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All issues Volume 15 (2020) Math. Model. Nat. Phenom., 15 (2020) 36 References
Issue
Math. Model. Nat. Phenom.
Volume 15, 2020
Coronavirus: Scientific insights and societal aspects
Article Number 36
Number of page(s) 18
DOI https://doi.org/10.1051/mmnp/2020025
Published online 14 July 2020
  1. D. Adam, P. Wu, J. Wong, E. Lau, T. Tsang, S. Cauchemez, G. Leung and B. Cowling, Clustering and superspreading potential of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections in Hong Kong. To appear in Res. Square (2020). DOI: 10.21203/rs.3.rs-29548/v1. [Google Scholar]
  2. F.R. Adler, The effects of averaging on the basic reproduction ratio. Math. Biosci. 111 (1992) 89–98. [Google Scholar]
  3. B.M. Althouse et al., Stochasticity and heterogeneity in the transmission dynamics of SARS-CoV-2. Available from: https://covid.idmod.org/ (2020). [Google Scholar]
  4. R.M. Anderson, B. Anderson and R.M. May, Infectious diseases of humans: dynamics and control, Oxford University Press, Oxford (1992). [Google Scholar]
  5. N. Bacaër, Un modèle mathématique des débuts de l'épidémie de coronavirus en France. MMNP 15 (2020) 29. [EDP Sciences] [Google Scholar]
  6. J.C. Blackwood and L.M. Childs, An introduction to compartmental modeling for the budding infectious disease modeler. Lett. Biomath. 5 (2018) 195–221. [Google Scholar]
  7. B. Buonomo, A. d' Onofrio and D. Lacitignola, Global stability of an SIR epidemic model with information dependent vaccination. Math. Biosci. 216 (2008) 9–16. [Google Scholar]
  8. R.M. Corless, G.H. Gonnet, D.E.G. Hare, D.J. Jeffrey and D.E. Knuth, On the Lambert W function. Adv. Comput. Math. 5 (1996) 329–359. [Google Scholar]
  9. A. Danchin, T.W.P. Ng and G. Turinici, A new transmission route for the propagation of the SARS-CoV-2 coronavirus. Preprint medRxiv 20022939v1 (2020). [Google Scholar]
  10. G. Di Domenico, L. Pullano, C.E. Sabbatini, P.-Y. Boëlle and V. Colizza, Expected impact of lockdown in Île-de-France and possible exit strategies. Available from: https://www.epicx-lab.com (2020). [Google Scholar]
  11. O. Diekmann and J.A.P. Heesterbeek, Mathematical epidemiology of infectious diseases: model building, analysis and interpretation, vol. 5. John Wiley & Sons, New Jersey (2000). [Google Scholar]
  12. O. Diekmann, J.A.P. Heesterbeek and J.A.J. Metz, On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28 (1990) 365–382. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  13. O. Diekmann, J.A.P. Heesterbeek and M.G. Roberts, The construction of next-generation matrices for compartmental epidemic models. J. R. Soc. Interface 7 (2009) 873–885. [Google Scholar]
  14. A. Endo, S. Abbott, A.J. Kucharski and S. Funk, Estimating the overdispersion in COVID-19 transmission using outbreak sizes outside China. Wellcome Open Res. 5 (2020) 67. [PubMed] [Google Scholar]
  15. Z. Feng, Final and peak epidemic sizes for SEIR models with quarantine and isolation. Math. Biosci. Eng. 4 (2007) 675. [CrossRef] [PubMed] [Google Scholar]
  16. A. Gerasimov, G. Lebedev, M. Lebedev and I. Semenycheva, Reaching collective immunity for COVID-19: an estimate with a heterogeneous model based on the data for Italy. Preprint medRxiv 20112045v1 (2020). [Google Scholar]
  17. M.G.M. Gomes, R.M. Corder, J.G. King, K.E. Langwig, C. Souto-Maior, J. Carneiro, G. Goncalves, C. Penha-Goncalves, M.U. Ferreira and R. Aguas, Individual variation in susceptibility or exposure to SARS-CoV-2 lowers the herd immunity threshold. Preprint medRxiv 20081893v1 (2020). [Google Scholar]
  18. Q. Griette, P. Magal and O. Seydi, Unreported cases for age dependent COVID-19 outbreak in Japan. Preprint medRxiv 20093807v1 (2020). [Google Scholar]
  19. G. Grossmann, M. Backenkoehler and V. Wolf, Importance of interaction structure and stochasticity for epidemic spreading: A COVID-19 case study. Preprint medRxiv 20091736v1 (2020). [Google Scholar]
  20. L. Hébert-Dufresne, B.M. Althouse, S.V. Scarpino and A. Allard, Beyond R0: Heterogeneity in secondary infections and probabilistic epidemic forecasting. Preprint medRxiv 20021725v1 (2020). [Google Scholar]
  21. H.W. Hethcote, Modeling heterogeneous mixing in infectious disease dynamics, in Models for infectious human diseases: their structure and relation to data. Cambridge University Press, Cambridge (1996) 215–238. [CrossRef] [Google Scholar]
  22. H.W. Hethcote, The mathematics of infectious diseases. SIAM Rev. 42 (2000) 599–653. [Google Scholar]
  23. H.W. Hethcote and J.W. Van Ark Epidemiological models for heterogeneous populations: proportionate mixing, parameter estimation, and immunization programs. Math. Biosci. 84 (1987) 85–118. [Google Scholar]
