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http://bura.brunel.ac.uk/handle/2438/8029
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. |
URI: | http://iopscience.iop.org/1742-5468/2010/11/P11019/ http://bura.brunel.ac.uk/handle/2438/8029 |
DOI: | http://dx.doi.org/10.1088/1742-5468/2010/11/P11019 |
ISSN: | 1742-5468 |
Appears in Collections: | Publications Dept of Mathematics Research Papers Mathematical Sciences |
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