{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T15:05:45Z","timestamp":1777993545477,"version":"3.51.4"},"reference-count":67,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2023,6,9]],"date-time":"2023-06-09T00:00:00Z","timestamp":1686268800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,6,9]],"date-time":"2023-06-09T00:00:00Z","timestamp":1686268800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100006690","name":"Politecnico di Milano","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100006690","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Bull Math Biol"],"published-print":{"date-parts":[[2023,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Diagnostic testing may represent a key component in response to an ongoing epidemic, especially if coupled with containment measures, such as mandatory self-isolation, aimed to prevent infectious individuals from furthering onward transmission while allowing non-infected individuals to go about their lives. However, by its own nature as an imperfect binary classifier, testing can produce false negative or false positive results. Both types of misclassification are problematic: while the former may exacerbate the spread of disease, the latter may result in unnecessary isolation mandates and socioeconomic burden. As clearly shown by the COVID-19 pandemic, achieving adequate protection for both people and society is a crucial, yet highly challenging task that needs to be addressed in managing large-scale epidemic transmission. To explore the trade-offs imposed by diagnostic testing and mandatory isolation as tools for epidemic containment, here we present an extension of the classical Susceptible-Infected-Recovered model that accounts for an additional stratification of the population based on the results of diagnostic testing. We show that, under suitable epidemiological conditions, a careful assessment of testing and isolation protocols can contribute to epidemic containment, even in the presence of false negative\/positive results. Also, using a multi-criterial framework, we identify simple, yet Pareto-efficient testing and isolation scenarios that can minimize case count, isolation time, or seek a trade-off solution for these often contrasting epidemic management objectives.<\/jats:p>","DOI":"10.1007\/s11538-023-01172-1","type":"journal-article","created":{"date-parts":[[2023,6,9]],"date-time":"2023-06-09T18:03:09Z","timestamp":1686333789000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Epidemic Management via Imperfect Testing: A Multi-criterial Perspective"],"prefix":"10.1007","volume":"85","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0210-268X","authenticated-orcid":false,"given":"Giuseppe","family":"Palma","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0939-8775","authenticated-orcid":false,"given":"Damiano","family":"Caprioli","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1326-9992","authenticated-orcid":false,"given":"Lorenzo","family":"Mari","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,6,9]]},"reference":[{"key":"1172_CR1","doi-asserted-by":"crossref","unstructured":"Aleta A, Martin-Corral D, Pastore y Piontti, A., Ajelli, M., Litvinova, M., Chinazzi, M. et al (2020) Modelling the impact of testing, contact tracing and household quarantine on second waves of COVID-19. Nature Human Behaviour 4(9):964\u2013971","DOI":"10.1038\/s41562-020-0931-9"},{"key":"1172_CR2","volume-title":"Infectious diseases of humans: dynamics and control","author":"RM Anderson","year":"1992","unstructured":"Anderson