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Identifiability Analysis of a Mathematical Model for the First Wave of COVID-19 in Türkiye

Year 2025, Volume: 14 Issue: 1, 494 - 512, 26.03.2025

Tuğba Akman

https://doi.org/10.17798/bitlisfen.1602308

Abstract

In this work, a structurally identifiable mathematical model is developed to capture the first peak of COVID-19 in Türkiye. The daily numbers of COVID-19 cases, deaths, prevalence in the ICU, and prevalence on ventilation, obtained from the open-access TURCOVID-19 database, during the first peak, are used as observations. Structural identifiability analysis is performed using the open-source software Julia. For parameter estimation, some parameters are fixed based on the literature while the remaining parameters are estimated using the Data2Dynamics software. Our results align well with the observations. Then, a practical identifiability analysis based on the profile likelihood method is conducted to investigate uncertainties in the parameter values. It reveals that three of the model parameters, namely the progression rate of symptomatically infectious individuals to hospital and the transmission rates associated with exposed and symptomatically infectious individuals, are not practically identifiable. This means that the implementation of intervention strategies via this model must be performed carefully.

Keywords

Structural identifiability practical identifiability COVID-19 mathematical modeling Türkiye

Ethical Statement

The study is compiled with research and publication ethics.

Thanks

The author would like to thank the anonymous reviewers for the constructive feedback.

