Research article Special Issues

Social contacts, epidemic spreading and health system. Mathematical modeling and applications to COVID-19 infection


  • Received: 18 January 2021 Accepted: 11 April 2021 Published: 15 April 2021
  • Lockdown and social distancing, as well as testing and contact tracing, are the main measures assumed by the governments to control and limit the spread of COVID-19 infection. In reason of that, special attention was recently paid by the scientific community to the mathematical modeling of infection spreading by including in classical models the effects of the distribution of contacts between individuals. Among other approaches, the coupling of the classical SIR model with a statistical study of the distribution of social contacts among the population, led some of the present authors to build a Social SIR model, able to accurately follow the effect of the decrease in contacts resulting from the lockdown measures adopted in various European countries in the first phase of the epidemic. The Social SIR has been recently tested and improved through a fruitful collaboration with the Health Protection Agency (ATS) of the province of Pavia (Italy), that made it possible to have at disposal all the relevant data relative to the spreading of COVID-19 infection in the province (half a million of people), starting from February 2020. The statistical analysis of the data was relevant to fit at best the parameters of the mathematical model, and to make short-term predictions of the spreading evolution in order to optimize the response of the local health system.

    Citation: Mattia Zanella, Chiara Bardelli, Mara Azzi, Silvia Deandrea, Pietro Perotti, Santino Silva, Ennio Cadum, Silvia Figini, Giuseppe Toscani. Social contacts, epidemic spreading and health system. Mathematical modeling and applications to COVID-19 infection[J]. Mathematical Biosciences and Engineering, 2021, 18(4): 3384-3403. doi: 10.3934/mbe.2021169

    Related Papers:

  • Lockdown and social distancing, as well as testing and contact tracing, are the main measures assumed by the governments to control and limit the spread of COVID-19 infection. In reason of that, special attention was recently paid by the scientific community to the mathematical modeling of infection spreading by including in classical models the effects of the distribution of contacts between individuals. Among other approaches, the coupling of the classical SIR model with a statistical study of the distribution of social contacts among the population, led some of the present authors to build a Social SIR model, able to accurately follow the effect of the decrease in contacts resulting from the lockdown measures adopted in various European countries in the first phase of the epidemic. The Social SIR has been recently tested and improved through a fruitful collaboration with the Health Protection Agency (ATS) of the province of Pavia (Italy), that made it possible to have at disposal all the relevant data relative to the spreading of COVID-19 infection in the province (half a million of people), starting from February 2020. The statistical analysis of the data was relevant to fit at best the parameters of the mathematical model, and to make short-term predictions of the spreading evolution in order to optimize the response of the local health system.