RM, May RM (1992) Infectious diseases of humans: dynamics and control. Oxford University Press, Oxford"},{"issue":"1","key":"1172_CR3","doi-asserted-by":"publisher","first-page":"3319","DOI":"10.1038\/s41467-022-30642-8","volume":"13","author":"T Ash","year":"2022","unstructured":"Ash T, Bento AM, Kaffine D, Rao A et al (2022) Disease-economy trade-offs under alternative epidemic control strategies. Nat Commun 13(1):3319","journal-title":"Nat Commun"},{"key":"1172_CR4","doi-asserted-by":"publisher","DOI":"10.1016\/j.epidem.2022.100631","volume":"41","author":"Y Baik","year":"2022","unstructured":"Baik Y, Cilloni L, Kendall E, Dowdy D et al (2022) Symptom-based vs asymptomatic testing for controlling SARS-CoV-2 transmission in low-and middle-income countries: A modelling analysis. Epidemics 41:100631","journal-title":"Epidemics"},{"key":"1172_CR5","doi-asserted-by":"crossref","unstructured":"Bergstrom T, Bergstrom CT et al. (2020) Frequency and accuracy of proactive testing for COVID-19. MedRxiv","DOI":"10.1101\/2020.09.05.20188839"},{"issue":"1","key":"1172_CR6","doi-asserted-by":"publisher","first-page":"4264","DOI":"10.1038\/s41467-020-18050-2","volume":"11","author":"E Bertuzzo","year":"2020","unstructured":"Bertuzzo E, Mari L, Pasetto D, Miccoli S, Casagrandi R, Gatto M et al (2020) The geography of COVID-19 spread in Italy and implications for the relaxation of confinement measures. Nat Commun 11(1):4264","journal-title":"Nat Commun"},{"issue":"32","key":"1172_CR7","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2107179118","volume":"118","author":"C Betsch","year":"2021","unstructured":"Betsch C, Sprengholz P, Siegers R, Eitze S, Korn L, Goldhahn L et al (2021) Empirical evidence to understand the human factor for effective rapid testing against SARS-CoV-2. Proc Natl Acad Sci 118(32):e2107179118","journal-title":"Proc Natl Acad Sci"},{"issue":"9","key":"1172_CR8","doi-asserted-by":"publisher","first-page":"1685","DOI":"10.3390\/diagnostics11091685","volume":"11","author":"I Bevan","year":"2021","unstructured":"Bevan I, Stage Baxter M, Stagg HR et al (2021) Knowledge, attitudes, and behavior related to COVID-19 testing: a rapid scoping review. Diagnostics 11(9):1685","journal-title":"Diagnostics"},{"issue":"13","key":"1172_CR9","doi-asserted-by":"publisher","first-page":"2317","DOI":"10.1002\/sim.9357","volume":"41","author":"R Bhaduri","year":"2022","unstructured":"Bhaduri R, Kundu R, Purkayastha S, Kleinsasser M, Beesley LJ, Mukherjee B et al (2022) Extending the susceptible-exposed-infected-removed (SEIR) model to handle the false negative rate and symptom-based administration of COVID-19 diagnostic tests: SEIR-fansy. Stat Med 41(13):2317\u20132337","journal-title":"Stat Med"},{"issue":"1","key":"1172_CR10","doi-asserted-by":"publisher","first-page":"9748","DOI":"10.1038\/s41598-021-89127-1","volume":"11","author":"R Bhattacharyya","year":"2021","unstructured":"Bhattacharyya R, Kundu R, Bhaduri R, Ray D, Beesley LJ, Salvatore M et al (2021) Incorporating false negative tests in epidemiological models for SARS-CoV-2 transmission and reconciling with seroprevalence estimates. Sci Rep 11(1):9748","journal-title":"Sci Rep"},{"issue":"1","key":"1172_CR11","doi-asserted-by":"publisher","first-page":"2001978","DOI":"10.2807\/1560-7917.ES.2020.26.1.2001978","volume":"26","author":"P Bosetti","year":"2021","unstructured":"Bosetti P, Kiem CT, Yazdanpanah Y, Fontanet A, Lina B, Colizza V et al (2021) Impact of mass testing during an epidemic rebound of SARS-CoV-2: a modelling study using the example of France. Eurosurveillance 