Scaling Symmetries and Parameter Reduction in Epidemic SI(R)S Models

Symmetry concepts in parametrized dynamical systems may reduce the number of external parameters by a suitable normalization prescription. If, under action symmetry group G, parameter space A becomes (locally) trivial principal bundle, A≅A/G×G, then normalized dynamics only depends on quotient A/G. In this way, fractional variables homogeneous epidemic SI(R)S models, with standard incidence, absence R-susceptibility and compartment independent birth death rates, turns out to be isomorphic (a marginally extended version of) Hethcote’s classic endemic model, first presented 1973. The paper studies 10-parameter master model constant I-linear vaccination vertical transmission rate for susceptible newborns. As recently shown author, all demographic are redundant. After adjusting time scale, remaining 5-parameter admits 3-dimensional abelian scaling symmetry. By we end up 2-parameter model. Thus, view concepts, reproving theorems bifurcation stability such models needless.