Effects of Interactions Between Individuals and Spatial Dynamics on The Spread of Infectious Diseases using Voronoi Tessellation and The Ising Model
Öz
This study investigates the spatial distribution of individuals within a randomly distributed sample population and their interactions with an infectious disease. For this purpose, an Ising model enhanced with Voronoi tessellation is used to create a more realistic framework for modeling disease spread. The model simulates the process of spreading infectious disease by considering the interactions between individuals and their movement dynamics. The sample population in this study was created for simulation purposes only and is not based on actual demographic of epidemiological data. To assess the infectiousness in the model, the parameter J, defined as the transmission coefficient, is analyzed.
Anahtar Kelimeler
Voronoi Tessellation Ising Model Monte Carlo Simulations Metropolis Algorithm Disease Spread Epidemiological Modeling
Etik Beyan
The study is complied with research and publication ethics.
Destekleyen Kurum
Fırat University Scientific Research Projects (BAP) Coordination Unit
Proje Numarası
FF.24.21
Teşekkür
This study is derived from the Master’s thesis of the first authors, titled “Dynamical Modeling of an Infectious Disease Using an Ising Model Constructed on Voronoi Tessellation”, and was supported by Fırat University Scientific Research Projects (BAP) Coordination Unit (Project No. FF.24.21).
Kaynakça
- R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, 1992.
- C. J. L. Murray, Epidemiology of Infectious Disease. WHO Publications, 2013.
- S. Hsiang, et al., “The Effect of Large-Scale Anti-Contagion Policies on the COVID-19 Pandemic”, Nature, 2020, pp. 262-267.
- D. Herlihy, The Black Death and the Transformation of the West. Harvard University Press.
- N. P. Jonhson, J. Mueller, “Updating the Accounts: Global Mortality of the 1918-1920 ‘Spanish’ Influenza Pandemic”, Bulletin of the History of Medicine, 2002, pp. 105-115.
- P. Piot, et al., “HIV/AIDS in Africa: Global Responses and Challenges”, Science, 2001, pp. 2149-2150.
- S. M. Kissler, et al., “Projecting the Transmission Dynamics of SARS-CoV-2 through the Postpandemic Period”, Science, 2020, pp. 860-868.
- F. Brauer, et al., Mathematical Models in Epidemiology. Springer, 2012.
- K. Dietz, J. A. P. Heesterbeek, “Daniel Bernoulli’s Epidemiological Model Revisited”, Mathematical Biosciences, 2002, pp. 1-21.
- W. O. Kermack, and A. G. McKendrick, “A Contribution to the Mathematical Theory of Epidemics”, Proceeding of the Royal Society A, 1927, pp. 700-721.
- M. Keeling, and P. Rohani, Modeling Infectious Disease in Humans and Animals. Princeton University Press, 2008.
- Z. Fengi, "Applications of SEIR Models in Epidemiology", Advances in Epidemiological Modeling, 2007, pp. 97-112.
- R. Singh, S. Ali, M. Jain, A. A. Raina, “Mathematical Model for Malaria with Mosquito-Dependent Coefficient for Human Population with Exposed Class”, Journal of the National Science Foundation of Sri Lanka, 2019, pp. 185-198.
- A. A. Raina, S. Ali, P. Kalra, U. M. Modibbo, “A Mathematical Model of Logistic Human Population Growth and Vector Population for Dengue Transmission Dynamics”, Journal of the Egyptian Society, 2024, pp. 23-55.
- O. Diekmann, et al., Mathematical Tools for Understanding Infectious Disease Dynamics. Princeton University Press, 2013.
- V. Colizza, et al., “Modeling the Worldwide Spread of Pandemic Influenza: Baseline Case and Containment Interventions”, PLoS Medicine, 2007.
- A. Okabe, B. Boots, K. Sugihara, S. N. Chiu, Spatial Tessellations: Concepts and Applications of Voronoi Diagrams. John Wiley & Sons, 2009.
- M. Menezes, et al., "Using Voronoi Diagrams for Spatial Dynamics in Disease Modeling”, Journal of Spatial Simulation, 2010.
- B. Boots, et al., “Voronoi Tessellation and Its Applications in Spatial Modeling”, Geographical Analysis, 2006.
- T. Suzuki, and N. Egami, “Applications of Voronoi Diagrams in Neuron Distribution Analysis”, Computational Biology, 2006.
- E. Ising, “Beitrag zur Theorie des Ferromagnetismus”, Zeitschrift für Physik, 1925, pp. 253-258.
- S. G. Brush, “History of the Lenz-Ising Model”, Review of Modern Physics, 1967, pp. 883-893.
- R. J. Glauber, “Time-dependent Statistics of the Ising Model”, 1963, pp. 294-307.
