Abstract
In this paper, we propose the use of Cellular Automata paradigm to simulate an infectious disease outbreak. The simulator facilitates the study of dynamics of epidemics of different infectious diseases, and has been applied to study the effects of spread vaccination and ring vaccination strategies. Fundamentally the simulator loosely simulates SIR (Susceptible Infected Removed) and SEIR (Susceptible Exposed Infected Removed). The Geo-spatial model with global interaction and our approach of global stochastic cellular automata are also discussed. The global stochastic cellular automata takes into account the demography, culture of a region. The simulator can be used to study the dynamics of disease epidemics over large geographic regions. We analyze the effects of distances and interaction on the spread of various diseases.
Keywords: Cellular Automaton, Contact Rate, Infectious Period, Global Interaction, Infectious Disease Outbreak
Contributor Information
Thomas Böhme, Email: thomas.boehme@tu-ilmenau.de.
Victor M. Larios Rosillo, Email: vlarios@acm.org
Helena Unger, Email: helena@cucea.udg.mx.
Herwig Unger, Email: hunger@informatik.uni-rostock.de.
Sangeeta Venkatachalam, Email: venkatac@cs.unt.edu.
Armin R. Mikler, Email: mikler@cs.unt.edu
References
- 1.Ahmed E., Agiza H.N. On Modeling epidemics. Including latency, incubation and variable susceptibility Physica A. 1998;253:347–352. [Google Scholar]
- 2.Ahmed E., Elgazzar A.S. On some applications of cellular automata. Physica A. 2002;296:529–538. doi: 10.1016/S0378-4371(01)00182-0. [DOI] [Google Scholar]
- 3.Bagni R., Berchi R., Cariello P. A comparison of simulation models applied to epidemics. Journal of Artificial Societies and Social Simulation. 2002;5:3. [Google Scholar]
- 4.Barfoot, T.D., D’Eleuterio, G.M.T.: Multiagent Coordination by Stochastic Cellular Automata. Presented at the International Joint Conference on Artificial Intelligence (2001)
- 5.Boccara N., Cheong K. Critical behavior of a probabilistic automata network SIS model for the spread of an infectious disease in a population of moving individuals. Journal of Physics A :Mathematical and General. 1993;26(5):3707–3717. doi: 10.1088/0305-4470/26/15/020. [DOI] [Google Scholar]
- 6.Boccara N., Cheong K., Oram M. A probabilistic automata network epidemic model with births and deaths exhibiting cyclic behavior. Journal of Physics A :Mathematical and General. 1994;27:1585–1597. doi: 10.1088/0305-4470/27/5/022. [DOI] [Google Scholar]
- 7.Del Giudice, G.: Vaccine. 21 Suppl 2:S83-8 (2003) [DOI] [PubMed]
- 8.Stefano B.D., Fukś H., Lawniczak A.T. 2000 Canadian Conference on electrical and Computer Engineering. Los Alamitos: IEEE; 2000. Object-oriented implementation of CA/LGCA modelling applied to the spread of epidemics; pp. 26–31. [Google Scholar]
- 9.Fukś H., Lawniczak A.T. Individual-based lattice model for spatial spread of epidemics. Discrete Dynamics in Nature and Society. 2001;6:191–200. doi: 10.1155/S1026022601000206. [DOI] [Google Scholar]
- 10.Situngkir, H.: Epidemiology through Cellular Automata Case of Study: Avian Influenza Indonesia Working Paper WPF, Bandung Fe Institute (2004)
- 11.Thomas J.C., Weber D.J. Epidemiologic Methods for the Study of Infectious Diseases. Oxford: Oxford Press; 2001. [Google Scholar]
- 12.Kleczkowski A., Grenfell B.T. Mean-field-type equations for spread of epidemics: The ‘small world’ model. Physica A. 1999;274(1-2):355–360. doi: 10.1016/S0378-4371(99)00393-3. [DOI] [Google Scholar]
- 13.Mansilla, R., Gutierrez, J.L.: Deterministic site exchange cellular automata models for the spread of diseases in human settlements. Bulletin of Mathematical Biology
- 14.Fu, S.C., Milne, G.: Epidemic Modelling Using Cellular Automata. To appear in Australian Conference on Artificial Life (2003)
- 15.Wolfram, S.: Statistical Mechanics of Cellular Automata. Reviews of Modern. Physics 55, 601–644
- 16.Yaganehdoost A., Graviss E.A., Ross M.W., et al. Complex transmission dynamics of clonally related virulent Mycobacterium tuberculosis associated with barhopping by predominantly human immunodeficiency virus-positive gay men. Journal of Infect Diseases. 1999;180(4):1245–1251. doi: 10.1086/314991. [DOI] [PubMed] [Google Scholar]
- 17.Youngblut, C.: Educational uses of virtual reality technology. Technical Report IDA Document D-2128, Institute for Defense Analyses, Alexandria, VA (1998)