Open AccessDynamics of an ultra-discrete SIR epidemic model with time delay
Author(s) -
Masaki Sekiguchi,
Emiko Ishiwata,
Yukihiko Nakata
Publication year - 2018
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2018029
Subject(s) - discretization , epidemic model , convergence (economics) , mathematics , delay differential equation , discrete time and continuous time , differential equation , property (philosophy) , statistical physics , lattice (music) , computer science , mathematical analysis , statistics , physics , population , demography , philosophy , epistemology , sociology , economics , economic growth , acoustics
We propose an ultra-discretization for an SIR epidemic model with time delay. It is proven that the ultra-discrete model has a threshold property concerning global attractivity of equilibria as shown in differential and difference equation models. We also study an interesting convergence pattern of the solution, which is illustrated in a two-dimensional lattice.