Geodesic
COVID-19 pandemic control: balancing detection policy and lockdown intervention under ICU sustainability
Arthur Charpentier1 ; Romuald Elie2 ; Mathieu Laurière3 ; Viet Chi Tran2
1 Faculté des Sciences, Université du Québec à Montréal (UQAM), Montreal, Québec, Canada.
2 LAMA, Univ Gustave Eiffel, Univ Paris Est Creteil, CNRS, 77454 Marne-la-Vallée, France.
3 ORFE Department, Princeton University, Princeton, USA.
Mathematical modelling of natural phenomena, Tome 15 (2020), article no. 57.

Voir la notice de l'article provenant de la source EDP Sciences

An extended SIR model, including several features of the recent COVID-19 outbreak, is considered: the infected and recovered individuals can either be detected or undetected and we also integrate an intensive care unit (ICU) capacity. We identify the optimal policy for controlling the epidemic dynamics using both lockdown and detection intervention levers, and taking into account the trade-off between the sanitary and the socio-economic cost of the pandemic, together with the limited capacity level of ICU. With parametric specification based on the COVID-19 literature, we investigate the sensitivities of various quantities on the optimal strategies. The optimal lockdown policy is structured into 4 phases: First a quick and strong lockdown intervention to stop the exponential growth of the contagion; second a short transition to reduce the prevalence of the virus; third a long period with full ICU capacity and stable virus prevalence; finally a return to normal social interactions with disappearance of the virus. The optimal scenario avoids the second wave of infection, provided the lockdown is released sufficiently slowly. Whenever massive resources are introduced to detect infected individuals, the pressure on social distancing can be released, whereas the impact of detection of immune individuals reveals to be more moderate.
DOI : 10.1051/mmnp/2020045

Arthur Charpentier 1 ; Romuald Elie 2 ; Mathieu Laurière 3 ; Viet Chi Tran 2

1 Faculté des Sciences, Université du Québec à Montréal (UQAM), Montreal, Québec, Canada.
2 LAMA, Univ Gustave Eiffel, Univ Paris Est Creteil, CNRS, 77454 Marne-la-Vallée, France.
3 ORFE Department, Princeton University, Princeton, USA. 
@article{MMNP_2020_15_a17,
     author = {Arthur Charpentier and Romuald Elie and Mathieu Lauri\`ere and Viet Chi Tran},
     title = {COVID-19 pandemic control: balancing detection policy and lockdown intervention under {ICU} sustainability},
     journal = {Mathematical modelling of natural phenomena},
     eid = {57},
     publisher = {mathdoc},
     volume = {15},
     year = {2020},
     doi = {10.1051/mmnp/2020045},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1051/mmnp/2020045/}
}
TY  - JOUR
AU  - Arthur Charpentier
AU  - Romuald Elie
AU  - Mathieu Laurière
AU  - Viet Chi Tran
TI  - COVID-19 pandemic control: balancing detection policy and lockdown intervention under ICU sustainability
JO  - Mathematical modelling of natural phenomena
PY  - 2020
VL  - 15
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.1051/mmnp/2020045/
DO  - 10.1051/mmnp/2020045
LA  - en
ID  - MMNP_2020_15_a17
ER  - 
%0 Journal Article
%A Arthur Charpentier
%A Romuald Elie
%A Mathieu Laurière
%A Viet Chi Tran
%T COVID-19 pandemic control: balancing detection policy and lockdown intervention under ICU sustainability
%J Mathematical modelling of natural phenomena
%D 2020
%V 15
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.1051/mmnp/2020045/
%R 10.1051/mmnp/2020045
%G en
%F MMNP_2020_15_a17
Arthur Charpentier; Romuald Elie; Mathieu Laurière; Viet Chi Tran. COVID-19 pandemic control: balancing detection policy and lockdown intervention under ICU sustainability. Mathematical modelling of natural phenomena, Tome 15 (2020), article  no. 57. doi : 10.1051/mmnp/2020045. https://geodesic-test.mathdoc.fr/articles/10.1051/mmnp/2020045/

[1] A. Abakuks An optimal isolation policy for an epidemic J. Appl. Probab. 1973 247 62

[2] A. Abakuks Optimal immunisation policies for epidemics Adv. Appl. Probab. 1974 494 511

[3] D. Acemoglu, V. Chernozhukov, I. Werning, M. Whinston A multi-risk SIR model with optimally targeted lockdown NBER Working Paper 27102 2020 1 38

[4] F. Agusto, A. Adekunle Optimal control of a two-strain tuberculosis-HIV/AIDS co-infection model. Biosystems 2014 20 44

[5] J.A. Al-Tawfiq Asymptomatic coronavirus infection: MERS-CoV and SARS-CoV-2 (COVID-19) Travel Med. Infect. Dis. 101608 2020

[6] R. Aldridge, D. Lewer, S. Beale, A. Johnson, M. Zambon, A. Hayward, E. Fragaszy, 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. 2020 52

[7] F. Alvarez, D. Argente, F. Lippe A simple planning problem for COVID-19 lockdown Natl. Bureau Eco. Res. 2020 1 35

[8] R. Anderson and R. May, Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, Oxford (1991).