26(1):2001978","journal-title":"Eurosurveillance"},{"key":"1172_CR12","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1007\/978-3-540-78911-6_2","volume-title":"Mathematical epidemiology","author":"F Brauer","year":"2008","unstructured":"Brauer F (2008) Compartmental models in epidemiology. In: Brauer F, van den Driessche P, Jianhong W (eds) Mathematical epidemiology. Springer, Berlin, pp 19\u201379"},{"issue":"6531","key":"1172_CR13","doi-asserted-by":"publisher","first-page":"eabd9338","DOI":"10.1126\/science.abd9338","volume":"371","author":"JM Brauner","year":"2021","unstructured":"Brauner JM, Mindermann S, Sharma M, Johnston D, Salvatier J, Gaven\u010diak T et al (2021) Inferring the effectiveness of government interventions against COVID-19. Science 371(6531):eabd9338","journal-title":"Science"},{"issue":"1","key":"1172_CR14","doi-asserted-by":"publisher","first-page":"20451","DOI":"10.1038\/s41598-021-99712-z","volume":"11","author":"J Chen","year":"2021","unstructured":"Chen J, Vullikanti A, Santos J, Venkatramanan S, Hoops S, Mortveit H et al (2021) Epidemiological and economic impact of COVID-19 in the US. Sci Rep 11(1):20451","journal-title":"Sci Rep"},{"key":"1172_CR15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2020.110568","volume":"512","author":"W Choi","year":"2021","unstructured":"Choi W, Shim E (2021) Optimal strategies for social distancing and testing to control COVID-19. J Theor Biol 512:110568","journal-title":"J Theor Biol"},{"issue":"6492","key":"1172_CR16","doi-asserted-by":"publisher","first-page":"713","DOI":"10.1126\/science.abb5659","volume":"368","author":"S Cobey","year":"2020","unstructured":"Cobey S (2020) Modeling infectious disease dynamics. Science 368(6492):713\u2013714","journal-title":"Science"},{"issue":"1","key":"1172_CR17","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1186\/s12916-020-01698-4","volume":"18","author":"L Di Domenico","year":"2020","unstructured":"Di Domenico L, Pullano G, Sabbatini CE, Bo\u00eblle PY et al (2020) Impact of lockdown on COVID-19 epidemic in \u00cele-de-France and possible exit strategies. BMC Med 18(1):240","journal-title":"BMC Med"},{"issue":"4","key":"1172_CR18","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1007\/BF00178324","volume":"28","author":"O Diekmann","year":"1990","unstructured":"Diekmann O, Heesterbeek JAP et al (1990) On the definition and the computation of the basic reproduction ratio $$R_0$$ in models for infectious diseases in heterogeneous populations. J Math Biol 28(4):365\u2013382","journal-title":"J Math Biol"},{"issue":"47","key":"1172_CR19","doi-asserted-by":"publisher","first-page":"873","DOI":"10.1098\/rsif.2009.0386","volume":"7","author":"O Diekmann","year":"2010","unstructured":"Diekmann O, Heesterbeek JAP et al (2010) The construction of next-generation matrices for compartmental epidemic models. J R Soc Interface 7(47):873\u2013885","journal-title":"J R Soc Interface"},{"key":"1172_CR20","volume-title":"Multicriteria optimization","author":"M Ehrgott","year":"2005","unstructured":"Ehrgott M (2005) Multicriteria optimization. Springer, Berlin"},{"key":"1172_CR21","doi-asserted-by":"crossref","unstructured":"Emanuel EJ, Persad G, Upshur R, Thome B, Parker M, Glickman A et al (2020) Fair allocation of scarce medical resources in the time of COVID-19 (vol. 382) (no. 21). Mass Medical Soc","DOI":"10.1056\/NEJMsb2005114"},{"issue":"6491","key":"1172_CR22","doi-asserted-by":"publisher","first-page":"eabb6936","DOI":"10.1126\/science.abb6936","volume":"368","author":"L Ferretti","year":"2020","unstructured":"Ferretti