The authors propose a small-world network model that combines cellular automata with the social mirror identities of daily-contact networks for purposes of performing epidemiological simulations. The social mirror identity concept was established to integrate human long-distance movement and daily visits to fixed locations. After showing that the model is capable of displaying such small-world effects as low degree of separation and relatively high degree of clustering on a societal level, the authors offer proof of its ability to display R0 properties—considered central to all epidemiological studies. To test their model, they simulated the 2003 severe acute respiratory syndrome (SARS) outbreak.
Masuda, N. , N. Konno , and K. Aihara . 2004. Transmission of severe acute respiratory syndrome in dynamical small-world networks . Physical Review E69: 031917 .
2.
Newman, M. E. J.2002. Spread of epidemic disease on networks . Physical Review E66: 016128 .
3.
Ahmed, E. , A. S. Hegazi , and A. S. Elgazzar . 2002. An epidemic model on small-world networks and ring vaccination . International Journal of Modern Physics C13: 189-198 .
4.
Sirakoulis, G. C. , I. Karafyllidis , and A. Thanailakis . 2000. A cellular automaton model for the effects of population movement and vaccination on epidemic propagation . Ecological Modelling133: 209-223 .
5.
Moore, C. , and M. E. J. Newman . 2000. Epidemics and percolation in small-world networks . Physical Review E61: 5678-5682 .
6.
Newman, M. E. J. , I. Jensen , and R. M. Ziff . 2002. Percolation and epidemics in a two-dimensional small world . Physical Review E65: 021904 .
7.
World Health Organization (WHO) . 2003. WHO consensus document on the epidemiology of severe acute respiratory syndrome (SARS). http://www.who.int/csr/sars/en/WHOconsensus.pdf
8.
Kleczkowski, A. , and B. T. Grenfell . 1999. Mean-field-type equations for spread of epidemics: The ’small world’ model . Physica A274: 355-360 .
9.
Kuperman, M. , and G. Abramson . 2001. Small world effect in an epidemiological model . Physical Review Letters86: 2909-2912 .
10.
Sebastian, B. , and C. Hoffmann . 2003. SARS reference. http://www.sarsreference.com
11.
Peiris, J. S. , S. T. Lai , L. L. Poon , Y. Guan , L. Y. Yam , W. Lim , J. Nicholls , W. K. Yee , W. W. Yan , M. T. Cheung , V. C. Cheng , K. H. Chan , D. N. Tsang , R. W. Yung , T. K. Ng , K. Y. Yuen , and SARS Study Group . 2003. Coronavirus as a possible cause of severe acute respiratory syndrome . Lancet361 (9366): 1319-1325 .
12.
Boccara, N. , and K. Cheong . 1993. 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 A26: 3707-3717 .
13.
Boccara, N. , and K. Cheong . 1992. Automata network SIR models for the spread of infectious disease in populations of moving individuals . Journal of Physics A25: 2447-2461 .
14.
Boccara, N. , K. Cheong , and M. Oram . 1994. A Probabilistic-automata network epidemic model with births and deaths exhibiting cyclic behavior . Journal of Physics A27: 1585-1597 .
15.
Miramontes, O. , and B. Luque . 2002. Dynamical small-world behavior in an epidemical model of mobile individuals . Physica D168: 379-385 .
16.
Watts, D. J. , and S. H. Strogatz . 1998. Collective dynamics of ‘small-world’ networks . Nature393: 440-442 .
17.
Newman, M. E. J.2000. Models of the small world: A review . Journal of Statistical Physics101: 819-841 .
18.
Wang, X. F. , and G. Chen . 2003. Complex networks: Small-world, scale-free and beyond . IEEE Circuits and Systems Magazine First Quarter: 6-20 .
19.
Watts, D. J.1999. Small worlds: The dynamics of networks between order and randomness. Princeton, NJ: Princeton University Press .
20.
Kermack, W. O. , and A. G. McKendrick . 1927. Contributions to the mathematical theory of epidemics . Proceedings of the Royal Society of London115: 700-721 .
21.
Edeletein-Keshet, L.1988. Mathematical models in biology. New York: Random House .
22.
Lipsitch, M. , T. Cohen , B. Cooper , J. M. Robins , S. Ma , L. James , G. Gopalakrishna , S. K. Chew , C. C. Tan , M. H. Samore , D. Fisman , and M. Murray . 2003. Transmission dynamics and control of severe acute respiratory syndrome . Science300: 1966-1970 .
