Modeling and Visualizing the Dynamic Spread of Epidemic Diseases—The COVID-19 Case

• Published in: AppliedMath 2024-03, Vol.4 (1), p.1-19
• Main Authors: Zachilas, Loukas, Benos, Christos
• Format: Article
• Language: English
• Subjects: COVID-19; epidemics; epidemiology; infection diffusion; lattice simulation; SARS-CoV-2
• ISSN: 2673-9909; 2673-9909
• DOI: 10.3390/appliedmath4010001

Our aim is to provide an insight into the procedures and the dynamics that lead the spread of contagious diseases through populations. Our simulation tool can increase our understanding of the spatial parameters that affect the diffusion of a virus. SIR models are based on the hypothesis that populations are “well mixed”. Our model constitutes an attempt to focus on the effects of the specific distribution of the initially infected individuals through the population and provide insights, considering the stochasticity of the transmission process. For this purpose, we represent the population using a square lattice of nodes. Each node represents an individual that may or may not carry the virus. Nodes that carry the virus can only transfer it to susceptible neighboring nodes. This important revision of the common SIR model provides a very realistic property: the same number of initially infected individuals can lead to multiple paths, depending on their initial distribution in the lattice. This property creates better predictions and probable scenarios to construct a probability function and appropriate confidence intervals. Finally, this structure permits realistic visualizations of the results to understand the procedure of contagion and spread of a disease and the effects of any measures applied, especially mobility restrictions, among countries and regions.