Dynamics of an ultra-discrete SIR epidemic model with time delay | Zendy

Masaki Sekiguchi | Zendy; Emiko Ishiwata | Zendy; Yukihiko Nakata | Zendy

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Dynamics 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.

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