| [1] |
Vabret, N.; Britton, G. J.; Gruber, C.; Hegde, S.; Kim, J.; Kuksin, M.; Levantovsky, R.; Malle, L.; Moreira, A.; Park, M. D.; Pia, L.; Risson, E.; Saffern, M.; Salome, B.; Selvan, M. E.; Spindler, M. P.; Tan, J.; van der Heide, V.; Gregory, J. K.; Alexandropoulos, K.; Bhardwaj, N.; Brown, B. D.; Greenbaum, B.; Gumus, Z. H.; Homann, D.; Horowitz, A.; Kamphorst, A. O.; de Lafaille, M. A.C.; Mehandru, S.; Merad, M.; Samstein, R. M.; Project, S. I.R., Immunology of COVID-19: current state of the science, Immunity, 52, 6, 910-941 (2020) |
| [2] |
Goodell, J. W., COVID-19 and finance: agendas for future research, Finance Res. Lett., 35 (2020) |
| [3] |
Sharifi, A.; Khavarian-Garmsir, A. R., The COVID-19 pandemic: impacts on cities and major lessons for urban planning, design, and management, Sci. Total Environ., 749, 142391 (2020) |
| [4] |
Cruz, C. H.d. B., Social distancing in São Paulo State: demonstrating the reduction in cases using time series analysis of deaths due to COVID-19, Rev. Bras. Epidemiol., 23, e200056 (2020) |
| [5] |
Flaxman, S.; Mishra, S.; Gandy, A.; Unwin, H. J.T.; Mellan, T. A.; Coupland, H.; Whittaker, C.; Zhu, H.; Berah, T.; Eaton, J. W.; Monod, M.; Ghani, A. C.; Donnelly, C. A.; Riley, S.; Vollmer, M. A.C.; Ferguson, N. M.; Okell, L. C.; Bhatt, S., Estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe, Nature, 584, 7820, 257-261 (2020) |
| [6] |
Dong, E.; Du, H.; Gardner, L., An interactive web-based dashboard to track COVID-19 in real time, Lancet Infect. Dis., 20, 5, 533-534 (2020) |
| [7] |
Diekmann, O.; Heesterbeek, H.; Britton, T., Mathematical tools for understanding infectious diseases dynamics, Princeton Series in Theoretical and Computational Biology (2013), Princeton University Press · Zbl 1304.92009 |
| [8] |
Hethcote, H. W., The mathematics of infectious diseases, SIAM Rev., 42, 4, 599-653 (2000) · Zbl 0993.92033 |
| [9] |
He, S.; Peng, Y.; Sun, K., SEIR modeling of the COVID-19 and its dynamics, Nonlinear Dyn., 101, 3, SI, 1667-1680 (2020) |
| [10] |
S. Bhatt, N. Ferguson, S. Flaxman, A. Gandy, S. Mishra, J.A. Scott, Semi-mechanistic Bayesian modeling of COVID-19 with renewal processes, 2020, arXiv:2012.00394 |
| [11] |
Champredon, D.; Dushoff, J.; Earn, D. J.D., Equivalence of the erlang-distributed SEIR epidemic model and the renewal equation, SIAM J. Appl. Math., 78, 6, 3258-3278 (2018) · Zbl 1404.92173 |
| [12] |
Bailey, N. T.J., The Mathematical Theory of Epidemics (1957), Charles Griffin & Co., Ltd., London |
| [13] |
Viboud, C.; Simonsen, L.; Chowell, G., A generalized-growth model to characterize the early ascending phase of infectious disease outbreaks, Epidemics, 15, 27-37 (2016) |
| [14] |
Abbasi, M.; Bollini, A.; Castillo, J.; Deppman, A.; Guidio, J.; Matuoka, P.; Meirelles, A.; Policarpo, J.; Ramos, A.; Simionatto, S.; Varona, A.; Andrade-II, E.; Panjeh, H.; Trevisan, L., Fractal signatures of the COVID-19 spread, Chaos, Solitons Fractals, 140, 110119 (2020) · Zbl 1495.92066 |
| [15] |
Jahanshahi, H.; Munoz-Pacheco, J. M.; Bekiros, S.; Alotaibi, N. D., A fractional-order SIRD model with time-dependent memory indexes for encompassing the multi-fractional characteristics of the COVID-19, Chaos, Solitons Fractals, 143 (2021) |
