Abstract
The numerical studies of disease spreading processes are almost one-century old. The mainstream of these analyses is based on the ordinary differential equations which enable to estimate, especially, the epidemic curves for some assumed values of parameters describing the aggregate probabilities of passing through different phases if illness. In our paper, we present some results which can be obtained for the more individualized model, based on the analysis of direct interactions between the members of the community. We use the concepts of the SEIR model but we apply the different mechanisms to study the process of transfer of illness based on the representation of the community as the scale-free network. We can obtain the typical epidemic curves, study their spread, and also analyze the epidemic process in the internal groups of the community.
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References
Kermack, W.O., McKendrick, A., Walker, G.T.: A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. A115, 700–721 (1927)
Nakamura, G., Martinez, A.: Hamiltonian dynamics of the SIS epidemic model with stochastic fluctuations. Sci. Rep. 9, 1–9 (2019)
Sirakoulis, G., Karafyllidis, I., Thanailakis, A.: A cellular automaton model for the effects of population movement and vaccination on epidemic propagation. Ecol. Model. 133, 209–223 (2000)
Holko, A., Mędrek, M., Pastuszak, Z., Phusavat, K.: Epidemiological modeling with a population density map-based cellular automata simulation system. Expert Syst. Appl. 48, 1–8 (2016)
Ferguson, N., Cummings, D., Fraser, C., Cajka, J., Cooley, P., Burke, D.: Strategies for mitigating an influenza pandemic. Nature 442, 448–452 (2006)
Ferguson, N., et al.: Impact of non-pharmaceutical interventions (NPIS) to reduce covid19 mortality and healthcare demand. Technical report, Imperial College London (2020)
Aron, J.L., Schwartz, I.B.: Seasonality and period-doubling bifurcations in an epidemic model. J. Theor. Biol. 110, 665–679 (1984)
Erdös, P., Rényi, A.: On random graphs I. Publicationes Mathematicae Debrecen 6, 290 (1959)
Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)
Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)
Gwizdałła, T.M.: Viral disease spreading in grouped population. Comput. Methods Programs Biomed. 197, 105715 (2020)
Linton, N.M., et al.: Incubation period and other epidemiological characteristics of 2019 novel coronavirus infections with right truncation: a statistical analysis of publicly available case data. J. Clin. Med. 9(2020), 538 (2019)
Orzechowska, J., Fordon, D., Gwizdałła, T.M.: Size effect in cellular automata based disease spreading model. In: Mauri, G., El Yacoubi, S., Dennunzio, A., Nishinari, K., Manzoni, L. (eds.) ACRI 2018. LNCS, vol. 11115, pp. 146–153. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-99813-8_13
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Gwizdałła, T.M., Lepa, K. (2021). The Disease Spreading Analysis on the Grouped Network. In: Gwizdałła, T.M., Manzoni, L., Sirakoulis, G.C., Bandini, S., Podlaski, K. (eds) Cellular Automata. ACRI 2020. Lecture Notes in Computer Science(), vol 12599. Springer, Cham. https://doi.org/10.1007/978-3-030-69480-7_25
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DOI: https://doi.org/10.1007/978-3-030-69480-7_25
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