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Special issue In memory of Fred Brauer

A computational approach to identifiability analysis for a model of the propagation and control of COVID-19 in Chile

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Article: 2256774 | Received 29 Dec 2022, Accepted 30 Aug 2023, Published online: 14 Sep 2023

References

  • A. Adiga, D. Dubhashi, B. Lewis, M. Marathe, S. Venkatramanan, and A. Vullikanti, Mathematical models for COVID-19 pandemic: A comparative analysis, J. Indian Inst. Sci. 100 (2020), pp. 793–807.
  • A. Afzal, C. Saleel, S. Bhattacharyya, N. Satish, O.D. Samuel, and I.A. Badruddin, Merits and limitations of mathematical modeling and computational simulations in mitigation of COVID-19 pandemic: A comprehensive review, Arch. Comput. Meth. Eng. 29 (2022), pp. 1311–1337.
  • R.M. Anderson and R.M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, 1991.
  • M. Biggerstaff, R. Slayton, M. Johansson, and J. Butler, Improving pandemic response: Employing mathematical modeling to confront xoronavirus disease 2019, Clin. Infect. Dis. 74 (2022), pp. 913–917.
  • F. Brauer and C. Castillo-Chavez, Mathematical Models in Population Biology and Epidemiology, Springer, New York, 2012.
  • J.H. Buckner, G. Chowell, and M.R. Springborn, Dynamic prioritization of COVID-19 vaccines when social distancing is limited for essential workers, Proc. Nat. Acad. Sci. 118(16) (2021), p. e2025786118.
  • R. Bürger, G. Chowell, and L.Y. Lara-Díaz, Comparative analysis of phenomenological growth models applied to epidemic outbreaks, Math. Biosci. Eng. 16 (2019), pp. 4250–4273.
  • R. Bürger, G. Chowell, and L.Y. Lara-Díaz, Measuring differences between phenomenological growth models applied to epidemiology, Math. Biosci. 334 (2021), p. 108558. https://doi.org/10.1016/j.mbs.2021.108558
  • T. Burki, COVID-19 in Latin America, Lancet Infect. Dis. 20(5) (2020), pp. 547–548. https://doi.org/10.1016/s1473-3099(20)30303-0
  • Census Chile, Census Chile (2017). Accessed February 7, 2021. Available at http://www.censo2017.cl/descargas/home/sintesis-de-resultados-censo2017.pdf.
  • J.W. Chan, S. Yuan, K. Kok, K.W. To, H. Chu, J. Yang, F. Xing, J. Liu, C.Y. Yip, R.W.S. Poon, H.W. Tsoi, S.K.F. Lo, K.H. Chan, V.K.M. Poon, W.M. Chan, J.D. Ip, J.P. Cai, V.C.C. Cheng, H. Chen, C.K.M. Hui, and K.Y. Yuen, A familial cluster of pneumonia associated with the 2019 novel coronavirus indicating person-to-person transmission: A study of a family cluster, Lancet 395 (2020), pp. 514–523.
  • J. Chapman and N. Evans, The structural identifiability of susceptible–infective–recovered type epidemic models with incomplete immunity and birth targeted vaccination, Biomed. Signal Process. Control 4 (2009), pp. 278–284.
  • O.T. Chis, J.R. Banga, and E. Balsa-Canto, Structural identifiability of systems biology models: A critical comparison of methods, PLoS One 6(11) (2011), p. e27755.
  • G. Chowell, Fitting dynamic models to epidemic outbreaks with quantified uncertainty: A primer for parameter uncertainty, identifiability, and forecast, Infect. Disease Model. 2 (2017), pp. 379–398.
  • G. Chowell, D. Chowell, K. Roosa, R. Dhillon, and S. Devabhaktuni, Sustainable social distancing through facemask use and testing during the COVID-19 pandemic, preprint (2020). Available at medRXiv.
  • G. Chowell, S. Dahal, Y. Liyanage, A. Tariq, and N. Tuncer, Structural identifiability analysis of epidemic models based on differential equations: A primer, preprint (2022). Available at arXiv.