| [16] |
Vasconcelos, G.; Macêdo, A.; Duarte-Filho, G., Power law behaviour in the saturation regime of fatality curves of the COVID-19 pandemic, Sci. Rep., 11, 4619 (2021) |
| [17] |
Padhy, S.; Dimri, V. P., Apparent scaling of virus surface roughness—An example from the pandemic SARS-nCoV, Physica D, 414, 132704 (2020) |
| [18] |
Thurner, S.; Klimek, P.; Hanel, R., A network-based explanation of why most COVID-19 infection curves are linear, Proc. Natl. Acad. Sci., 117, 37, 22684-22689 (2020) · Zbl 1485.92159 |
| [19] |
Kabir, K. A.; Kuga, K.; Tanimoto, J., Analysis of sir epidemic model with information spreading of awareness, Chaos, Solitons Fractals, 119, 118-125 (2019) · Zbl 1448.92302 |
| [20] |
Kuga, K.; Tanimoto, J., Effects of void nodes on epidemic spreads in networks, Sci. Rep., 12, 1, 3957 (2022) |
| [21] |
Tanimoto, J., Sociophysics Approach to Epidemics, vol. 23 (2021), Springer · Zbl 1495.92002 |
| [22] |
Newman, M. E., The structure and function of complex networks, SIAM Rev., 45, 2, 167-256 (2003) · Zbl 1029.68010 |
| [23] |
Barabási, A.-L.; Albert, R., Emergence of scaling in random networks, Science, 286, 5439, 509-512 (1999) · Zbl 1226.05223 |
| [24] |
Albert, R.; Barabási, A. L., Statistical mechanics of complex networks, Rev. Mod. Phys., 74, 47-97 (2002) · Zbl 1205.82086 |
| [25] |
Song, C.; Havlin, S.; Makse, H. A., Self-similarity of complex networks, Nature, 433, 392 (2005) |
| [26] |
Kopelman, R., Fractal reaction kinetics, Science, 241, 4873, 1620-1626 (1988) |
| [27] |
A. Deppman, E.O.A. Segundo, Flux of information in scale-free networks, 2021, arXiv:2106.08959 |
| [28] |
Keeling, M. J.; Eames, K. T.D., Networks and epidemic models, J. R. Soc. Interface, 2, 295-307 (2005) |
| [29] |
Pastor-Satorras, R.; Castellano, C.; Mieghem, P. V.; Vespignani, A., Epidemic processes in complex networks, Rev. Mod. Phys., 87, 925-979 (2015) |
| [30] |
Pastor-Satorras, R.; Vespignani, A., Epidemic spreading in scale-free networks, Phys. Rev. Lett., 86, 3200-3203 (2001) |
| [31] |
Kosmidis, K.; Macheras, P., A fractal kinetics SI model can explain the dynamics of COVID-19 epidemics, PLoS One, 15 (2020) |
| [32] |
Abbey, H., An examination of the reed-frost theory of epidemics, Hum. Biol., 24, 3, 201 (1952) |
| [33] |
Tsallis, C., Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys., 52, 479-487 (1988) · Zbl 1082.82501 |
| [34] |
Tsallis, C.; Tirnakli, U., Predicting COVID-19 peaks around the world, Front. Phys., 8, 217 (2020) |
| [35] |
Tirnakli, U.; Tsallis, C., Epidemiological model with anomalous kinetics: early stages of the COVID-19 pandemic, Front. Phys., 8, 613168 (2020) |
| [36] |
Deppman, A., Thermodynamics with fractal structure, Tsallis statistics, and hadrons, Phys. Rev. D, 93, 5 (2016) |
| [37] |
Deppman, A.; Frederico, T.; Megias, E.; Menezes, D. P., Fractal structure and non-extensive statistics, Entropy, 20, 9 (2018) |
| [38] |
IBGE | Cidades@ | São Paulo | São Caetano do Sul | Panorama, 2021, https://cidades.ibge.gov.br/brasil/sp/sao-caetano-do-sul/panorama. Accessed Jul. 18, 2021. |
| [39] |