L, Wymant C, Kendall M, Zhao L, Nurtay A, Abeler-D\u00f6rner L et al (2020) Quantifying SARS-CoV-2 transmission suggests epidemic control with digital contact tracing. Science 368(6491):eabb6936","journal-title":"Science"},{"issue":"7820","key":"1172_CR23","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1038\/s41586-020-2405-7","volume":"584","author":"S Flaxman","year":"2020","unstructured":"Flaxman S, Mishra S, Gandy A, Unwin HJT, Mellan TA, Coupland H et al (2020) Estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe. Nature 584(7820):257\u2013261","journal-title":"Nature"},{"issue":"4","key":"1172_CR24","doi-asserted-by":"publisher","first-page":"834","DOI":"10.1007\/s13280-021-01544-8","volume":"50","author":"C Folke","year":"2021","unstructured":"Folke C, Polasky S, Rockstr\u00f6m J, Galaz V, Westley F, Lamont M et al (2021) Our future in the Anthropocene biosphere. Ambio 50(4):834\u2013869","journal-title":"Ambio"},{"issue":"19","key":"1172_CR25","doi-asserted-by":"publisher","first-page":"10484","DOI":"10.1073\/pnas.2004978117","volume":"117","author":"M Gatto","year":"2020","unstructured":"Gatto M, Bertuzzo E, Mari L, Miccoli S, Carraro L, Casagrandi R et al (2020) Spread and dynamics of the COVID-19 epidemic in Italy: effects of emergency containment measures. Proc Natl Acad Sci 117(19):10484\u201310491","journal-title":"Proc Natl Acad Sci"},{"issue":"6","key":"1172_CR26","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1007\/s11538-022-01018-2","volume":"84","author":"A Gharouni","year":"2022","unstructured":"Gharouni A, Abdelmalek FM, Earn DJ, Dushoff J et al (2022) Testing and isolation efficacy: insights from a simple epidemic model. Bull Math Biol 84(6):66","journal-title":"Bull Math Biol"},{"issue":"6","key":"1172_CR27","doi-asserted-by":"publisher","first-page":"855","DOI":"10.1038\/s41591-020-0883-7","volume":"26","author":"G Giordano","year":"2020","unstructured":"Giordano G, Blanchini F, Bruno R, Colaneri P, Di Filippo A, Di Matteo A et al (2020) Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy. Nat Med 26(6):855\u2013860","journal-title":"Nat Med"},{"issue":"12","key":"1172_CR28","doi-asserted-by":"publisher","first-page":"1381","DOI":"10.1016\/S1473-3099(20)30630-7","volume":"20","author":"NC Grassly","year":"2020","unstructured":"Grassly NC, Pons-Salort M, Parker EP, White PJ, Ferguson NM, Ainslie K et al (2020) Comparison of molecular testing strategies for COVID-19 control: a mathematical modelling study. Lancet Infect Dis 20(12):1381\u20131389","journal-title":"Lancet Infect Dis"},{"issue":"10","key":"1172_CR29","doi-asserted-by":"publisher","first-page":"e0240775","DOI":"10.1371\/journal.pone.0240775","volume":"15","author":"N Gray","year":"2020","unstructured":"Gray N, Calleja D, Wimbush A, Miralles-Dolz E, Gray A, De Angelis M et al (2020) Is no test better than a bad test: impact of diagnostic uncertainty on the spread of COVID-19. PLoS ONE 15(10):e0240775","journal-title":"PLoS ONE"},{"issue":"4","key":"1172_CR30","doi-asserted-by":"publisher","first-page":"529","DOI":"10.1038\/s41562-021-01079-8","volume":"5","author":"T Hale","year":"2021","unstructured":"Hale T, Angrist N, Goldszmidt R, Kira B, Petherick A, Phillips T et al (2021) A global panel database of pandemic policies (Oxford COVID-19 Government Response Tracker). Nat Hum Behav 5(4):529\u2013538","journal-title":"Nat Hum Behav"},{"issue":"4","key":"1172_CR31","doi-asserted-by":"publisher","first-page":"e488","DOI":"10.1016\/S2214-109X(20)30074-7","volume":"8","author":"J