Algorithmic Methods for Investigating Equilibria in Epidemic Modeling

A. Dolzmann, A. Seidl und Thomas Sturm (Editoren)
C. W. Brown, M. El Kahoui, Dominik Novotni und Andreas Weber
In proceedings of Algorithmic Algebra and Logic, pages 59-63, Apr. 2005
Präsentiert: Algorithmic Algebra and Logic
 

Abstract

The calculation of threshold conditions for models of infectious diseases is of central importance for developing vaccination policies. These models are often coupled systems of ordinary differential equations, in which case the computation of threshold conditions can be reduced to the question of stability of the disease-free equilibrium. This paper shows how computing threshold conditions for such models can be done fully algorithmically using quantifier elimination for real closed fields and related simplification methods for quantifier-free formulas. Using efficient quantifier elimination techniques for special cases that have been developed by Weispfenning and others, we can can also compute whether there are ranges of parameters for which sub-threshold endemic equilibria exist.

Stichwörter: epidemic modelling, quantifier elimination

Bibtex

@INPROCEEDINGS{brown-2005-algorithmic,
      author = {Brown, C. W. and El Kahoui, M. and Novotni, Dominik and Weber, Andreas},
      editor = {Dolzmann, A. and Seidl, A. and Sturm, Thomas},
       pages = {59--63},
       title = {Algorithmic Methods for Investigating Equilibria in Epidemic Modeling},
   booktitle = {Algorithmic Algebra and Logic},
        year = {2005},
       month = apr,
        note = {Extended abstract},
    keywords = {epidemic modelling, quantifier elimination},
    abstract = {The calculation of threshold conditions for models of
                infectious
                         diseases is of central importance for developing vaccination
                         policies. These models are often coupled systems of ordinary
                         differential equations, in which case the computation of threshold
                         conditions can be reduced to the question of stability of the
                         disease-free equilibrium. This paper shows how computing
                         threshold conditions for such models can be done fully
                         algorithmically using quantifier elimination for
                         real closed fields and related simplification methods for
                         quantifier-free formulas.  Using efficient quantifier elimination
                         techniques for special cases that have been developed by
                         Weispfenning and others, we can can also compute whether there are
                         ranges of parameters for which sub-threshold endemic equilibria
                         exist.},
        isbn = {3-8334-2669-1},
  conference = {Algorithmic Algebra and Logic}
}