Abstract
In this paper a Spatial Markov Chain Cellular Automata model for the spread of viruses is proposed. The model is based on a graph with connected nodes, where the nodes represent individuals and the connections between the nodes denote the relations between humans. In this way, a graph is connected where the probability of infectious spread from person to person is determined by the intensity of interpersonal contact. Infectious transfer is determined by chance. The model is extended to incorporate various lockdown scenarios. Simulations with different lockdowns are provided. In addition, under logistic regression, the probability of death as a function of age and gender is estimated, as well as the duration of the disease given that an individual dies from it. The estimations have been done based on actual data of RIVM (from the Netherlands).
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References
worldometer. COVID-19 CORONAVIRUS PANDEMIC. https://www.worldometers.info/coronavirus/?utm_campaign=homeAdvegas1?%22%20%5Cl%20%22countries
WHO. Naming the coronavirus disease (COVID-19) and the virus that causes it (2020). https://www.who.int/emergencies/diseases/novel-coronavirus-2019/technical-guidance/naming-the-coronavirus-disease-(covid-2019)-and-the-virus-that-causes-it
Staff, M.C.: Covid-19 (coronavirus): Long-term effects, May 2021. https://www.mayoclinic.org/diseases-conditions/coronavirus/in-depth/coronavirus-long-term-effects/art-20490351
Kermack, W.O., McKendrick, A.G.: A contribution to the mathematical theory of epidemics. In: Proceedings of the royal society of London. Series A, Containing Papers of a Mathematical and Physical Character, vol. 115, no. 772, pp. 700–721 (1927)
Getz, W.M., Salter, R., Muellerklein, O., Yoon, H.S., Tallam, K.: Modeling epidemics: a primer and numerus model builder implementation. Epidemics 25, 9–19 (2018)
Alleman, T.W., Vergeynst, J., De Visscher, L., Rollier, M., Torfs, E., Nopens, I., Baetens, J.: Assessing the effects of non-pharmaceutical interventions on SARS-CoV-2 transmission in Belgium by means of an extended SEIQRD model and public mobility data. Epidemics 37, 100505 (2021)
Allen, L.J.: A primer on stochastic epidemic models: formulation, numerical simulation, and analysis. Infect. Dis. Model. 2(2), 128–142 (2017)
Pellis, L., et al.: Eight challenges for network epidemic models. Epidemics 10, 58–62 (2015)
Walters, C.E., Meslé, M.M., Hall, I.M.: Modelling the global spread of diseases: a review of current practice and capability. Epidemics 25, 1–8 (2018)
Duan, W., Fan, Z., Zhang, P., Guo, G., Qiu, X.: Mathematical and computational approaches to epidemic modeling: a comprehensive review. Front. Comput. Sci. 9(5), 806–826 (2014). https://doi.org/10.1007/s11704-014-3369-2
Britton, T.: Stochastic epidemic models: a survey. Math. Biosci. 225(1), 24–35 (2010)
O’Neill, P.D.: A tutorial introduction to Bayesian inference for stochastic epidemic models using Markov chain monte Carlo methods. Math. Biosci. 180(1–2), 103–114 (2002)
Vermolen, F., Pölönen, I.: Uncertainty quantification on a spatial markov-chain model for the progression of skin cancer. J. Math. Biol. 80(3), 545–573 (2020)
Chen, F.: Better modelling of infectious diseases: lessons from covid-19 in china. BMJ 375, 2363 (2021)
Fanelli, D., Piazza, F.: Analysis and forecast of covid-19 spreading in china, Italy and France. Chaos, Solitons Fractals 134, 109761 (2020)
Yang, C., Wang, J.: A mathematical model for the novel coronavirus epidemic in Wuhan, china. Math. Biosci. Eng. 17(3), 2708–2724 (2020)
Caccavo, D.: Chinese and italian covid-19 outbreaks can be correctly described by a modified sird model, medRxiv (2020)
Al-Raeei, M.: The forecasting of covid-19 with mortality using SIRD epidemic model for the united states, Russia, China, and the Syrian Arab republic. AIP Adv. 10(6), 065325 (2020)
Rajagopal, K., Hasanzadeh, N., Parastesh, F., Hamarash, I.I., Jafari, S., Hussain, I.: A fractional-order model for the novel coronavirus (covid-19) outbreak. Nonlinear Dyn. 101(1), 711–718 (2020)
Lan, L., et al.: Positive RT-PCR test results in patients recovered from COVID-19. JAMA 323(15), 1502–1503 (2020). https://doi.org/10.1001/jama.2020.2783
Agel, F.: Antibodies, immunity low after COVID-19 recovery. https://www.dw.com/en/coronavirus-antibodies-immunity/a-54159332
Cooper, I., Mondal, A., Antonopoulos, C.G.: A sir model assumption for the spread of covid-19 in different communities. Chaos, Solitons Fractals 139, 110057 (2020)
Grimm, V., Heinlein, A., Klawonn, A., Lanser, M., Weber, J.: Estimating the time-dependent contact rate of sir and seir models in mathematical epidemiology using physics-informed neural networks,” Universität zu Köln, Technical Report, September 2020. https://kups.ub.uni-koeln.de/12159/
Irons, N.J., Raftery, A.E.: Estimating sars-cov-2 infections from deaths, confirmed cases, tests, and random surveys. In: Proceedings of the National Academy of Sciences, vol. 118, no. 31 (2021). https://www.pnas.org/content/118/31/e2103272118
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Lu, J., Vermolen, F. (2023). A Spatial Markov Chain Cellular Automata Model for the Spread of Viruses. In: Tavares, J.M.R.S., Bourauel, C., Geris, L., Vander Slote, J. (eds) Computer Methods, Imaging and Visualization in Biomechanics and Biomedical Engineering II. CMBBE 2021. Lecture Notes in Computational Vision and Biomechanics, vol 38. Springer, Cham. https://doi.org/10.1007/978-3-031-10015-4_1
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