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In this paper we explore a time-depended SEIR model, in which the dynamics ofthe infection in four groups from a selected target group (population), dividedaccording to the infection, are modeled by a system of nonlinear ordinarydifferential equations. Several basic parameters are involved in the model:coefficients of infection rate, incubation rate, recovery rate. Thecoefficients are adaptable to each specific infection, for each individualcountry, and depend on the measures to limit the spread of the infection andthe effectiveness of the methods of treatment of the infected people in therespective country. If such coefficients are known, solving the nonlinearsystem is possible to be able to make some hypotheses for the development ofthe epidemic. This is the reason for using Bulgarian COVID-19 data to first ofall, solve the so-called "inverse problem" and to find the parameters of thecurrent situation. Reverse logic is initially used to determine the parametersof the model as a function of time, followed by computer solution of theproblem. Namely, this means predicting the future behavior of these parameters,and finding (and as a consequence applying mass-scale measures, e.g.,distancing, disinfection, limitation of public events), a suitable scenario forthe change in the proportion of the numbers of the four studied groups in thefuture. In fact, based on these results we model the COVID-19 transmissiondynamics in Bulgaria and make a two-week forecast for the numbers of new casesper day, active cases and recovered individuals. Such model, as we show, hasbeen successful for prediction analysis in the Bulgarian situation. We alsoprovide multiple examples of numerical experiments with visualization of theresults.

Mathematical and Computer Modeling of COVID-19 Transmission Dynamics in Bulgaria by Time-depended Inverse SEIR Model