The aim of the article is to develop and apply a modelling system to support decision-making regarding the spread of infectious diseases. The recent course of the COVID-19 pandemic worldwide has emphasised the need for software tools to prevent, analyse, and manage the epidemic process. Although by the time the pandemic began, there were already quite a few mathematical tools for modelling infectious diseases, practical experience with their application revealed their weaknesses and limitations. One of the main shortcomings of mathematical models is the uncertainty of parameters in the case of an epidemic caused by a new, unknown infection. When there is not enough time to conduct medical experiments to determine the properties of the virus, the challenge arises to develop algorithms for calibrating models based on available observational data. This work develops a modelling system for managing the epidemic process, which allows for the prediction of the spread of the COVID-19 viral infection, taking into account the age groups of the population and their spatial heterogeneity. It also includes a parameter optimisation block that allows for flexible adjustment of the model as new information about the virus and new statistical data become available. Model parameter calibration is based on comparing the predicted results with observed data by solving a nonlinear constrained least squares problem. The modelling system was applied to simulate four waves of COVID-19 in Ukraine.