Math. Model. Nat. Phenom.
Volume 15, 2020
Coronavirus: Scientific insights and societal aspects
Article Number 57
Number of page(s) 42
Published online 30 November 2020
  1. A. Abakuks, An optimal isolation policy for an epidemic. J. Appl. Probab. 10 (1973) 247–62. [CrossRef] [Google Scholar]
  2. A. Abakuks, Optimal immunisation policies for epidemics. Adv. Appl. Probab. 6 (1974) 494–511. [CrossRef] [Google Scholar]
  3. D. Acemoglu, V. Chernozhukov, I. Werning and M. Whinston, A multi-risk SIR model with optimally targeted lockdown. NBER Working Paper 27102 (2020) 1–38. [Google Scholar]
  4. F. Agusto and A. Adekunle, Optimal control of a two-strain tuberculosis-HIV/AIDS co-infection model. Biosystems 119 (2014) 20–44. [CrossRef] [PubMed] [Google Scholar]
  5. J.A. Al-Tawfiq, Asymptomatic coronavirus infection: MERS-CoV and SARS-CoV-2 (COVID-19). Travel Med. Infect. Dis. 101608 (2020). [CrossRef] [PubMed] [Google Scholar]
  6. R. Aldridge, D. Lewer, S. Beale, A. Johnson, M. Zambon, A. Hayward, E. Fragaszy and n. null, Seasonality and immunity to laboratory-confirmed seasonal coronaviruses (HCoV-NL63, HCoV-OC43, and HCoV-229E): results from the flu watch cohort study. Wellcome Open Res. 5 (2020) 52. [CrossRef] [PubMed] [Google Scholar]
  7. F. Alvarez, D. Argente and F. Lippe, A simple planning problem for COVID-19 lockdown. Natl. Bureau Eco. Res. 26981 (2020) 1–35. [Google Scholar]
  8. R. Anderson and R. May, Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, Oxford (1991). [Google Scholar]
  9. F. Ball, T. Britton, C. Larédo, E. Pardoux, D. Sirl and V. Tran, Stochastic Epidemic Models with Inference, edited by T. Britton and E. Pardoux, Lecture Notes in Mathematics. Springer (2019). [Google Scholar]
  10. E. Barclay, The US doesn’t just need to flatten the curve. it needs to “raise the line”. Available from (2020). [Google Scholar]
  11. H. Behncke, Optimal control of deterministic epidemics. Optim. Control Appl. Methods 21 (2000) 269–285. [Google Scholar]
  12. D.W. Berger, K.F. Herkenhoff and S. Mongey, An SEIR infectious disease model with testing and conditional quarantine. Workingpaper 26901. National Bureau of Economic Research, Inc. (2020). [Google Scholar]
  13. J. Bernstein, A.W. Richter and N. Throckmorton, Covid-19: A view from the labor market. Federal Reserve Bank of Dallas Working Paper 2010 (2020). [Google Scholar]
  14. L. Bobisud, Optimal control of a deterministic epidemic. Math. Biosci. 35 (1977) 165–174. [CrossRef] [Google Scholar]
  15. M. Chinazzi, J.T. Davis, M. Ajelli, C. Gioannini, M. Litvinova, S. Merler, A. Pastore y Piontti, K. Mu, L. Rossi, K. Sun, C. Viboud, X. Xiong, H. Yu, M.E. Halloran, I.M. Longini and A. Vespignani, The effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID-19) outbreak. Science 368 (2020) 395–400. [CrossRef] [Google Scholar]
  16. P. Choe, R. Perera, W. Park, K. Song, J. Bang, E. Kim and M. Oh, MERS-CoV antibody responses 1 year after symptom onset, South Korea, 2015. Emerg. Infect. Dis. 23 (2017) 1079–1084. [CrossRef] [Google Scholar]
  17. S. Clémençon, V. Tran and H.D. Arazoza, A stochastic SIR model with contact-tracing: large population limits and statistical inference. J. Biol. Dyn. 2 (2008) 391–414. [Google Scholar]
  18. C.W. Cobb and P.H. Douglas, A theory of production. Am. Eco. Rev. 18 (1928) 139–165. [Google Scholar]
