On some qualitatively adequate discrete space-time models of epidemic propagation

I. Faragó, Róbert Horváth

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Most of the models of epidemic propagations do not take into account the spatial distribution of the individuals. They give only the temporal change of the number of the infected, susceptible and recovered patients. In this paper we give some spatial discrete one-step iteration models for disease propagation and give conditions that guarantee some basic qualitative properties of the original process to the discrete models. Since the discrete models can be considered as the finite difference discretizations of continuous models of disease propagation given in the form of systems of partial differential equations, we can deduce conditions for the mesh size and the time step. Some of the results are demonstrated on numerical tests.

Original languageEnglish
Pages (from-to)45-54
Number of pages10
JournalJournal of Computational and Applied Mathematics
Volume293
DOIs
Publication statusPublished - Jan 22 2015

Fingerprint

Space-time Models
Propagation
Discrete Model
Qualitative Properties
Systems of Partial Differential Equations
Spatial Distribution
Deduce
Finite Difference
Discretization
Mesh
Model
Iteration
Spatial distribution
Partial differential equations

Keywords

  • Epidemic models
  • Finite difference method
  • Nonnegativity
  • Qualitative properties of systems of PDEs

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

On some qualitatively adequate discrete space-time models of epidemic propagation. / Faragó, I.; Horváth, Róbert.

In: Journal of Computational and Applied Mathematics, Vol. 293, 22.01.2015, p. 45-54.

Research output: Contribution to journalArticle

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