Hellewell","year":"2020","unstructured":"Hellewell J, Abbott S, Gimma A, Bosse NI, Jarvis CI, Russell TW et al (2020) Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts. Lancet Glob Health 8(4):e488\u2013e496","journal-title":"Lancet Glob Health"},{"issue":"1","key":"1172_CR32","first-page":"150","volume":"68","author":"RM Houben","year":"2019","unstructured":"Houben RM, Lalli M, Kranzer K, Menzies NA, Schumacher SG et al (2019) What if they don\u2019t have tuberculosis? The consequences and trade-offs involved in false-positive diagnoses of tuberculosis. Clin Infect Dis 68(1):150\u2013156","journal-title":"Clin Infect Dis"},{"issue":"7820","key":"1172_CR33","doi-asserted-by":"publisher","first-page":"262","DOI":"10.1038\/s41586-020-2404-8","volume":"584","author":"S Hsiang","year":"2020","unstructured":"Hsiang S, Allen D, Annan-Phan S, Bell K, Bolliger I, Chong T et al (2020) The effect of large-scale anti-contagion policies on the COVID-19 pandemic. Nature 584(7820):262\u2013267","journal-title":"Nature"},{"issue":"4","key":"1172_CR34","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/s11538-023-01137-4","volume":"85","author":"M Igoe","year":"2023","unstructured":"Igoe M, Casagrandi R, Gatto M, Hoover CM, Mari L, Ngonghala CN et al (2023) Reframing optimal control problems for infectious disease management in low-income countries. Bull Math Biol 85(4):31","journal-title":"Bull Math Biol"},{"issue":"Supplement-1","key":"1172_CR35","doi-asserted-by":"publisher","first-page":"S77","DOI":"10.1093\/oxrep\/graa018","volume":"36","author":"M Kasy","year":"2020","unstructured":"Kasy M, Teytelboym A (2020) Adaptive targeted infectious disease testing. Oxf Rev Econ Policy 36(Supplement-1):S77\u2013S93","journal-title":"Oxf Rev Econ Policy"},{"issue":"1","key":"1172_CR36","doi-asserted-by":"publisher","first-page":"2425","DOI":"10.1038\/s41598-021-81869-2","volume":"11","author":"M Kocha\u0144czyk","year":"2021","unstructured":"Kocha\u0144czyk M, Lipniacki T (2021) Pareto-based evaluation of national responses to COVID-19 pandemic shows that saving lives and protecting economy are non-trade-off objectives. Sci Rep 11(1):2425","journal-title":"Sci Rep"},{"issue":"6490","key":"1172_CR37","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1126\/science.abb4218","volume":"368","author":"MU Kraemer","year":"2020","unstructured":"Kraemer MU, Yang CH, Gutierrez B, Wu CH, Klein B, Pigott DM et al (2020) The effect of human mobility and control measures on the COVID-19 epidemic in China. Science 368(6490):493\u2013497","journal-title":"Science"},{"issue":"10","key":"1172_CR38","doi-asserted-by":"publisher","first-page":"1151","DOI":"10.1016\/S1473-3099(20)30457-6","volume":"20","author":"AJ Kucharski","year":"2020","unstructured":"Kucharski AJ, Klepac P, Conlan AJ, Kissler SM, Tang ML, Fry H et al (2020) Effectiveness of isolation, testing, contact tracing, and physical distancing on reducing transmission of SARS-CoV-2 in different settings: A mathematical modelling study. Lancet Infect Dis 20(10):1151\u20131160","journal-title":"Lancet Infect Dis"},{"issue":"5","key":"1172_CR39","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1016\/S1473-3099(20)30144-4","volume":"20","author":"AJ Kucharski","year":"2020","unstructured":"Kucharski AJ, Russell TW, Diamond C, Liu Y, Edmunds J, Funk S et al (2020) Early dynamics of transmission and control of COVID-19: a mathematical modelling study. Lancet Infect Dis 20(5):553\u2013558","journal-title":"Lancet Infect Dis"},{"issue":"4","key":"1172_CR40","doi-asserted-by":"publisher","first-page":"262","DOI":"10.7326\/M20-1495","volume":"173","author":"LM