Leal, F. E.; Mendes-Correa, M. C.; Buss, L. F.; Costa, S. F.; Bizario, J. C.; De Souza, S. R.; Thomaz, O.; Tozetto-Mendoza, T. R.; Villas-Boas, L. S.; De Oliveira-Da Silva, L. C., Clinical features and natural history of the first 2073 suspected COVID-19 cases in the corona São Caetano primary care programme: a prospective cohort study, BMJ Open, 11, 1, e042745 (2021) |
| [40] |
Peixoto, P. S.; Marcondes, D.; Peixoto, C.; Oliva, S. M., Modeling future spread of infections via mobile geolocation data and population dynamics. An application to COVID-19 in brazil, PLoS One, 15, 7, e0235732 (2020) |
| [41] |
Candido, D. S.; Claro, I. M.; de Jesus, J. G.; Souza, W. M.; Moreira, F. R.; Dellicour, S.; Mellan, T. A.; Plessis, L. D.; Pereira, R. H.; Sales, F. C., Evolution and epidemic spread of SARS-CoV-2 in Brazil, Science, 369, 6508, 1255-1260 (2020) |
| [42] |
Faria, N. R.; Mellan, T. A.; Whittaker, C.; Claro, I. M.; Candido, D.da S.; Mishra, S.; Crispim, M. A.; Sales, F. C.; Hawryluk, I.; McCrone, J. T., Genomics and epidemiology of the P.1 SARS-CoV-2 lineage in Manaus, Brazil, Science, 372, 6544, 815-821 (2021) |
| [43] |
Buss, L. F.; Prete, C. A.; Abrahim, C. M.; Mendrone, A.; Salomon, T.; de Almeida-Neto, C.; França, R. F.; Belotti, M. C.; Carvalho, M. P.; Costa, A. G., Three-quarters attack rate of SARS-CoV-2 in the Brazilian amazon during a largely unmitigated epidemic, Science, 371, 6526, 288-292 (2021) |
| [44] |
e2020GL088748 |
| [45] |
Sabino, E. C.; Buss, L. F.; Carvalho, M. P.; Prete, C. A.; Crispim, M. A.; Fraiji, N. A.; Pereira, R. H.; Parag, K. V.; Peixoto, P.d. S.; Kraemer, M. U., Resurgence of COVID-19 in Manaus, Brazil, despite high seroprevalence, Lancet, 397, 10273, 452-455 (2021) |
| [46] |
Bettencourt, L. M.A., The origins of scaling in cities, Science, 340, 6139, 1438-1441 (2013) · Zbl 1355.91063 |
| [47] |
Bettencourt, L. M.A.; Lobo, J.; Helbing, D.; Kühnert, C.; West, G. B., Growth, innovation, scaling, and the pace of life in cities, Proc. Natl. Acad. Sci., 104, 17, 7301-7306 (2007) |
| [48] |
Batty, M., A theory of city size, Science, 340, 6139, 1418-1419 (2013) |
| [49] |
Parag, K.; Donnelly, C., Using information theory to optimise epidemic models for real-time prediction and estimation, PLoS Comput. Biol., 16, e1007990 (2020) |
| [50] |
Gonçalves, B.; Perra, N.; Vespignani, A., Modeling users’ activity on twitter networks: validation of Dunbar’s number, PLoS One, 6 (2011) |
| [51] |
Adrian, Z.; Tymon, M., A new extraordinary means of appeal in the Polish criminal procedure: the basic principles of a fair trial and a complaint against a cassatory judgment, AJEE, 6, 1-18 (2023) |
| [52] |
Backstrom, L.; Boldi, P.; Rosa, M.; Ugander, J.; Vigna, S., Four degrees of separation, Proceedings of the 3rd Annual ACM Web Science Conference, 33-42 (2012) |
| [53] |
Wang, Z.; Yang, Z.; Shan, H.; Shi, J., A measurement analysis of information propagation in online social network, 2013 Third International Conference on Instrumentation, Measurement, Computer, Communication and Control, 23-27 (2013) |
| [54] |
