Development of mathematical epidemic models taking into account the effects of isolating individuals in a population

The paper analyzes the effect of isolation of individuals of the population on the dynamics of the epidemic. Based on the SIR model, a SIRDi model was built, which takes into account the isolation of individuals, as well as the presence of deceased patients, which is appropriate to use in cases of extensive spread of infection, when the number of infected is comparable to the number of susceptible (i.e., those who can be infected). Simplified IRD and IRDi models are proposed for studying the spread of an infectious disease at the initial stage of an epidemic (or for the case when the infection rate is not high). It was found that there is a threshold value of the isolation coefficient (fraction), which delimits the qualitatively different behavior of the epidemic indicators of a system. A comparison is made between different models. It is shown that the simplified (IRDi) and more complete (SIRDi) models at the initial stage of the epidemic give approximately the same results.