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Title: Travelling waves for an epidemic model with non-smooth treatment rates
Authors: Hussaini, N
Winter, M
Keywords: Epidemic modelling;Dynamics (theory);Population dynamics (experiment);Population dynamics (theory)
Issue Date: 2010
Publisher: IOP Publishing Ltd
Citation: Journal of Statistical Mechanics: Theory and Experiment, vol 2010, Article number P11019, 2010
Abstract: We consider a susceptible–infected–removed (SIR) epidemic model with two types of nonlinear treatment rates: (i) piecewise linear treatment rate with saturation effect, (ii) piecewise constant treatment rate with a jump (Heaviside function). For case (i), we compute travelling front solutions whose profiles are heteroclinic orbits which connect either the disease-free state to an infective state or two endemic states with each other. For case (ii), it is shown that the profile has the following properties: the number of susceptibles is monotonically increasing and the number of infectives approaches zero at infinity, while their product converges to a constant. Numerical simulations are performed for all these cases. Abnormal behaviour like travelling waves with non-monotonic profile or oscillations is observed.
Description: This is the post-print version of the final published paper that is available from the link below. Copyright @ 2010 IOP Publishing Ltd and SISSA.
ISSN: 1742-5468
Appears in Collections:Publications
Dept of Mathematics Research Papers
Mathematical Sciences

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