UDC 614
DOI: 10.36871/2618-9976.2023.11.005
Authors
Alexey O. Nedosekin,
Doctor of Economics Sciences, PhD in Technical Sciences, Academician of IAELPS, Institute of Financial
Technologies, Saint-Petersburg,
Russia
Zinaida I. Abdulaeva,
North-Western
State Medical University named after I.I. Mechnikov
Daniil E. Murashev,
North-Western
State Medical University named after I.I. Mechnikov
Abstract
Target. Obtain an analytical form of an approximate solution for
a system of firstorder
nonlinear differential equations that describes
the dynamics of the epidemic in the SIR model of three
cohorts: healthy – infected – immune.
Methodology. The solution for cohort S is sought in the form
of a logistic curve in the form of a normal distribution function Ф.
By eliminating the dependence of S(t) on the recovery rate γ it was
possible to construct a dependence for I(t) as an integral of the
shape of S(t).
Results. Quantitative examples demonstrate that with an increase
in the infection rate β, the mode of the form I(t) shifts to the left
along the abscissa axis, and the maximum value in this mode
increases according to the trend. The system maintains parametric
stability for values of 0.15 ≤ β ≤ 0.4.
Conclusion. The solution for the SIR model can be generalized
to a model with a larger number of cohorts.
Keywords
SIR model, Possibilistic process, General fuzzy number (GFN), Logistic curve
