UDC 517: 616-036.22
DOI: 10.36871/2618-9976.2023.10.003
Authors
Alexey O. Nedosekin,
Doctor of Economics Sciences, PhD in Technical Sciences, Academician of IAELPS, Institute of Financial
Technologies, Saint-Petersburg,
Russia
Abstract
The aim of the study is to obtain a new probabilistic distribution
of the random moment T of complete transition of patients from cohort
S (susceptible to infection) to cohort R (recovered and cured).
Methodology. The distribution is constructed under the assumption
that in the SIR Kermack – McKendrick model, the nonlinear
system of firstorder
differential equations has an approximate
solution in the form of logistic functions based on the profile
of the normal probability distribution F. The obtained distribution
AN(t) has an analytical form and is threeparameter,
and all these parameters of the distribution can be represented in
a fuzzy form (fuzzified). Thus, T is a fuzzy random variable (FRV)
and AN(t) takes the form of a fuzzy function of general form.
Results. The form of the distribution function AN(t) and the density
distribution an(t) with fuzzy parameters of transition frequencies
β and γ from cohort S to cohort I (infected) and from
cohort I to cohort R, respectively, are obtained.
Conclusion. Similar distributions, given on the time axis t, can be
obtained for all other cohorts.
Keywords
SIR model, Possibilistic process, Fuzzy number of general form (FNGF), Logistic curve, ANdistribution, Fuzzy random variable (FRV)