Kucirka","year":"2020","unstructured":"Kucirka LM, Lauer SA, Laeyendecker O, Boon D et al (2020) Variation in false-negative rate of reverse transcriptase polymerase chain reaction-based SARS-CoV-2 tests by time since exposure. Ann Intern Med 173(4):262\u2013267","journal-title":"Ann Intern Med"},{"issue":"7825","key":"1172_CR41","doi-asserted-by":"publisher","first-page":"410","DOI":"10.1038\/s41586-020-2293-x","volume":"585","author":"S Lai","year":"2020","unstructured":"Lai S, Ruktanonchai NW, Zhou L, Prosper O, Luo W, Floyd JR et al (2020) Effect of non-pharmaceutical interventions to contain COVID-19 in China. Nature 585(7825):410\u2013413","journal-title":"Nature"},{"key":"1172_CR42","doi-asserted-by":"publisher","DOI":"10.3389\/fpubh.2021.620770","volume":"9","author":"S Lasaulce","year":"2021","unstructured":"Lasaulce S, Zhang C, Varma V et al (2021) Analysis of the tradeoff between health and economic impacts of the COVID-19 epidemic. Front Public Health 9:620770","journal-title":"Front Public Health"},{"key":"1172_CR43","doi-asserted-by":"publisher","DOI":"10.1201\/9781420011418","volume-title":"Optimal control applied to biological models","author":"S Lenhart","year":"2007","unstructured":"Lenhart S, Workman JT (2007) Optimal control applied to biological models. Chapman and Hall\/CRC, Boca Raton"},{"issue":"1","key":"1172_CR44","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1186\/s12929-020-00695-2","volume":"27","author":"YD Li","year":"2020","unstructured":"Li YD, Chi WY, Su JH, Ferrall L, Hung CF et al (2020) Coronavirus vaccine development: from SARS and MERS to COVID-19. J Biomed Sci 27(1):104","journal-title":"J Biomed Sci"},{"issue":"5627","key":"1172_CR45","doi-asserted-by":"publisher","first-page":"1966","DOI":"10.1126\/science.1086616","volume":"300","author":"M Lipsitch","year":"2003","unstructured":"Lipsitch M, Cohen T, Cooper B, Robins JM, Ma S, James L et al (2003) Transmission dynamics and control of severe acute respiratory syndrome. Science 300(5627):1966\u20131970","journal-title":"Science"},{"key":"1172_CR46","doi-asserted-by":"publisher","first-page":"1","DOI":"10.18637\/jss.v061.i08","volume":"61","author":"M L\u00f3pez-Rat\u00f3n","year":"2014","unstructured":"L\u00f3pez-Rat\u00f3n M, Rodr\u00edguez-\u00c1lvarez MX, Cadarso-Su\u00e1rez C et al (2014) Optimalcutpoints: an R package for selecting optimal cutpoints in diagnostic tests. J Stat Softw 61:1\u201336","journal-title":"J Stat Softw"},{"issue":"1","key":"1172_CR47","doi-asserted-by":"publisher","first-page":"2752","DOI":"10.1038\/s41467-021-22878-7","volume":"12","author":"L Mari","year":"2021","unstructured":"Mari L, Casagrandi R, Bertuzzo E, Pasetto D, Miccoli S, Rinaldo A et al (2021) The epidemicity index of recurrent SARS-CoV-2 infections. Nat Commun 12(1):2752","journal-title":"Nat Commun"},{"issue":"7","key":"1172_CR48","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1038\/s41576-021-00360-w","volume":"22","author":"TR Mercer","year":"2021","unstructured":"Mercer TR, Salit M (2021) Testing at scale during the COVID-19 pandemic. Nat Rev Genet 22(7):415\u2013426","journal-title":"Nat Rev Genet"},{"issue":"6525","key":"1172_CR49","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1126\/science.abe9187","volume":"371","author":"MJ Mina","year":"2021","unstructured":"Mina MJ, Andersen KG (2021) COVID-19 testing: one size does not fit all. Science 371(6525):126\u2013127","journal-title":"Science"},{"issue":"1","key":"1172_CR50","doi-asserted-by":"publisher","first-page":"828","DOI":"10.1186\/s12879-021-06528-3","volume":"21","author":"DA