Mathematical Modelling of the Epidemic Evolution

Mathematical models describing epidemics are very important in epidemiology, there are many different types of them, however, within the framework of this report, we discussed the SIRD model of the epidemic evolution built on Kermack and McKendrick's SIR model, which allows us to predict how the epidemic will behave over time. Through MatLab, we observed the given model and its actions when the parameters changed, based on which we analyzed the obtained results. After that, to improve the model, we took into account time delays (incubation period and loss of immunity), through time delay differential equations we were able to model the evolution of the epidemic for these shifts, we compared the given results with the real statistics of Covid-19 in Georgia, and we also observed the similarity of the epidemic model with the Bateman equation describing radioactive decay families with the results of the systems.