Algorithmic Methods for Investigating Equilibria in Epidemic Modeling

C. W. Brown, M. El Kahoui, Dominik Novotni, and Andreas Weber
In: Journal of Symbolic Computation (2006), 41:11(1157-1173)
 

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.

Keywords: epidemic modelling, quantifier elimination

Bibtex

@ARTICLE{brown-2006-algorithmic,
    author = {Brown, C. W. and El Kahoui, M. and Novotni, Dominik and Weber, Andreas},
     pages = {1157--1173},
     title = {Algorithmic Methods for Investigating Equilibria in Epidemic Modeling},
   journal = {Journal of Symbolic Computation},
    volume = {41},
    number = {11},
      year = {2006},
      note = {Special Issue on the Occasion of Volker Weispfenning's 60th Birthday},
  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.},
      issn = {0747-7171},
       doi = {10.1016/j.jsc.2005.09.011}
}