# Numerical solution of a problem in the theory of epidemics

Research output: Contribution to journalArticle

5 Citations (Scopus)

### 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) 533-543 11 Applied Numerical Mathematics 56 3-4 SPEC. ISS. https://doi.org/10.1016/j.apnum.2005.04.019 Published - Mar 2006

### Fingerprint

Numerical Solution
Numerical Algorithms
Infection
Delay-differential Systems
Delay Differential Equations
Model
Tolerance
Differential equations
Unknown
Numerical Results
Interval
Evaluation

### Keywords

• Delay-differential system
• Numerical simulation
• Theory of epidemics

### ASJC Scopus subject areas

• Applied Mathematics
• Computational Mathematics
• Modeling and Simulation

### Cite this

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

In: Applied Numerical Mathematics, Vol. 56, No. 3-4 SPEC. ISS., 03.2006, p. 533-543.

Research output: Contribution to journalArticle

Hoppensteadt, F. C. ; Jackiewicz, Zdzislaw. / Numerical solution of a problem in the theory of epidemics. In: Applied Numerical Mathematics. 2006 ; Vol. 56, No. 3-4 SPEC. ISS. pp. 533-543.
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