Numerical solution of threshold problems in epidemics and population dynamics

Z. Bartoszewski; Zdzislaw Jackiewicz; Yang Kuang

doi:10.1016/j.cam.2014.10.020

Numerical solution of threshold problems in epidemics and population dynamics

Z. Bartoszewski, Zdzislaw Jackiewicz, Yang Kuang

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	40-56
Number of pages	17
Journal	Journal of Computational and Applied Mathematics
Volume	279
DOIs	https://doi.org/10.1016/j.cam.2014.10.020
State	Published - 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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10.1016/j.cam.2014.10.020

Cite this

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title = "Numerical solution of threshold problems in epidemics and population dynamics",

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.",

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T1 - Numerical solution of threshold problems in epidemics and population dynamics

AU - Bartoszewski, Z.

AU - Jackiewicz, Zdzislaw

AU - Kuang, Yang

PY - 2015/5/1

Y1 - 2015/5/1

N2 - 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.

AB - 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.

KW - Bisection method

KW - Continuous

KW - Convergence analysis

KW - Delay-differential equations

KW - Local error estimation

KW - RungeKutta methods

KW - Threshold conditions

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Numerical solution of threshold problems in epidemics and population dynamics

Abstract

Keywords

ASJC Scopus subject areas

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