23.
Riley, S. , C. Fraser , C. A. Donnelly , A. C. Ghani , L. J. Abu-Raddad , A. J. Hedley , G. M. Leung , L. M. Ho , T. H. Lam , T. Q. Thach , P. Chau , K. P. Chan , P.Y. Leung , T. Tsang , W. Ho , K. H. Lee , E. M. C. Lau , N. M. Ferguson , and R. M. Anderson . 2003. Transmission dynamics of the etiological agent of SARS in Hong Kong: Impact of public health interventions . Science300: 1961-1966 .
24.
Donnelly, C. A. , A. C. Ghani , G. M. Leung , A. J. Hedley , C. Fraser , and S. Riley . 2003. Epidemiological determinants of spread of causal agent of severe acute respiratory syndrome in Hong Kong . Lancet361: 1761-1766 .
25.
Chowell, G. , P.W. Fenimore , M.A. Castillo-Garsow , and C. Castillo-Chavez . 2003. SARS outbreaks in Ontario, Hong Kong and Singapore: The role of diagnosis and isolation as a control mechanism . Journal of Theoretical Biology224: 1-8 .
26.
Ng, T. W. , G. Turinici , and A. Danchin . 2003. A double epidemic model for the SARS propagation . BMC Infectious Disease3 (19): 1-16 .
27.
Anderson, R. M. , and R. M. May . 1982. Directly transmitted infections diseases: Control by vaccination . Science215 (4536): 1053-1060 .
28.
Becker, N. G.1992. Infectious-diseases of humans: Dynamics and control . Australian Journal of Public Health16: 208-209 .
29.
Koopman, J.2004. Modeling infection transmission . Annual Review of Public Health25: 303-326 .
30.
Ahmed, E. , and A. S. Elgazzar . 2001. On some applications of cellular automata . Physica A296: 529-538 .
31.
Erdös, P. , and A. Renyi . 1959. On the evolution of random graphs . Publication of the Mathematical Institute of the Hungarian Academy of Science5: 17-60 .
32.
Benyoussef, A. , N. E. Hafidallah , A. Elkenz , H. Ez-Zahraouy , and M. Loulidi . 2003. Dynamics of HIV infection on 2D cellular automata . Physica A322: 506-520 .
33.
Yacoubi, S. El , and A. El Jai . 2002. Cellular automata modelling and spreadability . Mathematical and Computer Modelling36: 1059-1074 .
34.
Fuentes, M. A. , and M. N. Kuperman . 1999. Cellular automata and epidemiological models with spatial dependence . Physica A267: 471-486 .
35.
Martins, M. L. , G. Ceotto , S. G. Alves , C. C. B. Bufon , J. M. Silva , and F. F. Laranjeira . 2001. A cellular automata model for citrus variegated chlorosis . Physica A295: 42-48 .
36.
Boccara, N. , E. Goles , S. Martinez , and P. Picco . 1993. Cellular automata and cooperative phenomena. Dordrecht, The Netherlands: Kluwer Academic .
37.
Ahmed, E. , and H. N. Agiza . 1998. On modeling epidemics: Including latency, incubation and variable susceptibility . Physica A253: 347-352 .
38.
Rapoport, A.1957. A contribution to the theory of random and biased nets . Bulletin of Mathematical Biophysics19: 257-571 .
39.
Milgram, S.1967. The small world problem . Psychology Today2: 60-67 .
40.
Comellas, F. , and M. Sampels . 2002. Deterministic small-world networks . Physica A309: 231-235 .
41.
Centers for Disease Control and Prevention (CDC) . 2003. SARS: Frequently asked questions. http://www.cdc.gov/mmwr/mguide_sars.html
CDC . 2003. Update: SARS—Worldwide and U.S . Morbidity and Mortality Weekly Report52 (28): 664-665 .
47.
CDC . 2003. Use of quarantine to prevent transmission of SARS—Taiwan . Morbidity and Mortality Weekly Report52 (29): 680-683 .
48.
CDC . 2003. Revised U.S. surveillance case definition for severe acute respiratory syndrome (SARS) and update on SARS cases—United States and worldwide . Morbidity and Mortality Weekly Report52 (49): 1202-1206 .
