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Scaling Symmetries and Parameter Reduction in Epidemic Si(r)s Models
Version 1
: Received: 26 May 2023 / Approved: 30 May 2023 / Online: 30 May 2023 (05:08:53 CEST)
A peer-reviewed article of this Preprint also exists.
Nill, F. Scaling Symmetries and Parameter Reduction in Epidemic SI(R)S Models. Symmetry 2023, 15, 1390. Nill, F. Scaling Symmetries and Parameter Reduction in Epidemic SI(R)S Models. Symmetry 2023, 15, 1390.
Abstract
Symmetry concepts in parametrized dynamical systems may reduce the number of external parameters by a suitable normalization prescription. If, under the action of a symmetry group G, parameter space A becomes a (locally) trivial principal bundle, A ~ A/G x G, then the normalized dynamics only depends on the quotient A/G. In this way, the dynamics of fractional variables in homogeneous epidemic SI(R)S models, with standard incidence, absence of R-susceptibility and compartment independent birth and death rates, turns out to be isomorphic to (a marginally extended version of) Hethcote's classic endemic model, first presented in 1973. The paper studies a 10-parameter master model with constant and I -linear vaccination rates, vertical transmission and a vaccination rate for susceptible newborns. As recently shown by the author, all demographic parameters are redundant. After adjusting time scale, the remaining 5-parameter model admits a 3-dimensional abelian scaling symmetry. By normalization we end up with Hethcote's extended 2-parameter model. Thus, in view of symmetry concepts, reproving theorems on endemic bifurcation and stability in such models becomes needless.
Keywords
Symmetries in parametric dynamical systems; SIRS model; classic endemic model; parameter reduction; normalization
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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