Algorithmic Reduction of Biological Networks with Multiple Time Scales

Abstract We present a symbolic algorithmic approach that allows to compute invariant manifolds and corresponding reduced systems for differential equations modeling biological networks which comprise chemical reaction cellular biochemistry, compartmental models pharmacology, epidemiology ecology. Multiple time scales of given network are obtained by scaling, based on tropical geometry. Our reduction is mathematically justified within singular perturbation setting. The existence subject hyperbolicity conditions, we propose an test Hurwitz criteria. finally obtain sequence nested respective those manifolds. theoretical results generally accompanied rigorous descriptions suitable direct implementation existing off-the-shelf software systems, specifically computation libraries Satisfiability Modulo Theories solvers. computational examples taken from the well-known BioModels database using our own prototypical implementations.