[9] F. Ball, T. Britton, C. Larédo, E. Pardoux, D. Sirl, V. Tran, T. Britton, E. Pardoux Lecture Notes in Mathematics 2019

[10] E. Barclay, The US doesn’t just need to flatten the curve. it needs to “raise the line”. Available from https://www.vox.com/2020/4/7/21201260/coronavirus-usa-chart-mask-shortage-ventilators-flatten-the-curve (2020).

[11] H. Behncke Optimal control of deterministic epidemics Optim. Control Appl. Methods 2000 269 285

[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).

[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).

[14] L. Bobisud Optimal control of a deterministic epidemic Math. Biosci. 1977 165 174

[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, A. Vespignani The effect of travel restrictions on the spread of the 2019 novel coronavirus (COVID-19) outbreak Science 395 400

[16] P. Choe, R. Perera, W. Park, K. Song, J. Bang, E. Kim, M. Oh MERS-CoV antibody responses 1 year after symptom onset, South Korea, 2015 Emerg. Infect. Dis. 2017 1079 1084

[17] S. Clémençon, V. Tran, H.D. Arazoza A stochastic SIR model with contact-tracing: large population limits and statistical inference J. Biol. Dyn. 2008 391 414

[18] C.W. Cobb, P.H. Douglas A theory of production Am. Eco. Rev. 1928 139 165

[19] J. Cohen Vaccine designers take first shots at COVID-19 Science 2020 14 16

[20] J. Cohen, K. Kupferschmidt Countries test tactics in ‘war’ against COVID-19 Science 2020 1287 1288

[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.

[22] M. Day COVID-19: identifying and isolating asymptomatic people helped eliminate virus in Italian village Br. Med. J. 2020

[23] O. Diekmann, J. Heesterbeek, 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. 1990 365 382

[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).

[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).

[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).

[27] K. Eames, M. Keeling Contact tracing and disease control Proc. R. Soc. London B 2003 2565 2571

[28] M.S. Eichenbaum, S. Rebelo and M. Trabandt, The macroeconomics of epidemics. Working Paper 26882. National Bureau of Economic Research (2020).

[29] R. Elie Finite time Merton strategy under drawdown constraint: a viscosity solution approach Appl. Math. Optim. 2008 411 431

[30] R. Elie, E. Hubert and G. Turinici, Contact rate epidemic control of COVID-19: an equilibrium view. Preprint arXiv:2004.08221 (2020).

[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).

[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).

[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).

[34] C. Gelardi, Colonialism made puerto rico vulnerable to coronavirus catastrophe. Available from: https://www.thenation.com/article/politics/puerto-rico-coronavirus/ (2020).

[35] K. Gostic, A.C. Gomez, R.O. Mummah, A.J. Kucharski, J.O. Lloyd-Smith Estimated effectiveness of symptom and risk screening to prevent the spread of COVID-19. eLife 2020 e55570

[36] D. Greenhalg Some results on optimal control applied to epidemics Math. Biosci. 1988 125 158

[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).

[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).

[39] E. Hansen, T. Day Optimal control of epidemics with limited resources J. Math. Biol. 2011 423 451

[40] X. He, E. Lau, P. Wu, X. Deng, J. Wang, X. Hao Temporal dynamics in viral shedding and transmissibility of COVID-19 Nat. Med. 2020 672 5

[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, R. Eggo Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts Lancet Glob. Health 2020 488 496

[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, R.M. Eggo Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts Lancet Glob. Health 2020 e488 e496

[43] T. House, M. Keeling The impact of contact tracing in clustered populations PLoS Comput. Biol. 2010 e1000721

[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).

[45] D. Iacoviello, 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

[46] F. Jiang, L. Deng, L. Zhang Review of the Clinical Characteristics of Coronavirus Disease 2019 (COVID-19) J. Gen. Inter. Med. 2020 1545 9

[47] W. Kermack, A. Mckendrick A contribution to the mathematical theory of epidemics Proc. R. Soc. London 1927 700 721

[48] S. Kim, J. Lee, E. Jung Mathematical model of transmission dynamics and optimal control strategiesfor 2009 A/H1N1 influenza in the Republic of Korea J. Theor. Biol. 2017 74 85

[49] I. Kiss, D. Green, R. Kao Infectious disease control using contact tracing in random and scale-free networks J. R. Soc. Interface 2013 55 62

[50] S.M. Kissler, C. Tedijanto, M. Lipsitch and Y. Grad, Social distancing strategies for curbing the COVID-19 epidemic. Preprint medRxiv 20041079v1 (2020).

[51] C.C. Ku, T.-C. Ng, 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

[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).