  19. J. Cohen, Vaccine designers take first shots at COVID-19. Science 368 (2020) 14–16. [CrossRef] [Google Scholar]
  20. J. Cohen and K. Kupferschmidt, Countries test tactics in ‘war’ against COVID-19. Science 367 (2020) 1287–1288. [CrossRef] [Google Scholar]
  21. A.R. da Cruz, R.T.N. Cardoso and R.H.C. Takahashi, Multiobjective dynamic optimization of vaccination campaigns using convex quadratic approximation local search, in Evolutionary Multi-Criterion Optimization, edited by R.H.C. Takahashi, K. Deb, E.F. Wanner and S. Greco. Springer, Berlin (2011) 404–417. [Google Scholar]
  22. M. Day, COVID-19: identifying and isolating asymptomatic people helped eliminate virus in Italian village. Br. Med. J. 368 (2020). [Google Scholar]
  23. O. Diekmann, J. Heesterbeek and 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]
  24. O. Diekmann, H. Heesterbeek and T. Britton, Mathematical Tools for Understanding Infectious Disease Dynamics. Princeton Series in Theoretical and Computational Biology. Princeton University Press, New Jersey (2012). [Google Scholar]
  25. R. Djidjou-Demasse, Y. Michalakis, M. Choisy, M.T. Sofonea and S. Alizon, Optimal COVID-19 epidemic control until vaccine deployment. Preprint medRxiv 20049189v1 (2020). [Google Scholar]
  26. L.D. Domenico, G. Pullano, C. Sabbatini, P.-Y. Boëlle and V. Colizza, Expected impact of lockdown in Ile-de-France and possible exit strategies. Preprint medrxiv 20063933v1 (2020). [Google Scholar]
  27. K. Eames and M. Keeling, Contact tracing and disease control. Proc. R. Soc. London B 270 (2003) 2565–2571. [CrossRef] [Google Scholar]
  28. M.S. Eichenbaum, S. Rebelo and M. Trabandt, The macroeconomics of epidemics. Working Paper 26882. National Bureau of Economic Research (2020). [Google Scholar]
  29. R. Elie, Finite time Merton strategy under drawdown constraint: a viscosity solution approach. Appl. Math. Optim. 58 (2008) 411–431. [CrossRef] [Google Scholar]
  30. R. Elie, E. Hubert and G. Turinici, Contact rate epidemic control of COVID-19: an equilibrium view. Preprint arXiv:2004.08221 (2020). [Google Scholar]
  31. T. Evgeniou, M. Fekom, A. Ovchinnikov, R. Porcher, C. Pouchol and N. Vayatis, Epidemic models for personalised COVID-19 isolation and exit policies using clinical risk predictions. Preprint medRxiv 20074054v1 (2020). [Google Scholar]
  32. N. Ferguson, D. Laydon, G. Nedjati-Gilani, N. Imai, K. Ainslie, M. Baguelin, S. Bhatia, A. Boonyasiri, Z. Cucunubá, G. Cuomo-Dannenburg, A. Dighe, I. Dorigatti, H. Fu, K. Gaythorpe, W. Green, A. Hamlet, W. Hinsley, L.C. Okell, S. van Elsland and A.C. Ghani, Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand. Imperial College COVID-19 Response Team 9 (2020). [Google Scholar]
  33. S. Flaxman, S. Mishra, A. Gandy, J. Unwin, H. Coupland, a.Z. Thomas A Mellan, T. Berah, A. Ghani, C.A. Donnelly, S. Riley, L.C. Okell, M.A.C. Vollmer, N.M. Ferguson and S. Bhatt, Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in 11 European countries. Imperial College COVID-19 Response Team 13 (2020). [Google Scholar]
  34. C. Gelardi, Colonialism made puerto rico vulnerable to coronavirus catastrophe. Available from: (2020). [Google Scholar]
  35. K. Gostic, A.C. Gomez, R.O. Mummah, A.J. Kucharski and J.O. Lloyd-Smith, Estimated effectiveness of symptom and risk screening to prevent the spread of COVID-19. eLife 9 (2020) e55570. [Google Scholar]
