Development of Mathematical Models Taking into Account the Effect of Isolating Individuals in a Population

The effect of the isolation of individuals in the population on the dynamics of the epidemic is analyzed. Based on the SIR model, a SIRDi model is built that takes into account the isolation of individuals, as well as the presence of deceased patients, which is appropriate to use in cases of widespread infection, when the number of infected is comparable to the number of susceptible individuals. 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 rate of infection is not high). It is found that there is a threshold value of the coefficient (fraction) of isolation, which delimits the qualitatively different behavior of the epidemic indicators of the population system. A comparison is made between different models. It is shown that the simplified (IRDi) and more complex (SIRDi) models at the initial stage of the epidemic give approximately the same results.