Numerical simulations of the spread of rabies in two-dimensional space

Khalaf M. Alanazi, Zdzislaw Jackiewicz, Horst Thieme

Research output: Contribution to journalArticle

Abstract

We extend our previous work on the spatial spread of fox rabies from one dimension to two dimensions. We consider the case when the latent period has fixed length. We use the method of lines to replace the spatial derivatives and the integral equations with algebraic approximations, then we apply the explicit continuous Runge–Kutta method of fourth order and discrete Runge–Kutta method of third order with six stages to numerically integrate the resulting systems of ordinary and delay differential equations. We discuss and confirm some of the major results we obtained in earlier work. The asymptotic speeds of spread observed in the two-dimensional simulations and in earlier work are discussed and compared with those found in nature.

Original languageEnglish (US)
JournalApplied Numerical Mathematics
DOIs
StateAccepted/In press - Jan 1 2018

Fingerprint

Runge-Kutta Methods
Integral equations
Differential equations
Derivatives
Numerical Simulation
Method of Lines
Computer simulation
Delay Differential Equations
System of Ordinary Differential Equations
One Dimension
Fourth Order
Integral Equations
Two Dimensions
Integrate
Derivative
Approximation
Simulation

Keywords

  • Continuous Runge–Kutta method
  • Diffusing versus territorial rabid foxes
  • Latent period
  • Method of lines
  • Spreading speed

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

Numerical simulations of the spread of rabies in two-dimensional space. / Alanazi, Khalaf M.; Jackiewicz, Zdzislaw; Thieme, Horst.

In: Applied Numerical Mathematics, 01.01.2018.

Research output: Contribution to journalArticle

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