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The paper discusses new mathematical models that describe the early stages of the spread of the SARS-CoV-2 virus. The first model considers two groups of people: without healthy immunity and asymptomatic infected. The second model considers three groups of people: without healthy immunity, asymptomatic infected and detected infected.
In the first model, the infectivity variable coefficient is taken as a linear incremental function of two unknown function variables. The first integral has been obtained. The Cauchy’s problem is solved analytically exactly. In the second model, in the case of constant infection coefficients, the first two integrals of a three-dimensional dynamic system have been found and the problem is reduced to the Cauchy’s problem for one unknown function.