  • G. Chowell, P. Fenimore, M. Castillo-Garsow, and C. Castillo-Chavez, SARS outbreaks in Ontario, Hong Kong and Singapore: The role of diagnosis and isolation as a control mechanism, J. Theor. Biol. 224 (2003), pp. 1–8.
  • O. Diekmann, H. Heesterbeek, and T. Britton, Mathematical Tools for Understanding Infectious Disease Dynamics, Vol. 7. Princeton University Press, 2013.
  • N. Evans, L. White, M. Chapman, K. Godfrey, and M. Chappell, The structural identifiability of the susceptible infected recovered model with seasonal forcing, Math. Biosci. 194 (2005), pp. 175–197.
  • S. Flaxman, S. Mishra, A. Gandy, H.J.T. Unwin, T.A. Mellan, H. Coupland,E Eeeetal, H. Zhu, T. Berah, J.W. Eaton, M. Monod, A.C. Ghani, C.A. Donnelly, S. Riley, M.A.C. Vollmer, N.M. Ferguson, L.C. Okell, S. Bhatt, and Imperial College COVID-19 Response Team, Estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe, Nature 194 (2005), pp. 175–197.
  • D. Freire-Flores, N. Llanovarced-Kawles, A. Sanchez-Daza, and Á. Olivera-Nappa, On the heterogeneous spread of COVID-19 in Chile, Chaos Solit. Fract. 150 (2021), p. 111156. Available at https://www.sciencedirect.com/science/article/pii/S0960077921005105.
  • L. Gallo, M. Frasca, V. Latora, and G. Russo, Lack of practical identifiability may hamper reliable predictions in COVID-19 epidemic models, Sci. Adv. 8 (2022), p. eabg5234. https://doi.org/10.1126/sciadv.abg5234.
  • P.J. Garcia, A. Alarcón, A. Bayer, P. Buss, G. Guerra, H. Ribeiro, K. Rojas, R. Saenz, N. Salgado de Snyder, G. Solimano, R. Torres, S. Tobar, R. Tuesca, G. Vargas, and R. Atun, COVID-19 response in Latin America, Am. J. Trop. Med. Hyg. 103 (2020), pp. 1765–1772.
  • Government of Chile, COVID-19 data. Accessed February 16, 2021. Official COVID-19. Available at https://www.gob.cl/coronavirus/cifrasoficiales/#reportes.
  • H. Hong, A. Ovchinnikov, G. Pogudin, and C. Yap, SIAN: Software for structural identifiability analysis of ODE models, Bioinformatics 35 (2019), pp. 2873–2874. https://doi.org/10.1093/bioinformatics/bty1069.
  • J. Jia, J. Ding, S. Liu, G. Liao, J. Li, B. Duan, G. Wang, and R. Zhang, Modeling the control of COVID-19: Impact of policy interventions and meteorological factors (2020).
  • Y.H. Kao and M.C. Eisenberg, Practical unidentifiability of a simple vector-borne disease model: Implications for parameter estimation and intervention assessment, Epidemics 25 (2018), pp. 89–100.Available at https://www.sciencedirect.com/science/article/pii/S1755436517301627.
  • W. Kermack and A. McKendrick, A contribution to the mathematical theory of epidemics, Proc. Roy. Soc. A 115 (1927), pp. 700–721.
  • E. Kharazmi, M. Cai, X. Zheng, Z. Zhang, G. Lin, and G.E. Karniadakis, Identifiability and predictability of integer- and fractional-order epidemiological models using physics-informed neural networks, Nature Comput. Sci. 1 (2021), pp. 744–753.
  • T. Kirby, South America prepares for the impact of COVID-19, Lancet Respir. Med. 8(6) (2020), pp. 551–552.
  • H.J. Li, L. Wan, Z. Wang, C.X.Z. u, A. Moustakas, and S. Pei, Mathematical modelling of the pandemic of 2019 novel coronavirus (COVID-19): Patterns, dynamics, prediction, and control, Front. Phys. 9 (2021), p. 738602.