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    [1] G. Giordano, F. Blanchini, R. Bruno, P. Colaneri, A. Di Filippo, A. Di Matteo, et al., Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy, Nat. Med., 26 (2020), 855–860.
    [2] M. Gatto, E. Bertuzzo, L. Mari, S. Miccoli, L. Carraro, R. Casagrandi, et al., Spread and dynamics of the COVID-19 epidemic in Italy: Effects of emergency containment measures, PNAS, 117 (2020), 10484–10491.
    [3] W. O. Kermack, A. G. McKendrick, Contributions to the mathematical theory of epidemics, Proc. Roy. Soc. London Ser. A, 115 (1927), 700–721.
    [4] G. Dimarco, L. Pareschi, G. Toscani, M. Zanella, Wealth distribution under the spread of infectious diseases, Phys. Rev. E, 102 (2020), 022303.
    [5] H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42 (2000), 599–653.
    [6] M. Iannelli, F. A. Milner, A. Pugliese, Analytical and numerical results for the age-structured SIS epidemic model with mixed inter-intracohort transmission, SIAM J. Math. Anal., 23 (1992), 662–688.
    [7] E. Dong, H. Du, L. Gardner, An interactive web-based dashboard to track COVID-19 in real time, Lancet Infect. Dis., 20 (2020).
    [8] S. Flaxman, S. Mishra, A. Gandy, H. Juliette, T. Unwin, T. A. Mellan, et al., Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in 11 European countries, Nature, 584 (2020), 257–261.
    [9] G. Beraud, S. Kazmercziak, P. Beutels, D. Levy-Bruhl, X. Lenne, N. Mielcarek, et al., The French connection: The first large population-based contact survey in France relevant for the spread of infectious diseases, PLoS ONE, 10 (2015), e0133203.
    [10] K. Prem, A. R. Cook, M. Jit, Projecting social contact matrices in 152 countries using contact surveys and demographic data, PLoS ONE, 13 (2017), e1005697.
    [11] G. Dimarco, B. Perthame, G. Toscani, M. Zanella, Kinetic models for epidemic dynamics with social heterogeneity, preprint, arXiv: 2009.01140v1.
    [12] N. M. Ferguson, D. A. T. Cummings, C. Fraser, J. C. Cajka, P. C. Cooley, D. S. Burke, Strategies for mitigating an influenza pandemic, Nature, 442 (2006), 448–452.
    [13] S. Riley, C. Fraser, C. A. Donnelly, A. C. Ghani, L. J. Abu-Raddad, A. J. Hedley, et al., Transmission dynamics of the etiological agent of SARS in Hong Kong: Impact of public health interventions, Science, 300 (2003), 1961–1966.
    [14] J. Dolbeault, G. Turinici, Heterogeneous social interactions and the COVID-19 lockdown outcome in a multi-group SEIR model, Math. Model. Nat. Pheno., 15 (2020), 36.
    [15] L. Fumanelli, M. Ajelli, P. Manfredi, A. Vespignani, S. Merler, Inferring the structure of social contacts from demographic data in the analysis of infectious diseases spread, PLoS Comput. Biol., 8 (2012), e1002673.
    [16] J. Mossong, N. Hens, M. Jit, P. Beutels, K. Auranen, R. Mikolajczyk, et al., Social contacts and mixing patterns relevant to the spread of infectious diseases, PLoS Med., 5 (2008), e74.
    [17] F. Brauer, C. Castillo-Chavez, Z. Feng, Mathematical Models in Epidemiology, Springer, New York, 2019.
    [18] O. Diekmann, J. A. P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, John Wiley & Sons, Chichester, UK, 2000.
    [19] G. Dimarco, G.Toscani, Kinetic modeling of alcohol consumption, J. Stat. Phys., 177 (2019), 1022–1042.
    [20] P. L. Bhatnagar, E. P. Gross, M. Krook, A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems, Phys. Rev., 94 (1954), 511–525.
    [21] J. Zhang, M. Litvinova, Y. Liang, Y. Wang, S. Zhao, Q. Wu, et al., Changes in contact patterns shape the dynamics of the COVID-19 outbreak in China, Science, 368 (2020), 1481–1486.
    [22] J. Chen, H. Lu, G. Melino, S. Boccia, M. Piacentini, W. Ricciardi, et al., COVID-19 infection: the China and Italy perspectives, Cell Death Dis., 11 (2020), 438.
    [23] E. Lavezzo, E. Franchin, C. Ciavarella, G. Cuomo-Dannenburg, L. Barzon, C. Del Vecchio, et al., Suppression of a SARS-CoV-2 outbreak in the Italian municipality of Vo', Nature, 584 (2020), 425–429.
    [24] S. J. Kang, S. I. Jung, Age-related morbidity and mortality among patients with COVID-19, Infect. Chemother., 52 (2020), 154.
    [25] Y. Liu, A. A. Gayle, A. Wilder-Smith, J. Rocklöv, The reproductive number of COVID-19 is higher compared to SARS coronavirus, J. Travel Med., 27 (2020), 1–4.
    [26] Istituto Nazionale di Statistica, Primi risultati dell'indagine di sieroprevalenza sul SARS-CoV-2. Available from: https://www.istat.it/it/files//2020/08/ReportPrimiRisultatiIndagineSiero.pdf.
    [27] G. Albi, L. Pareschi, M. Zanella, Control with uncertain data of socially structured compartmental epidemic models, preprint, arXiv: 2004.13067.
    [28] A. Capaldi, S. Behrend, B. Berman, J. Smith, J. Wrigth, A. L. Lloyd, Parameter estimation and uncertainty quantification for an epidemic model, Math. Biosci. Eng., 9 (2012), 553–576.
    [29] G. Chowell, Fitting dynamics models to epidemic outbreaks with quantified uncertainty: A primer for parameter uncertainty, identifiability, and forecast, Infect. Dis. Model., 2 (2017), 379–398.
    [30] M. G. Roberts, Epidemic models with uncertainty in the reproduction, J. Math. Biol., 66 (2013), 1463–1474.
    [31] A. Pugliese, S. Sottile, Inferring the COVID-19 infection curve in Italy, preprint, arXiv: 2004.09404.
    [32] D. Xiu, Numerical Methods for Stochastic Computations: A Spectral Method Approach, Princeton University Press, 2010.
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