SOME ASPECTS ABOUT MATHEMATICAL MODELING FOR EPIDEMIC MANAGEMENT

Abstract

The mathematical study of epidemics and their management has been performed for many years, however, in the last few years, new models have been published. Public health is considered very important and has to be monitored, as it is permanently under risk due to the appearance of even more types of microorganisms. Compartmental models, such as exponential models, SI, SIS, SIR, SEIRS, SEIAR, MESIR models, other generalized SIR models were and still are remarkable for studying the spread of an epidemic and for their simulations in software such as MATLAB, Maple, GLEAMviz, etc. The paper has two main objectives: a. to present new simulations in Maple and GLEAMviz for the spread of COVID-19; b. to suggest a generalization of the SIR model for analyzing the spread of COVID-19 and a simulation of it in GLEAMviz. The conclusions are that, generally, mathematical models show a value of a reproduction threshold, which can be used to forecast whether the pandemic is the increasing or decreasing phase, and that mathematical models and simulations in various programs facilitate the improvement of methods of analysis of an epidemic situation and the management of the public health system.

Keywords

• mathematical modeling, epidemiological dynamics, covid-19, maple, gleamviz