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November  2009, 12(4): 865-882. doi: 10.3934/dcdsb.2009.12.865

Distributed susceptibility: A challenge to persistence theory in infectious disease models

Horst R. Thieme 1,

1. 

Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287-1804, United States

Received  August 2008 Revised  December 2008 Published  August 2009

We consider an S-I(-R) type infectious disease model where the susceptibles differ by their susceptibility to infection. This model presents several challenges. Even existence and uniqueness of solutions is non-trivial. Further it is difficult to linearize about the disease-free equilibrium in a rigorous way. This makes disease persistence a necessary alternative to linearized instability in the superthreshold case. Application of dynamical systems persistence theory faces the difficulty of finding a compact attracting set. One can work around this obstacle by using integral equations and limit equations making it the special case of a persistence theory where the state space is just a set.
Keywords: compact attractor, semiflow, Laplace transform., limit solutions, uniform persistence, dynamical system, reproduction number, integral equation, Epidemic model, translation invariance.
Mathematics Subject Classification: Primary: 44A10, 45G10, 45M10, 45M20; Secondary: 92D3.
Citation: Horst R. Thieme. Distributed susceptibility: A challenge to persistence theory in infectious disease models. Discrete and Continuous Dynamical Systems - B, 2009, 12 (4) : 865-882. doi: 10.3934/dcdsb.2009.12.865
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