Mistry","year":"2021","unstructured":"Mistry DA, Wang JY, Moeser ME, Starkey T et al (2021) A systematic review of the sensitivity and specificity of lateral flow devices in the detection of SARS-CoV-2. BMC Infect Dis 21(1):828","journal-title":"BMC Infect Dis"},{"issue":"5","key":"1172_CR51","doi-asserted-by":"publisher","first-page":"1077","DOI":"10.1016\/j.cell.2020.08.021","volume":"182","author":"DM Morens","year":"2020","unstructured":"Morens DM, Fauci AS (2020) Emerging pandemic diseases: how we got to COVID-19. Cell 182(5):1077\u20131092","journal-title":"Cell"},{"key":"1172_CR52","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1016\/j.ijsu.2020.04.018","volume":"78","author":"M Nicola","year":"2020","unstructured":"Nicola M, Alsafi Z, Sohrabi C, Kerwan A, Al-Jabir A, Iosifidis C et al (2020) The socio-economic implications of the coronavirus pandemic (COVID-19): a review. Int J Surg 78:185\u2013193","journal-title":"Int J Surg"},{"issue":"1","key":"1172_CR53","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1038\/s41591-020-01204-6","volume":"27","author":"OF Norheim","year":"2021","unstructured":"Norheim OF, Abi-Rached JM, Bright LK, B\u00e6r\u00f8e K, Ferraz OL, Gloppen S et al (2021) Difficult trade-offs in response to COVID-19: the case for open and inclusive decision making. Nat Med 27(1):10\u201313","journal-title":"Nat Med"},{"key":"1172_CR54","doi-asserted-by":"crossref","unstructured":"Pavelka M, Van-Zandvoort K, Abbott S, Sherratt K, Majdan M, CMMID COVID-19 working group, et al (2021) The impact of population-wide rapid antigen testing on SARS-CoV-2 prevalence in Slovakia. Science 372(6542):635\u2013641","DOI":"10.1126\/science.abf9648"},{"issue":"11","key":"1172_CR55","doi-asserted-by":"publisher","first-page":"e02225","DOI":"10.1128\/JCM.02225-20","volume":"58","author":"MA Pettengill","year":"2020","unstructured":"Pettengill MA, McAdam AJ (2020) Can we test our way out of the COVID-19 pandemic? J Clin Microbiol 58(11):e02225-20","journal-title":"J Clin Microbiol"},{"key":"1172_CR56","doi-asserted-by":"publisher","DOI":"10.3389\/fmicb.2020.631736","volume":"11","author":"J Piret","year":"2021","unstructured":"Piret J, Boivin G (2021) Pandemics throughout history. Front Microbiol 11:631736","journal-title":"Front Microbiol"},{"issue":"11","key":"1172_CR57","doi-asserted-by":"publisher","first-page":"1438","DOI":"10.1016\/j.jval.2020.07.003","volume":"23","author":"S Reed","year":"2020","unstructured":"Reed S, Gonzalez JM et al (2020) Willingness to accept trade-offs among COVID-19 cases, social-distancing restrictions, and economic impact: a nationwide US study. Value Health 23(11):1438\u20131443","journal-title":"Value Health"},{"key":"1172_CR58","doi-asserted-by":"publisher","DOI":"10.3389\/fpsyg.2020.577684","author":"V Saladino","year":"2020","unstructured":"Saladino V, Algeri D et al (2020) The psychological and social impact of COVID-19: new perspectives of well-being. Front Psychol. https:\/\/doi.org\/10.3389\/fpsyg.2020.577684","journal-title":"Front Psychol"},{"key":"1172_CR59","unstructured":"Sasikumar H, Varma M (2021) Quality-quantity trade-offs in tests for management of COVID-19-like epidemics. arXiv preprint arXiv:2106.08591"},{"key":"1172_CR60","doi-asserted-by":"crossref","unstructured":"Thompson J, Wattam S (2021) Estimating the impact of interventions against COVID-19: From lockdown to vaccination. PLoS one