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.
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