  36. D. Greenhalg, Some results on optimal control applied to epidemics. Math. Biosci. 88 (1988) 125–158. [CrossRef] [Google Scholar]
  37. S.K. Gudi, K. Undela, R. Venkataraman, U.V. Mateti, M. Chhabra, S. Nyamagoud and K.K. Tiwari, Knowledge and beliefs towards universal safety precautions to flatten the curve during novel coronavirus disease (nCOVID-19) pandemic among general public in India: Explorations from a national perspective. Preprint medRxiv 20047126v1 (2020). [Google Scholar]
  38. V. Guerrieri, G. Lorenzoni, L. Straub and I. Werning, Macroeconomic implications of COVID-19: Can negative supply shocks cause demand shortages? Working Paper 26918, National Bureau of Economic Research (2020). [Google Scholar]
  39. E. Hansen, and T. Day, Optimal control of epidemics with limited resources. J. Math. Biol. 62 (2011) 423–451. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  40. X. He, E. Lau, P. Wu, X. Deng, J. Wang and X. Hao, Temporal dynamics in viral shedding and transmissibility of COVID-19. Nat. Med. 26 (2020) 672–5. [CrossRef] [PubMed] [Google Scholar]
  41. J. Hellewell, S. Abbott, A. Gimma, N. Bosse, C. Jarvis, T. Russell, J. Munday, A. Kucharski, J. Edmunds, C.C. W. Group, S. Funk and R. Eggo, Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts. Lancet Glob. Health 8 (2020) 488–496. [CrossRef] [Google Scholar]
  42. J. Hellewell, S. Abbott, A. Gimma, N.I. Bosse, C.I. Jarvis, T.W. Russell, J.D. Munday, A.J. Kucharski, W.J. Edmunds, F. Sun, S. Flasche, B.J. Quilty, N. Davies, Y. Liu, S. Clifford, P. Klepac, M. Jit, C. Diamond, H. Gibbs, K. [van Zandvoort], S. Funk, and R.M. Eggo, Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts. Lancet Glob. Health 8 (2020) e488–e496. [CrossRef] [Google Scholar]
  43. T. House and M. Keeling, The impact of contact tracing in clustered populations. PLoS Comput. Biol. 6 (2010) e1000721. [CrossRef] [PubMed] [Google Scholar]
  44. L. Huang, Y. Shi, B. Gong, L. Jiang, X. Liu, J. Yang, J. Tang, C. You, Q. Jiang, B. Long, T. Zeng, M. Luo, F. Zeng, F. Zeng, S. Wang, X. Yang and Z. Yang, Blood single cell immune profiling reveals the interferon-MAPK pathway mediated adaptive immune response for COVID-19. Preprint medRxiv 20033472v1 (2020). [Google Scholar]
  45. D. Iacoviello and G. Liuzzi, Optimal control for SIR epidemic model: A two treatments strategy. 2008 Mediterranean Conference on Control and Automation - Conference Proceedings, MED’08 (2008) 842–847. [CrossRef] [Google Scholar]
  46. F. Jiang, L. Deng and L. Zhang, Review of the Clinical Characteristics of Coronavirus Disease 2019 (COVID-19). J. Gen. Inter. Med. 35 (2020) 1545–9. [CrossRef] [Google Scholar]
  47. W. Kermack and A. McKendrick, A contribution to the mathematical theory of epidemics. Proc. R. Soc. London A 115 (1927) 700–721. [Google Scholar]
  48. S. Kim, J. Lee and E. Jung, Mathematical model of transmission dynamics and optimal control strategiesfor 2009 A/H1N1 influenza in the Republic of Korea. J. Theor. Biol. 412 (2017) 74–85. [CrossRef] [PubMed] [Google Scholar]
  49. I. Kiss, D. Green and R. Kao, Infectious disease control using contact tracing in random and scale-free networks. J. R. Soc. Interface 3 (2013) 55–62. [CrossRef] [PubMed] [Google Scholar]
  50. S.M. Kissler, C. Tedijanto, M. Lipsitch and Y. Grad, Social distancing strategies for curbing the COVID-19 epidemic. Preprint medRxiv 20041079v1 (2020). [Google Scholar]
