucial for proving the uniqueness as well, and the assumption holds for almost all cases in our model.
Keywords : endemic, S-I-R, uniqueness, inter-cohort, external force
MSC numbers : 92B05
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