Leskovec, J.; Lang, K. J.; Dasgupta, A.; Mahoney, M. W., Statistical properties of community structure in large social and information networks, Proceedings of the 17th International Conference on World Wide Web, ACM, New York, NY, USA (2008) |
| [55] |
Kwak, H.; Lee, C.; Park, H.; Moon, S., What is twitter, a social network or a news media?, Proceedings of the 19th International Conference on World Wide Web, ACM, New York, NY, USA (2010) |
| [56] |
Leung, K.; Jit, M.; Lau, E. H.Y.; Wu, J. T., Social contact patterns relevant to the spread of respiratory infectious diseases in Hong Kong, Sci. Rep., 7, 7974 (2017) |
| [57] |
Mossong, J.; Hens, N.; Jit, M.; Beutels, P.; Auranen, K.; Mikolajczyk, R.; Massari, M.; Salmaso, S.; Tomba, G. S.; Wallinga, J.; Heijne, J.; Sadkowska-Todys, M.; Rosinska, M.; Edmunds, W. J., Social contacts and mixing patterns relevant to the spread of infectious diseases, PLoS Med., 5, 3, e74 (2008) |
| [58] |
McAloon, C. G.; Wall, P.; Butler, F.; Codd, M.; Gormley, E.; Walsh, C.; Duggan, J.; Murphy, T. B.; Nolan, P.; Smyth, B.; O’Brien, K.; Teljeur, C.; Green, M. J.; O’Grady, L.; Culhane, K.; Buckley, C.; Carroll, C.; Doyle, S.; Martin, J.; More, S. J., Numbers of close contacts of individuals infected with SARS-CoV-2 and their association with government intervention strategies, BMC Public Health, 21, 1, 2238 (2021) |
| [59] |
Gimma, A.; Munday, J. D.; Wong, K. L.M.; Coletti, P.; van Zandvoort, K.; Prem, K., CMMID COVID-19 working group, (Klepac, P.; Rubin, G. J.; Funk, S.; Edmunds, W. J.; Jarvis, C. I., Changes in Social Contacts in England During the COVID-19 Pandemic Between March 2020 and March 2021 as Measured by the CoMix Survey: A Repeated Cross-Sectional Study, PLoS Med., vol. 19 (2022)), e1003907 |
| [60] |
Presença das linhagens por estado, 2021, http://www.genomahcov.fiocruz.br/presenca-das-linhagens-por-estado/. Accessed Jul. 26, 2021. |
| [61] |
Albert, R.; Barabási, A. L., Topology of evolving networks: local events and universality, Phys. Rev. Lett., 85, 5234-5237 (2000) |
| [62] |
Gong, H.; Guo, C.; Liu, Y., Measuring network rationality and simulating information diffusion based on network structure, Physica A, 564, 125501 (2021) |
| [63] |
Hamilton, M. J.; Milne, B. T.; Walker, R. S.; Burger, O.; Brown, J. H., The complex structure of hunter-gatherer social networks, Proc. R. Soc. B., 274, 2195-2203 (2007) |
| [64] |
Girvan, M.; Newman, M. E.J., Community structure in social and biological networks, Proc. Natl. Acad. Sci., 99, 12, 7821-7826 (2002) · Zbl 1032.91716 |
| [65] |
Youn, H.; Bettencourt, L. M.A.; Lobo, J.; Strumsky, D.; Samaniego, H.; West, G. B., Scaling and universality in urban economic diversification, J. R. Soc. Interface, 13, 114, 20150937 (2016) |
| [66] |
Brockmann, D.; Theis, F., Money circulation, trackable items, and the emergence of universal human mobility patterns, IEEE Pervasive Comput., 7, 4, 28-35 (2008) |
| [67] |
West, G. B.; Brown, J. H.; Enquist, B. J., The fourth dimension of life: fractal geometry and allometric scaling of organisms, Science, 284, 5420, 1677-1679 (1999) · Zbl 1226.37058 |
| [68] |
Cohen, R.; Erez, K.; ben Avraham, D.; Havlin, S., Resilience of the internet to random breakdowns, Phys. Rev. Lett., 85, 4626-4628 (2000) |