  24. J.M. Hyman and E. Stanley, Using mathematical models to understand the aids epidemic. Math. Biosci. 90 (1988) 415–473. [Google Scholar]
  25. J.A. Jacquez, C.P. Simon, J. Koopman, L. Sattenspiel and T. Perry, Modeling and analyzing HIV transmission: the effect of contact patterns. Math. Biosci. 92 (1988) 119–199. [Google Scholar]
  26. W.O. Kermack and A.G. McKendrick, A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond., Ser. A 115 (1927) 700–721. [CrossRef] [Google Scholar]
  27. A.J. Kucharski, P. Klepac, A. Conlan, S.M. Kissler, M. Tang, H. Fry, J. Gog and J. Edmunds, Effectiveness of isolation, testing, contact tracing and physical distancing on reducing transmission of SARS-CoV-2 in different settings. Preprint medRxiv 20077024v1 (2020). [Google Scholar]
  28. M. Lachiany and Y. Louzoun, Effects of distribution of infection rate on epidemic models. Phys. Rev. E 94 (2016). [Google Scholar]
  29. L. Laguzet and G. Turinici, Individual Vaccination as Nash Equilibrium in a SIR Model with Application to the 2009–2010 Influenza A (H1N1) Epidemic in France. Bull. Math. Biol. 77 (2015) 1955–1984. [Google Scholar]
  30. L. Landau and E. Lifshitz, Statistical Physics, 3rd edn. Vol. 5. Elsevier Science, Amsterdam (1980). [Google Scholar]
  31. X. Lin, Analysis of 25, 000 lab-confirmed Covid-19 cases in Wuhan: Epidemiological characteristics and non-pharmaceutical intervention effects. Department of Biostatistics and Department of Statistics, Harvard University and Broad Institute. Available from: https://cdn1.sph.harvard.edu/wp-content/uploads/sites/21/2020/03/COVID-19-03-16-2020-Lin.pdf (2020). [Google Scholar]
  32. Z. Liu, P. Magal, O. Seydi and G. Webb, A covid-19 epidemic model with latency period. Infect. Dis. Model. 5 (2020) 323–337. [PubMed] [Google Scholar]
  33. Z. Liu, P. Magal, O. Seydi and G. Webb, Predicting the cumulative number of cases for the Covid-19 epidemic in China from early data. Math. Biosc. Eng. 17 (2020) 3040–3051. [CrossRef] [Google Scholar]
  34. Z. Liu, P. Magal, O. Seydi and G. Webb, Understanding unreported cases in the Covid-19 epidemic outbreak in Wuhan, China, and the importance of major public health interventions. Biology 9 (2020) 50. [Google Scholar]
  35. P. Magaland G. Webb, Predicting the number of reported and unreported cases for the Covid-19 epidemic in South Korea, Italy, France and Germany. Preprint medRxiv 20040154v1 (2020). [Google Scholar]
  36. M. Martcheva, An introduction to mathematical epidemiology, Vol. 61 of Texts in Applied Mathematics. Springer, New York (2015). [CrossRef] [Google Scholar]
  37. R.M. May and R.M. Anderson, Spatial heterogeneity and the design of immunization programs. Math. Biosci. 72 (1984) 83–111. [Google Scholar]
  38. K. Prem, Y. Liu, T.W. Russell, A.J. Kucharski, R.M. Eggo, N. Davies, M. Jit, P. Klepac, S. Flasche, S. Clifford et al., The effect of control strategies to reduce social mixing on outcomes of the COVID-19 epidemic in Wuhan, China: a modelling study. Lancet Public Health 5 (2020) e261–e270. [Google Scholar]
  39. J. Riou and C.L. Althaus, Pattern of early human-to-human transmission of Wuhan 2019 novel coronavirus (2019-nCoV), December 2019 to January 2020. Euro Surveill. 25 (2020) 2000058. [Google Scholar]
  40. L. Roques, E.K. Klein, J. Papaïx, A. Sar and S. Soubeyrand, Impact of lockdown on the epidemic dynamics of COVID-19 in France. Front. Med. 7 (2020) 274. [Google Scholar]
  41. J. Roux, C. Massonnaud and P. Crépey, Covid-19: One-month impact of the french lockdown on the epidemic burden. Publications de l'équipe REPERES (Recherche en Pharmaco-épidémiologie et recours aux soins, UPRES EA-7449). Available from: https://www.ea-reperes.com/wp-content/uploads/2020/04/ImpactConfinement-EHESP-20200322v1.pdf (2020). [Google Scholar]
  42. H. Salje, C. Tran Kiem, N. Lefrancq, N. Courtejoie, P. Bosetti, J. Paireau, A. Andronico, N. Hozé, J. Richet, C.-L. Dubost et al. Estimating the burden of SARS-CoV-2 in France. Science (2020) eabc3517. Report available from: DOI: 10.1126/science.abc3517 (2020). [Google Scholar]
  43. Santé Publique France, French national public health agency. Available from: https://dashboard.covid19.data.gouv.fr (2020). [Google Scholar]
  44. H. Stanley, Introduction to Phase Transitions and Critical Phenomena, The International Series of Monographs on Physics. Oxford, Oxford University Press Inc. (1971). [Google Scholar]
  45. P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180 (2002) 29–48. [Google Scholar]

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