 Estimates for the spreading velocity of an epidemic modelO. Alves, C.E. Ferreira and F.P. Machado Mathematics and Computers in Simulation (MATCOM), 2004, vol. 64, issue 6, 609-616 Abstract: We present numerical estimates for the spreading velocity of an epidemic model. The model consists of a growing set of simple random walks (SRWs) on Zd (d=1, 2), also known as frog model. The dynamics is described as follows. It is a discrete time process in which at any time there are active particles, which perform independent SRWs on Zd, and inactive particles, which initially do not move. When an inactive particle is hit by an active particle, the former becomes active too. We consider the case where initially there is one inactive particle per site except for the active particle which is placed at the origin. Alves et al. [Ann. Appl. Probab. 12 (2) (2002) 533] have recently proved that the set of the original positions of all active particles, re-scaled by the elapsed time, converges to a compact convex set A without being able to identify rigorously the actual limit shape. Numerical estimates coming from simulations show that for d=2 the limit shape A is not an Euclidean ball. Keywords: Frog model; Growth model; Shape theorem; Edge velocity (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:64:y:2004:i:6:p:609-616 DOI: 10.1016/j.matcom.2003.11.014 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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