An Epidemic Model with Time Delays Determined by the Infectivity and Disease Durations.

Mathematical modeling of infectious diseases plays an essential role in the understanding of the dynamics of epidemic progression, in prediction of future epidemic outbreaks and elaboration of the appropriate control strategies. In this talk, we start by proposing an epidemiological model with distributed recovery and death rates. It represents an integro-differential system of equations for susceptible, exposed, infectious, recovered and dead classes. Then we show that this model can be reduced to the conventional ODE model under the assumption that recovery and death rates are uniformly distributed in time during disease duration. After that, we investigate another limiting case, where recovery and death rates are given by the delta-function, which leads to a new point-wise delay model with two time delays corresponding to the infectivity period and disease duration. Existence and positiveness of solutions for the distributed delay model and point-wise delay model are proved. We also calculate some characteristics of epidemic progression in the delay model. Next, we investigate the Omicron variant of the SARS-CoV-2 infection through our model, and compare it with the conventional ODE model. Finally, we present conclusions and further perspectives.