Abstract
A discrete nonlinear mathematical model of the epidemic development is proposed. It involves dividing the population into eight compartments (susceptible, exposed, asymptomatic, easily sick, hospitalized, critically ill, recovered and deceased). At the same time, the time spent in compartments of exposed and all forms of patients is considered limited. Thus, any person who has been in contact with an infected person, after a while, either gets sick or does not, leaving the exposed compartment, and any patient, over time, for sure, either goes to the group of more severe patients, dies or recovers. This deterministic model is presented in a discrete form and simulates the quantitative change of various groups by day during the spread of the epidemic. It is a transformation of the SEIR model. The article also presents a numerical analysis of the proposed model. The development of the COVID epidemic in Kazakhstan is considered as an example. At the end, forecasts are given based on preliminary data from the first months of quarantine. Various parameters of the model when starting numerical experiments were found based on computational experiments. At the same time, for a given deterministic one, the effect of wavelike changes in the number of infected is observed.