  • Y. Li, H. Campbell, D. Kulkarni, A. Harpur, M. Nundy, X. Wang, and H. Nair, The temporal association of introducing and lifting non-pharmaceutical interventions with the time-varying reproduction number (R) of SARS-CoV-2: A modelling study across 131 countries, Lancet Infect. Dis. 21 (2021), pp. 193–202. Available at https://www.sciencedirect.com/science/article/pii/S1473309920307854.
  • T.S. Ligon, F. Fröhlich, O.T. Chiş, J.R. Banga, E. Balsa-Canto, and J. Hasenauer, GenSSI 2.0: Multi-experiment structural identifiability analysis of SBML models, Bioinformatics 34 (2017), pp. 1421–1423. https://doi.org/10.1093/bioinformatics/btx735.
  • N. Linton, T. Kobayashi, Y. Yang, K. Hayashi, A. Akhmetzhanov, S.M. Jung, B. Yuan, R. Kinoshita, and H. Nishiura, Incubation period and other epidemiological characteristics of 2019 novel coronavirus infections with right truncation: A statistical analysis of publicly available case data, J. Clin. Med. 9 (2020), p. 538. https://doi.org/10.3390/jcm9020538.
  • M. Martcheva, An Introduction to Mathematical Epidemiology, Springer, New York, 2015.
  • T. McKinley, A.R. Cook, and R. Deardon, Inference in epidemic models without likelihoods, Int. J. Biostat. 5(1) 2009. https://doi.org/10.2202/1557-4679.1171.
  • N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E. Teller, Equation of state calculations by fast computing machines, J. Chem. Phys. 21 (2004), pp. 1087–1092. https://doi.org/10.1063/1.1699114.
  • H. Miao, C. Dykes, L.M. Demeter, J. Cavenaugh, S.Y. Park, A.S. Perelson, and H. Wu, Modeling and estimation of kinetic parameters and replicative fitness of HIV-1 from flow-cytometry-based growth competition experiments, Bull. Math. Biol. 70 (2008), pp. 1749–1771.
  • H. Miao, X. Xia, A.S. Perelson, and H. Wu, On identifiability of nonlinear ODE models and applications in viral dynamics, SIAM Rev. 53 (2011), pp. 3–39.
  • Ministerio de Salud, Chile, Ministerio de Salud, Chile. Accessed July 29, 2021. Available at http://www.minsal.cl.
  • Ministery of Science, Technology, Knowledge and Innovation of Chile, Website of the official database for COVID-19 research. Accessed February 16, 2021. Available at http://www.minciencia.gob.cl/covid19.
  • K. Mizumoto, K. Kagaya, A. Zarebski, and G. Chowell, Estimating the asymptomatic proportion of coronavirus disease 2019 (COVID-19) cases on board the Diamond Princess cruise ship, Yokohama, Japan, 2020, Euro Surveill. 25(10) (2020). https://doi.org/10.2807/1560-7917.es.2020.25.10.2000180.
  • A. Morciglio, B. Zhang, G. Chowell, J.M. Hyman, and Y. Jiang, Mask-ematics: Modeling the effects of masks in COVID-19 transmission in high-risk environments, Epidemiologia 2 (2021), pp. 207–226. https://doi.org/10.3390/epidemiologia2020016.
  • V.K. Murty and J. Wu, Mathematics of Public Health, Springer, Cham, 2022.
  • J.C. Navarro, J. Arrivillaga-Henríquez, J. Salazar-Loor, and A.J. Rodriguez-Morales, COVID-19 and dengue, co-epidemics in Ecuador and other countries in Latin America: Pushing strained health care systems over the edge, Travel Med. Infect. Dis. 37 (2020), p. 101656. Available at https://www.sciencedirect.com/science/article/pii/S1477893920301241.
  • H. Nishiura, T. Kobayashi, T. Miyama, A. Suzuki, S.M. Jung, K. Hayashi, R. Kinoshita, Y. Yang, B. Yuan, A.R. Akhmetzhanov, and N.M. Linton, Estimation of the asymptomatic ratio of novel coronavirus infections (COVID-19), Int. J. Infect. Dis 94 (2020), pp. 154–155.