e0261330","DOI":"10.1101\/2021.03.21.21254049"},{"issue":"1\u20132","key":"1172_CR61","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1016\/S0025-5564(02)00108-6","volume":"180","author":"P Van den Driessche","year":"2002","unstructured":"Van den Driessche P, Watmough J (2002) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci 180(1\u20132):29\u201348","journal-title":"Math Biosci"},{"issue":"34","key":"1172_CR62","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2200652119","volume":"119","author":"X Wang","year":"2022","unstructured":"Wang X, Du Z, James E, Fox SJ, Lachmann M, Meyers LA et al (2022) The effectiveness of COVID-19 testing and contact tracing in a US city. Proc Natl Acad Sci 119(34):e2200652119","journal-title":"Proc Natl Acad Sci"},{"issue":"1","key":"1172_CR63","doi-asserted-by":"publisher","first-page":"356","DOI":"10.1038\/s41467-020-20742-8","volume":"12","author":"CR Wells","year":"2021","unstructured":"Wells CR, Townsend JP, Pandey A, Moghadas SM, Krieger G, Singer B et al (2021) Optimal COVID-19 quarantine and testing strategies. Nat Commun 12(1):356","journal-title":"Nat Commun"},{"issue":"18","key":"1172_CR64","doi-asserted-by":"publisher","first-page":"1773","DOI":"10.1001\/jama.2020.5046","volume":"323","author":"DB White","year":"2020","unstructured":"White DB, Lo B (2020) A framework for rationing ventilators and critical care beds during the COVID-19 pandemic. JAMA 323(18):1773\u20131774","journal-title":"JAMA"},{"key":"1172_CR65","unstructured":"World Health Organization (2023) WHO Coronavirus (COVID-19) Dashboard. Available online at https:\/\/covid19.who.int\/. Last accessed on May 8, 2023"},{"issue":"4","key":"1172_CR66","doi-asserted-by":"publisher","first-page":"e0249676","DOI":"10.1371\/journal.pone.0249676","volume":"16","author":"H Wulkow","year":"2021","unstructured":"Wulkow H, Conrad TO, Djurdjevac Conrad N, M\u00fcller SA, Nagel K et al (2021) Prediction of COVID-19 spreading and optimal coordination of counter-measures: from microscopic to macroscopic models to Pareto fronts. PLoS ONE 16(4):e0249676","journal-title":"PLoS ONE"},{"issue":"10","key":"1172_CR67","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1007\/s11538-022-01065-9","volume":"84","author":"D Zhang","year":"2022","unstructured":"Zhang D, Britton T (2022) Analysing the effect of test-and-trace strategy in an sir epidemic model. Bull Math Biol 84(10):105","journal-title":"Bull Math Biol"}],"container-title":["Bulletin of Mathematical Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11538-023-01172-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11538-023-01172-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11538-023-01172-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,22]],"date-time":"2023-06-22T08:45:35Z","timestamp":1687423535000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11538-023-01172-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,9]]},"references-count":67,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2023,7]]}},"alternative-id":["1172"],"URL":"https:\/\/doi.org\/10.1007\/s11538-023-01172-1","relation":{},"ISSN":["0092-8240","1522-9602"],"issn-type":[{"value":"0092-8240","type":"print"},{"value":"1522-9602","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,9]]},"assertion":[{"value":"14 February 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 May 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 June 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors do not have any financial or non-financial interests that are either directly or indirectly related to this work.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"66"}}