Infekciya keselligi tarqalıwınıń matematikalıq modeli

Abstract

The paper studies the classical Kermack–McKendrick SIR model, which describes the spread of infectious diseases in a closed population. The model is formulated as a system of ordinary differential equations. In addition, the first integral of the system is considered, and the condition for the function of infected individuals to reach its maximum value is derived. It is shown that, despite its simplicity, the SIR model adequately reflects the fundamental patterns of the epidemic process and serves as a basis for more complex models of mathematical epidemiology.