  • R. Padmanabhan, H.S. Abed, N. Meskin, T. Khattab, M. Shraim, and M.A. Al-Hitmi, A review of mathematical model-based scenario analysis and interventions for COVID-19, Comput. Meth. Programs Biomed. 209 (2021), p. 106301. Available at https://www.sciencedirect.com/science/article/pii/S0169260721003758.
  • J. Paireau, A. Andronico, N. Hozé, M. Layan, P. Crépey, A. Roumagnac, M. Lavielle, P.Y. Boëlle, and S. Cauchemez, An ensemble model based on early predictors to forecast COVID-19 health care demand in France, Proc. Nat. Acad. Sci. 119 (2022), p. e2103302119. https://doi.org/10.1073/pnas.2103302119.
  • L. Peng, W. Yang, D. Zhang, C. Zhuge, and L. Hong, Epidemic analysis of COVID-19 in China by dynamical modeling, (2020). Available at medRxiv https://www.medrxiv.org/content/early/2020/02/18/2020.02.16.20023465.
  • M. Renardy, D. Kirschner, and M. Eisenberg, Structural identifiability analysis of age-structured pde epidemic models, J. Math. Biol. 84 (2022), pp. 1–30.
  • K. Roosa and G. Chowell, Assessing parameter identifiability in compartmental dynamic models using a computational approach: application to infectious disease transmission models, Theor. Biol. Med. Model. 16(1) (2019). https://doi.org/10.1186/s12976-018-0097-6.
  • T. Sauer, T. Berry, D. Ebeigbe, M.M. Norton, A.J. Whalen, and S.J. Schiff, Identifiability of infection model parameters early in an epidemic, SIAM J. Control Optim. 60(2) (2022), pp. S27–S48.
  • S. Shankar, S.S. Mohakuda, A. Kumar, P. Nazneen, A.K. Yadav, K. Chatterjee, and K. Chatterjee, Systematic review of predictive mathematical models of COVID-19 epidemic, Medical J. Armed Forc. India 77 (2021), pp. S385–S392. Special issue: COVID-19 – navigating through challenges. Available at https://www.sciencedirect.com/science/article/pii/S0377123721001258.
  • A. Tariq, T. Chakhaia, S. Dahal, A. Ewing, X. Hua, S.K. Ofori, O. Prince, A.D. Salindri, A.E. Adeniyi, J.M. Banda, P. Skums, R. Luo, L.Y. Lara-Díaz, R. Bürger, I.C.H. Fung, E. Shim, A. Kirpich, A. Srivastava, and G. Chowell, An investigation of spatial-temporal patterns and predictions of the coronavirus 2019 pandemic in colombia, 2020–2021, PLOS Negl. Trop. Dis. 16 (2022), p. e0010228. https://doi.org/10.1371/journal.pntd.0010228.
  • E.C.C.W. T.N.C.P.E.R.E. Team, The epidemiological characteristics of an outbreak of 2019 novel coronavirus diseases (COVID-19) −china (2020).
  • N. Tuncer and T.T. Le, Structural and practical identifiability analysis of outbreak models, Math. Biosci. 299 (2018), pp. 1–18. Available at https://www.sciencedirect.com/science/article/pii/S0025556417303164.
  • N. Tuncer, A. Timsina, M. Nuno, G. Chowell, and M. Martcheva, Parameter identifiability and optimal control of an SARS-CoV-2 model early in the pandemic, J. Biol. Dyn. 16 (2022), pp. 412–438.
  • E.A. Undurraga, G. Chowell, and K. Mizumoto, COVID-19 case fatality risk by age and gender in a high testing setting in Latin America: Chile, March–August 2020, Infect. Dis. Pov. 10(1) (2021).
  • P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002), pp. 29–48. Available at https://www.sciencedirect.com/science/article/pii/S0025556402001086.
  • E. Vynnycky, and R.E. White, An Introduction to Infectious Disease Modelling. OUP Oxford, 2010.
