  Mathematical models are traditionally used to analyze the long-term global
evolution of epidemics, to determine the potential and severity of an outbreak,
and to provide critical information for identifying the type of disease
interventions and intensity. One of the widely used mathematical models of
long-term spreading of epidemics are the so-called deterministic compartmental
models (SIR/SEIR type models). One of the main purposes of applying such models
is to assess how the expensive restriction measures imposed by the authorities
(home and social isolation/quarantine, travel restrictions, etc.) can
effectively reduce the control reproduction number of the disease and its
transmission risk. However the classical SIR/SEIR models have been primarily
studied in what may be called stationary case, where the main parameters, the
Transmission rate Beta (reflecting the virus spread by infected individuals)
and the Removed rate Gamma (reflecting the hospitalization/isolation measures)
remain constant during the whole period of interest. Hence, it is important to
extend the classical SIR/SEIR models by creating new ansatzes for the dynamics
of the transmission rates Beta(t) (which we will call further just Beta) and
removed rates Gamma(t) (which we will call further just Gamma). The main
purpose of the present research is to introduce a spline-based SEIR model with
Time-varying Beta and Gamma parameters, or abbreviated TVBG-SEIR model, which
is used to estimate the practical implications of the public health
interventions and measures. We have designed a Tool based on the TVBG-SEIR
model, which may be used as a Decision Support Tool to assist the health
decision- and policy-makers in creating predictive scenarios.
