### Abstract

We propose a numerical algorithm for a model of the spread of infection in the theory of epidemics. This model involves a threshold for becoming infective and leads to a system of delay-differential equations with the delay function which depends on the values of the unknowns over an interval. The numerical algorithm is based on diagonally implicit multistage integration formulas with stage order equal to the order of the method. This makes possible the efficient evaluation of past values to the accuracy compatible with the requested error tolerance. This algorithm is appicable to the general model without any simplifying assumptions on the parameters of the delay-differential system. Numerical results illustrate the effect of varying various parameters of the model on the spread of infection in a constant population.

Original language | English (US) |
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Pages (from-to) | 533-543 |

Number of pages | 11 |

Journal | Applied Numerical Mathematics |

Volume | 56 |

Issue number | 3-4 SPEC. ISS. |

DOIs | |

State | Published - Mar 2006 |

### Fingerprint

### Keywords

- Delay-differential system
- Numerical simulation
- Spread of infection
- Theory of epidemics

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Modeling and Simulation

### Cite this

*Applied Numerical Mathematics*,

*56*(3-4 SPEC. ISS.), 533-543. https://doi.org/10.1016/j.apnum.2005.04.019

**Numerical solution of a problem in the theory of epidemics.** / Hoppensteadt, F. C.; Jackiewicz, Zdzislaw.

Research output: Contribution to journal › Article

*Applied Numerical Mathematics*, vol. 56, no. 3-4 SPEC. ISS., pp. 533-543. https://doi.org/10.1016/j.apnum.2005.04.019

}

TY - JOUR

T1 - Numerical solution of a problem in the theory of epidemics

AU - Hoppensteadt, F. C.

AU - Jackiewicz, Zdzislaw

PY - 2006/3

Y1 - 2006/3

N2 - We propose a numerical algorithm for a model of the spread of infection in the theory of epidemics. This model involves a threshold for becoming infective and leads to a system of delay-differential equations with the delay function which depends on the values of the unknowns over an interval. The numerical algorithm is based on diagonally implicit multistage integration formulas with stage order equal to the order of the method. This makes possible the efficient evaluation of past values to the accuracy compatible with the requested error tolerance. This algorithm is appicable to the general model without any simplifying assumptions on the parameters of the delay-differential system. Numerical results illustrate the effect of varying various parameters of the model on the spread of infection in a constant population.

AB - We propose a numerical algorithm for a model of the spread of infection in the theory of epidemics. This model involves a threshold for becoming infective and leads to a system of delay-differential equations with the delay function which depends on the values of the unknowns over an interval. The numerical algorithm is based on diagonally implicit multistage integration formulas with stage order equal to the order of the method. This makes possible the efficient evaluation of past values to the accuracy compatible with the requested error tolerance. This algorithm is appicable to the general model without any simplifying assumptions on the parameters of the delay-differential system. Numerical results illustrate the effect of varying various parameters of the model on the spread of infection in a constant population.

KW - Delay-differential system

KW - Numerical simulation

KW - Spread of infection

KW - Theory of epidemics

UR - http://www.scopus.com/inward/record.url?scp=33644621054&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33644621054&partnerID=8YFLogxK

U2 - 10.1016/j.apnum.2005.04.019

DO - 10.1016/j.apnum.2005.04.019

M3 - Article

AN - SCOPUS:33644621054

VL - 56

SP - 533

EP - 543

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

IS - 3-4 SPEC. ISS.

ER -