Numerical solution of threshold problems in epidemics and population dynamics

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1 Scopus citations

Abstract

A new algorithm is proposed for the numerical solution of threshold problems in epidemics and population dynamics. These problems are modeled by the delay-differential equations, where the delay function is unknown and has to be determined from the threshold conditions. The new algorithm is based on embedded pair of continuous Runge-Kutta method of order p=4 and discrete Runge-Kutta method of order q=3 which is used for the estimation of local discretization errors, combined with the bisection method for the resolution of the threshold condition. Error bounds are derived for the algorithm based on continuous one-step methods for the delay-differential equations and arbitrary iteration process for the threshold conditions. Numerical examples are presented which illustrate the effectiveness of this algorithm.

Original languageEnglish (US)
Pages (from-to)40-56
Number of pages17
JournalJournal of Computational and Applied Mathematics
Volume279
DOIs
StatePublished - May 1 2015

Keywords

  • Bisection method
  • Continuous
  • Convergence analysis
  • Delay-differential equations
  • Local error estimation
  • RungeKutta methods
  • Threshold conditions

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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