  51. C.C. Ku, T.-C. Ng and H.-H. Lin, Epidemiological benchmarks of the COVID-19 outbreak control in China after Wuhan’s lockdown: A modelling study with an empirical approach. SSRN Electron. J. (2020) 3543589. [Google Scholar]
  52. A. Kucharski, P. Klepac, A. Conlan, S. Kissler, M. Tang, H. Fry, J. Gog, J. Edmunds and C.C. working group, 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]
  53. A. Kucharski, T. Russell, C. Diamond, Y. Liu, J. Edmunds, S. Funk and R. Eggo, Early dynamics of transmission and control of COVID-19: a mathematical modelling study. Lancet Infect. Dis. 20 (2020) 553–58. [CrossRef] [PubMed] [Google Scholar]
  54. A. Kumar and P.K. Srivastava, Vaccination and treatment as control interventions in an infectious disease model with their cost optimization. Commun. Nonlinear Sci. Numer. Simul. 44 (2017) 334–343. [CrossRef] [Google Scholar]
  55. C. Lagorio, M. Dickison, F. Vazquez, L.A. Braunstein, P.A. Macri, M.V. Migueles, S. Havlin and H.E. Stanley, Quarantine-generated phase transition in epidemic spreading. Phys. Rev. E 83 (2011) 026102. [CrossRef] [Google Scholar]
  56. S. Lai, N.W. Ruktanonchai, L. Zhou, O. Prosper, W. Luo, J.R. Floyd, A. Wesolowski, M. Santillana, C. Zhang, X. Du, H. Yu and A.J. Tatem, Effect of non-pharmaceutical interventions for containing the COVID-19 outbreak in China. Preprint medRxiv 20029843v1 (2020). [Google Scholar]
  57. W. Liu, Q. Zhang, J. Chen, R. Xiang, H. Song, S. Shu, L. Chen, L. Liang, J. Zhou, L. You, P. Wu, B. Zhang, Y. Lu, L. Xia, L. Huang, Y. Yang, F. Liu, M.G. Semple, B.J. Cowling, K. Lan, Z. Sun, H. Yu, and Y. Liu, Detection of Covid-19 in children in early January 2020 in Wuhan, China. New Engl. J. Med. 382 (2020) 1370–1371. [CrossRef] [Google Scholar]
  58. P. Magal and 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]
  59. J. Mossong, N. Hens, M. Jit, P. Beutels, K. Auranen and R. Mikolajczyk, Social contacts and mixing patterns relevant to the spread of infectious diseases. PLoS Med. 5 (2008) e74. [CrossRef] [Google Scholar]
  60. H. Nishiura, T. Kobayashi, A. Suzuki, S.-M. Jung, K. Hayashi, R. Kinoshita, Y. Yang, B. Yuan, A. Akhmetzhanov, N. Linton and T. Miyama, Estimation of the asymptomatic ratio of novel coronavirus infections (COVID-19). Int. J. Infect. Dis. 94 (2020) 154–155. [CrossRef] [Google Scholar]
  61. A. Oliver, A normative perspective on discounting health outcomes. J. Health Serv. Res. Policy 18 (2013) 186–189. [CrossRef] [PubMed] [Google Scholar]
  62. P.L. Ooi, S. Lim and S.K. Chew, Use of quarantine in the control of SARS in Singapore. Am. J. Infect. Control 33 (2005) 252–257. [CrossRef] [Google Scholar]
  63. M.G. Pedersen and M. Meneghini, A simple method to quantify country-specific effects of COVID-19 containment measures. Preprint medRxiv 20057075v1 (2020). [Google Scholar]
  64. J.Peto, COVID-19 mass testing facilities could end the epidemic rapidly. BMJ 368 (2020). [Google Scholar]
  65. F. Piguillem and L. Shi, Optimal COVID-19 quarantine and testing policies. EIEF Working Papers Series (2004) 2020. [Google Scholar]
  66. L. Pontryagin, G. Boltyanskii, R. Gamkrelidze and E. Mishchenko, Mathematical Theory of Optimal Processes, CRC Press, New York (1964). [Google Scholar]
  67. N. Qualls, A. Levitt and N. Kanade, Community mitigation guidelines to prevent pandemic influenza - United States. MMWR 66 (2017) 1–34. [Google Scholar]