  • P.G.T. Walker, C. Whittaker, O.J. Watson, M. Baguelin, P. Winskill, A. Hamlet, B.A. Djafaara, Z. Cucunubá, D.O. Mesa, W. Green, H. Thompson, S. Nayagam, K.E.C. Ainslie, S. Bhatia, S. Bhatt, A. Boonyasiri, O. Boyd, N.F. Brazeau, L. Cattarino, G. Cuomo-Dannenburg, A. Dighe, C.A. Donnelly, I. Dorigatti, S.L. van Elsland, R. FitzJohn, H. Fu, K.A.M. Gaythorpe, L. Geidelberg, N. Grassly, D. Haw, S. Hayes, W. Hinsley, N. Imai, D. Jorgensen, E. Knock, D. Laydon, S. Mishra, G. Nedjati-Gilani, L.C. Okell, H.J. Unwin, R. Verity, M. Vollmer, C.E. Walters, H. Wang, Y. Wang, X. Xi, D.G. Lalloo, N.M. Ferguson, and A.C. Ghani, The impact of COVID-19 and strategies for mitigation and suppression in low- and middle-income countries, Science 369 (2020), pp. 413–422. https://doi.org/10.1126/science.abc0035.
  • J. Wang, Mathematical models for COVID-19: applications, limitations, and potentials, J. Publ. Health Emerg. 4 (2020), pp. 9–9, https://doi.org/10.21037/jphe-2020-05.
  • Wikipedia Commons, Map of Chile. Accessed February 7, 2021. Available at https://commons.wikimedia.org/wiki/File:Mapa-chile.svg.
  • World Health Organization, WHO Director-General's opening remarks at the media briefing on COVID-19-11. March 2020 World Health Organization 2020 [April 23]. Available at https://bit.ly/2A8aCIO.
  • H. Wu, H. Zhu, H. Miao, and A. Perelson, Parameter identifiability and estimation of HIV/AIDS dynamic models, Bull. Math. Biol. 70 (2008), pp. 785–799.
  • P. Yan and G. Chowell, Quantitative Methods for Investigating Infectious Disease Outbreaks, Texts in Applied Mathematics, Springer, Cham, 2019.
  • C. You, Y. Deng, W. Hu, J. Sun, Q. Lin, F. Zhou, C.H. Pang, Y. Zhang, Z. Chen, and X.H. Zhou, Estimation of the time-varying reproduction number of COVID-19 outbreak in China, Int. J. Hyg. Environ. Health 228 (2020), p. 113555. Available at https://www.sciencedirect.com/science/article/pii/S1438463920302133.
  • C. Zhan, Y. Zheng, T.H.Z. ai, and B. Li, Identifying epidemic spreading dynamics of COVID-19 by pseudocoevolutionary simulated annealing optimizers, Neural Comput. Applic. 33 (2021), pp. 4915–4928.
  • S. Zhang, J. Ponce, Z. Zhang, G. Lin, and G. Karniadakis, An integrated framework for building trustworthy data-driven epidemiological models: Application to the COVID-19 outbreak in New York City, PLOS Comput. Biol. 17 (2021), pp. 1–29. https://doi.org/10.1371/journal.pcbi.1009334.
  • Z. Zhao, X. Li, F. Liu, G. Zhu, C. Ma, and L. Wang, Prediction of the COVID-19 spread in African countries and implications for prevention and control: A case study in South Africa, Egypt, Algeria, Nigeria, Senegal and Kenya, Sci. Tot. Environ. 729 (2020), p. 138959. Available at https://www.sciencedirect.com/science/article/pii/S0048969720324761.
  • C. Zhou, Evaluating new evidence in the early dynamics of the novel coronavirus COVID-19 outbreak in Wuhan, China with real time domestic traffic and potential asymptomatic transmissions, (2020). Available at medRxiv https://www.medrxiv.org/content/early/2020/02/20/2020.02.15.20023440.
  • L. Zou, F. Ruan, M. Huang, L. Liang, H. Huang, Z. Hong, J. Yu, M. Kang, Y. Song, J. Xia, Q. Guo, T. Song, J. He, H.L. Yen, M. Peiris, and J. Wu, SARS-CoV-2 viral load in upper respiratory specimens of infected patients, New Engl. J. Med. 382 (2020), pp. 1177–1179. PMID: 32074444. https://doi.org/10.1056/NEJMc2001737.