[53] A. Kucharski, T. Russell, C. Diamond, Y. Liu, J. Edmunds, S. Funk, R. Eggo Early dynamics of transmission and control of COVID-19: a mathematical modelling study Lancet Infect. Dis. 2020 553 58

[54] A. Kumar, P.K. Srivastava Vaccination and treatment as control interventions in an infectious disease model with their cost optimization Commun. Nonlinear Sci. Numer. Simul. 2017 334 343

[55] C. Lagorio, M. Dickison, F. Vazquez, L.A. Braunstein, P.A. Macri, M.V. Migueles, S. Havlin, H.E. Stanley Quarantine-generated phase transition in epidemic spreading Phys. Rev. E 2011 026102

[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).

[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, Y. Liu Detection of Covid-19 in children in early January 2020 in Wuhan, China New Engl. J. Med. 2020 1370 1371

[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).

[59] J. Mossong, N. Hens, M. Jit, P. Beutels, K. Auranen, R. Mikolajczyk Social contacts and mixing patterns relevant to the spread of infectious diseases PLoS Med. 2008 e74

[60] H. Nishiura, T. Kobayashi, A. Suzuki, S.-M. Jung, K. Hayashi, R. Kinoshita, Y. Yang, B. Yuan, A. Akhmetzhanov, N. Linton, T. Miyama Estimation of the asymptomatic ratio of novel coronavirus infections (COVID-19) Int. J. Infect. Dis. 2020 154 155

[61] A. Oliver A normative perspective on discounting health outcomes J. Health Serv. Res. Policy 2013 186 189

[62] P.L. Ooi, S. Lim, S.K. Chew Use of quarantine in the control of SARS in Singapore Am. J. Infect. Control 2005 252 257

[63] M.G. Pedersen and M. Meneghini, A simple method to quantify country-specific effects of COVID-19 containment measures. Preprint medRxiv 20057075v1 (2020).

[64] J. Peto COVID-19 mass testing facilities could end the epidemic rapidly BMJ 2020

[65] F. Piguillem, L. Shi Optimal COVID-19 quarantine and testing policies EIEF Working Papers Series 2004 2020

[66] L. Pontryagin, G. Boltyanskii, R. Gamkrelidze and E. Mishchenko, Mathematical Theory of Optimal Processes, CRC Press, New York (1964).

[67] N. Qualls, A. Levitt, N. Kanade Community mitigation guidelines to prevent pandemic influenza - United States MMWR 2017 1 34

[68] M.L. Ranney, V. Griffeth, A.K. Jha Critical supply shortages - the need for ventilators and personal protective equipment during the COVID-19 pandemic New Engl. J. Med. 2020 e41

[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).

[70] J. Roux, C. Massonnaud and P. Crépey, COVID-19: One-month impact of the French lockdown on the epidemic burden. Available from: https://www.ehesp.fr/wp-content/uploads/2020/04/Impact-Confinement-EHESP-20200322v1-1.pdf (2020).

[71] A. Sachdeva and A. Sheth, COVID-19, panic now!! a call to action because the numbers are deceptive. SSRN 3563419 (2020).

[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, N. Low COVID-19 epidemic in Switzerland: on the importance of testing, contact tracing and isolation Swiss medical weekly 2020 w20225

[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: https://hal-pasteur.archives-ouvertes.fr/pasteur-02548181 (2020).

[74] S.P. Sethi Optimal quarantine programmes for controlling an epidemic spread J. Operat. Res. Soc. 1978 265 268

[75] O. Sharomi, T. Malik Optimal control in epidemiology Ann. Operat. Res. 2017 55 71

[76] E. Tognotti Lessons from the history of quarantine, from plague to influenza A Emerg. Infect. Dis. 2013 254 259

[77] P. Trapman, F. Ball, J.-S. Dhersin, V. Tran, J. Wallinga, T. Britton Inferring R0 in emerging epidemics-the effect of common population structure is small J. R. Soc. Interf. 2016 20160288

[78] M. Van Der Pol, 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. 2002 79 96

[79] E. Verriest, F. Delmotte, M. Egerstedt Control of epidemics by vaccination Proceedings of the 2005, American Control Conference 2005 985 990

[80] J. Wallinga, P. Teunis, M. Kretzschmar Using Data on Social Contacts to Estimate Age-specific Transmission Parameters for Respiratory-spread Infectious Agents Am. J. Epidemiol. 2006 936 944

[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.

[82] World Health Organization, Coronavirus disease 2019 (COVID-19). Available from: https://www.who.int/emergencies/diseases/novel-coronavirus-2019 (2020).

[83] X. Yan, Y. Zou Optimal and sub-optimal quarantine and isolation control in SARS epidemics Math. Comput. Model. 2008 235 45

[84] X. Zhou, Y. Li, T. Li, W. Zhang Follow-up of the asymptomatic patients with SARS-CoV-2 infection Clin. Microbiol. Infect. 2020 957 959

Cité par Sources :