  68. M.L. Ranney, V. Griffeth and A.K. Jha, Critical supply shortages - the need for ventilators and personal protective equipment during the COVID-19 pandemic. New Engl. J. Med. 382 (2020) e41. [CrossRef] [Google Scholar]
  69. L. Roques, E. Klein, J. Papaix, A. Sar and S. Soubeyrand, Effect of a one-month lockdown on the epidemic dynamics of COVID-19 in France. Preprint medRxiv 20074054v1 (2020). [Google Scholar]
  70. J. Roux, C. Massonnaud and P. Crépey, COVID-19: One-month impact of the French lockdown on the epidemic burden. Available from: (2020). [Google Scholar]
  71. A. Sachdeva and A. Sheth, COVID-19, panic now!! a call to action because the numbers are deceptive. SSRN 3563419 (2020). [Google Scholar]
  72. M. Salathé, C.L. Althaus, R. Neher, S. Stringhini, E. Hodcroft, J. Fellay, M. Zwahlen, G. Senti, M. Battegay, A. Wilder-Smith, I. Eckerle, M. Egger and N. Low, COVID-19 epidemic in Switzerland: on the importance of testing, contact tracing and isolation. Swiss medical weekly 150 (2020) w20225. [PubMed] [Google Scholar]
  73. H. Salje, C.T. Kiem, N. Lefrancq, N. Courtejoie, P. Bosetti, J. Paireau, A. Andronico, N. Hoze, J. Richet, C.-L. Dubost, Y.L. Strat, J. Lessler, D.L. Bruhl, A. Fontanet, L. Opatowski, P.-Y. Boelle and S. Cauchemez, Estimating the burden of SARS-CoV-2 in France. Available from: (2020). [Google Scholar]
  74. S.P. Sethi, Optimal quarantine programmes for controlling an epidemic spread. J. Operat. Res. Soc. 29 (1978) 265–268. [CrossRef] [Google Scholar]
  75. O. Sharomi and T. Malik, Optimal control in epidemiology. Ann. Operat. Res. 251 (2017) 55–71. [CrossRef] [Google Scholar]
  76. E. Tognotti, Lessons from the history of quarantine, from plague to influenza A. Emerg. Infect. Dis. 19 (2013) 254–259. [CrossRef] [PubMed] [Google Scholar]
  77. P. Trapman, F. Ball, J.-S. Dhersin, V. Tran, J. Wallinga and T. Britton, Inferring R0 in emerging epidemics-the effect of common population structure is small. J. R. Soc. Interf. 13 (2016) 20160288. [CrossRef] [Google Scholar]
  78. M. van der Pol and J. Cairns, A comparison of the discounted utility model and hyperbolic discounting models in the case of social and private intertemporal preferences for health. J. Eco. Behav. Organ. 49 (2002) 79–96. [CrossRef] [Google Scholar]
  79. E. Verriest, F. Delmotte and M. Egerstedt, Control of epidemics by vaccination, Vol. 2 of Proceedings of the 2005, American Control Conference (2005) 985–990. [CrossRef] [Google Scholar]
  80. J. Wallinga, P. Teunis and M. Kretzschmar, Using Data on Social Contacts to Estimate Age-specific Transmission Parameters for Respiratory-spread Infectious Agents. Am. J. Epidemiol. 164 (2006) 936–944. [CrossRef] [Google Scholar]
  81. S. Wong, A. Vaughan, C. Quilty-Harper and L. Liverpool, Covid-19 news: Us not involved in global WHO plan to tackle pandemic. New Scientist April 24, 2020. [Google Scholar]
  82. World Health Organization, Coronavirus disease 2019 (COVID-19). Available from: (2020). [Google Scholar]
  83. X. Yan and Y. Zou, Optimal and sub-optimal quarantine and isolation control in SARS epidemics. Math. Comput. Model. 47 (2008) 235–45. [CrossRef] [PubMed] [Google Scholar]
  84. X. Zhou, Y. Li, T. Li and W. Zhang, Follow-up of the asymptomatic patients with SARS-CoV-2 infection. Clin. Microbiol. Infect. 26 (2020) P957–959. [CrossRef] [PubMed] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.