It is very important to know not only the current situation, but also to have forecasts of the evolution of the situation in different scenarios for decision making of crisis crew, which make the crucial decisions necessary to manage epidemics and pandemics. Modelling the spread of infectious diseases is currently a very actual topic.
Different types of theoretically justified mathematical models that have been experimentally verified in the past are used to predict the evolution of the epidemic. Some of them are also studied at the Institute of Mathematical Sciences and the Institute of Informatics of the Faculty of Science, UPJŠ. A simple example of the current pandemic evolution model that can be used to roughly predict is at: https://kiselak.shinyapps.io/corona/.
This model is based on real data available, shows the expected development of the epidemic (mainly the number of infected persons) in different countries and is based on the basic epidemiological SIR model. It is one of the simplest models of the spread of infectious diseases and is therefore very illustrative. Overall modeling required the use of several areas of mathematics such as dynamic systems, numerical mathematics, mathematical statistics and optimization. Based on this method, we can predict the time course of the number of infected, the duration of the epidemic or determine the critical limit of collective immunity or the basic reproductive number. In order to create a more accurate model, we would need more comprehensive data (population migration, relapses, preventive measures, age and health of the infected, etc.). However, it is almost impossible to estimate exactly how many people are infected as in any task where human behavior comes into play.
So far, mathematical models have been applied in various fields at the Institute of Mathematical Sciences and the Institute of Informatics, for example in distinguishing between malignant and benign tumor types (stochastic evolution equations), identifying different types of cyber attacks (methods of cluster analysis), modeling a transplant waiting list (stochastic models), in determining the state of methane and carbon dioxide emissions of swamp ecosystems (dynamic systems), modeling the development of gasoline prices or electricity consumption (economic time series).
Study programs offered by the Faculty of Science, UPJŠ in Košice are linked to this research. These are mainly study programs: Mathematics, Economic and Financial Mathematics, Data Analysis and Artificial Intelligence, Informatics and Applied Informatics. Graduates of these programs are able to model real situations similar to the current situation with the COVID-19 epidemic.
Those interested in this topic can learn more at the DAM seminar and weekend meetings called the Data Days.
