# Algorithmic Methods for Investigating Equilibria in Epidemic Modeling

## 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

@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} }