- L. Onsager, “Crystal Statistics. I. A Two-dimensional Model with an Order-Disorder Transition”, Physical Review Journals Archive, 1944, pp. 117-149.
- C. Castellano, S. Fortunato, and V. Loreto, “Statistical Physics of Social Dynamics”, Review of Modern Physics, 2009, pp. 591-646.
Öz
Proje Numarası
FF.24.21
Kaynakça
- R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, 1992.
- C. J. L. Murray, Epidemiology of Infectious Disease. WHO Publications, 2013.
- S. Hsiang, et al., “The Effect of Large-Scale Anti-Contagion Policies on the COVID-19 Pandemic”, Nature, 2020, pp. 262-267.
- D. Herlihy, The Black Death and the Transformation of the West. Harvard University Press.
- N. P. Jonhson, J. Mueller, “Updating the Accounts: Global Mortality of the 1918-1920 ‘Spanish’ Influenza Pandemic”, Bulletin of the History of Medicine, 2002, pp. 105-115.
- P. Piot, et al., “HIV/AIDS in Africa: Global Responses and Challenges”, Science, 2001, pp. 2149-2150.
- S. M. Kissler, et al., “Projecting the Transmission Dynamics of SARS-CoV-2 through the Postpandemic Period”, Science, 2020, pp. 860-868.
- F. Brauer, et al., Mathematical Models in Epidemiology. Springer, 2012.
- K. Dietz, J. A. P. Heesterbeek, “Daniel Bernoulli’s Epidemiological Model Revisited”, Mathematical Biosciences, 2002, pp. 1-21.
- W. O. Kermack, and A. G. McKendrick, “A Contribution to the Mathematical Theory of Epidemics”, Proceeding of the Royal Society A, 1927, pp. 700-721.
- M. Keeling, and P. Rohani, Modeling Infectious Disease in Humans and Animals. Princeton University Press, 2008.
- Z. Fengi, "Applications of SEIR Models in Epidemiology", Advances in Epidemiological Modeling, 2007, pp. 97-112.
- R. Singh, S. Ali, M. Jain, A. A. Raina, “Mathematical Model for Malaria with Mosquito-Dependent Coefficient for Human Population with Exposed Class”, Journal of the National Science Foundation of Sri Lanka, 2019, pp. 185-198.
- A. A. Raina, S. Ali, P. Kalra, U. M. Modibbo, “A Mathematical Model of Logistic Human Population Growth and Vector Population for Dengue Transmission Dynamics”, Journal of the Egyptian Society, 2024, pp. 23-55.
- O. Diekmann, et al., Mathematical Tools for Understanding Infectious Disease Dynamics. Princeton University Press, 2013.
- V. Colizza, et al., “Modeling the Worldwide Spread of Pandemic Influenza: Baseline Case and Containment Interventions”, PLoS Medicine, 2007.
- A. Okabe, B. Boots, K. Sugihara, S. N. Chiu, Spatial Tessellations: Concepts and Applications of Voronoi Diagrams. John Wiley & Sons, 2009.
- M. Menezes, et al., "Using Voronoi Diagrams for Spatial Dynamics in Disease Modeling”, Journal of Spatial Simulation, 2010.
- B. Boots, et al., “Voronoi Tessellation and Its Applications in Spatial Modeling”, Geographical Analysis, 2006.
- T. Suzuki, and N. Egami, “Applications of Voronoi Diagrams in Neuron Distribution Analysis”, Computational Biology, 2006.
- E. Ising, “Beitrag zur Theorie des Ferromagnetismus”, Zeitschrift für Physik, 1925, pp. 253-258.
- S. G. Brush, “History of the Lenz-Ising Model”, Review of Modern Physics, 1967, pp. 883-893.
- R. J. Glauber, “Time-dependent Statistics of the Ising Model”, 1963, pp. 294-307.
- L. Onsager, “Crystal Statistics. I. A Two-dimensional Model with an Order-Disorder Transition”, Physical Review Journals Archive, 1944, pp. 117-149.
- C. Castellano, S. Fortunato, and V. Loreto, “Statistical Physics of Social Dynamics”, Review of Modern Physics, 2009, pp. 591-646.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Biyolojik Matematik |
| Bölüm | Research Article |
| Yazarlar | |
| Proje Numarası | FF.24.21 |
| Erken Görünüm Tarihi | 27 Haziran 2025 |
| Yayımlanma Tarihi | 30 Haziran 2025 |
| Gönderilme Tarihi | 13 Kasım 2024 |
| Kabul Tarihi | 24 Haziran 2025 |
| Yayımlandığı Sayı | Yıl 2025 Cilt: 14 Sayı: 2 |