References

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  • A. Şimşek, “Estimating the expected influence capacities of nodes in complex networks under the susceptible-infectious-recovered model,” Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 13, no. 2, pp. 408–417.
  • 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,” Computer Methods and Programs in Biomedicine, vol. 209, p. 106301, 2021.
  • I. Rahimi, F. Chen, and A. H. Gandomi, “A review on COVID-19 forecasting models,” Neural Computing and Applications, vol. 35, no. 33, pp. 23671–23681, 2023.
  • Y. Xiang, Y. Jia, L. Chen, L. Guo, B. Shu, and E. Long, “COVID-19 epidemic prediction and the impact of public health interventions: A review of COVID-19 epidemic models,” Infectious Disease Modelling, vol. 6, pp. 324–342, 2021.
  • S. E. Eikenberry, M. Mancuso, E. Iboi, T. Phan, K. Eikenberry, Y. Kuang, E. Kostelich, and A. B. Gumel, “To mask or not to mask: Modeling the potential for face mask use by the general public to curtail the COVID-19 pandemic,” Infectious Disease Modelling, vol. 5, pp. 293–308, 2020.
  • S. K. Biswas, J. K. Ghosh, S. Sarkar, and U. Ghosh, “COVID-19 pandemic in India: a mathematical model study,” Nonlinear Dynamics, vol. 102, pp. 537–553, 2020.
  • O. Torrealba-Rodriguez, R. Conde-Gutiérrez, and A. Hernández-Javier, “Modeling and prediction of COVID-19 in Mexico applying mathematical and computational models,” Chaos, Solitons & Fractals, vol. 138, p. 109946, 2020.
  • A. J. Kucharski, T. W. Russell, C. Diamond, Y. Liu, J. Edmunds, S. Funk, R. M. Eggo, F. Sun, M. Jit, and J. D. Munday, “Early dynamics of transmission and control of COVID-19: a mathematical modelling study,” The Lancet Infectious Diseases, vol. 20, no. 5, pp. 553–558, 2020.
  • M. Carlsson and C. Söderberg-Nauclér, “COVID-19 modeling outcome versus reality in Sweden,” Viruses, vol. 14, no. 8, p. 1840, 2022.
  • A. R. Tuite, D. N. Fisman, and A. L. Greer, “Mathematical modelling of COVID-19 transmission and mitigation strategies in the population of Ontario, Canada,” CMAJ, vol. 192, no. 19, pp. E497–E505, 2020.
  • T. Akman, E. Köse, and N. Tuncer, “Assessment of vaccination and underreporting on COVID-19 infections in based on effective reproduction number,” International Journal of Biomathematics, pp. 2350102 – Online ready, 2024. [Online]. Available: https://doi.org/10.1142/S1793524523501024
  • S. Moore, E. M. Hill, M. J. Tildesley, L. Dyson, and M. J. Keeling, “Vaccination and non-pharmaceutical interventions for COVID-19: a mathematical modelling study,” The Lancet Infectious Diseases, vol. 21, no. 6, pp. 793–802, 2021.
  • S. S. Musa, S. Qureshi, S. Zhao, A. Yusuf, U. T. Mustapha, and D. He, “Mathematical modeling of COVID-19 epidemic with effect of awareness programs,” Infectious Disease Modelling, vol. 6, pp. 448–460, 2021.
  • S. Gao, P. Binod, C. W. Chukwu, T. Kwofie, S. Safdar, L. Newman, S. Choe, B. K. Datta, W. K. Attipoe, W. Zhang, and B. K. Datta, “A mathematical model to assess the impact of testing and isolation compliance on the transmission of COVID-19,” Infectious Disease Modelling, vol. 8, no. 2, pp. 427–444, 2023.
  • A. Malik, N. Kumar, and K. Alam, “Estimation of parameter of fractional order COVID-19 SIQR epidemic model,” Materials Today: Proceedings, vol. 49, pp. 3265–3269, 2022.
  • A. Malik, K. Alam, and N. Kumar, “Coefficient identification in SIQR model of inverse problem of COVID-19,” European Journal of Molecular and Clinical Medicine, vol. 7, 2020.
  • L. Wanika, J. R. Egan, N. Swaminathan, C. A. Duran-Villalobos, J. Branke, S. Goldrick, and M. Chappell, “Structural and practical identifiability analysis in bioengineering: a beginner’s guide,” Journal of Biological Engineering, vol. 18, no. 1, p. 20, 2024.
  • U. Abdullah, Ş. Arslan, H. S. Manap, T. Gürkan, M. Çalışkan, A. Dayıoğlu, H. N. Efe, M. Yılmaz, A. Z. İbrahimoğlu, E. Gültekin, R. Durna, R. Başar, F. B. Osmanoğlu, and S. Ören, “Türkiye COVID-19 pandemi izleme ekranı,” [Online]. Available: https://turcovid19.com/, August 2020.
  • 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,” Journal of Biological Dynamics, vol. 16, no. 1, pp. 412–438, 2022.
  • A. Raue, C. Kreutz, T. Maiwald, J. Bachmann, M. Schilling, U. Klingmüller, and J. Timmer, “Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood,” Bioinformatics, vol. 25, no. 15, pp. 1923–1929, 2009.
  • J. K. Hale, “Functional differential equations,” in Analytic Theory of Differential Equations: The Proceedings of the Conference at Western Michigan University, Kalamazoo, from 30 April to 2 May 1970. Berlin, Heidelberg: Springer Berlin Heidelberg, Aug. 2006, pp. 9–22.
  • C. Kreutz, A. Raue, and J. Timmer, “Likelihood based observability analysis and confidence intervals for predictions of dynamic models,” BMC Systems Biology, vol. 6, pp. 1–9, 2012.
  • R. Dong, C. Goodbrake, H. Harrington, and P. G., “Differential elimination for dynamical models via projections with applications to structural identifiability,” SIAM Journal on Applied Algebra and Geometry, vol. 7, no. 1, pp. 194–235, 2023.
  • G. Chowell, S. Dahal, Y. R. Liyanage, A. Tariq, and N. Tuncer, “Structural identifiability analysis of epidemic models based on differential equations: a tutorial-based primer,” Journal of Mathematical Biology, vol. 87, no. 6, p. 79, 2023.
  • E. Walter and L. Pronzato, Identifiability of Parametric Models: From Experimental Data. Springer, 1997.
  • U. Abdullah, Ş. Arslan, H. S. Manap, T. Gürkan, M. Çalışkan, A. Dayıoğlu, H. N. Efe, M. Yılmaz, A. Z. İbrahimoğlu, E. Gültekin, R. Durna, R. Başar, F. B. Osmanoğlu, and S. Ören, “Türkiye’de COVID-19 pandemisinin monitorizasyonu için interaktif ve gerçek zamanlı bir web uygulaması: TURCOVID19 (An interactive web-based dashboard for COVID-19 pandemic in real-time monitorization in Türkiye: TURCOVID19),” Anadolu Kliniği Tıp Bilimleri Dergisi, vol. 25, no. Special Issue on COVID-19, pp. 154–155, 2020.
  • N. Tuncer and T. T. Le, “Structural and practical identifiability analysis of outbreak models,” Mathematical Biosciences, vol. 299, pp. 1–18, 2018.
  • H. Pohjanpalo, “System identifiability based on the power series expansion of the solution,” Mathematical Biosciences, vol. 41, no. 1–2, pp. 21–33, 1978.
  • G. Massonis and A. F. Villaverde, “Finding and breaking Lie symmetries: implications for structural identifiability and observability in biological modelling,” Symmetry, vol. 12, no. 3, p. 469, 2020.
  • Y. Lecourtier, F. Lamnabhi-Lagarrigue, and E. Walter, “Volterra and generating power series approaches to identifiability testing,” Identifiability of Parametric Models, pp. 50–66, 1987.
  • L. Ljung and T. Glad, “On global identifiability for arbitrary model parametrizations,” Automatica, vol. 30, no. 2, pp. 265–276, 1994.
  • J. Bezanson, A. Edelman, S. Karpinski, and V. B. Shah, “Julia: A fresh approach to numerical computing,” SIAM Review, vol. 59, no. 1, pp. 65–98, 2017.
  • R. Dong, C. Goodbrake, H. A. Harrington, and G. Pogudin, “Differential elimination for dynamical models via projections with applications to structural identifiability,” SIAM Journal on Applied Algebra and Geometry, vol. 7, no. 1, pp. 194–235, 2023.
  • Y. R. Liyanage, N. Heitzman-Breen, N. Tuncer, and S. M. Ciupe, “Identifiability investigation of within-host models of acute virus infection,” 2024. [Online]. Available: https://www.biorxiv.org/content/early/2024/05/10/2024.05.09.593464
  • F.-G. Wieland, A. L. Hauber, M. Rosenblatt, C. Tönsing, and J. Timmer, “On structural and practical identifiability,” Current Opinion in Systems Biology, vol. 25, pp. 60–69, 2021.
  • A. Raue, J. Karlsson, M. P. Saccomani, M. Jirstrand, and J. Timmer, “Comparison of approaches for parameter identifiability analysis of biological systems,” Bioinformatics, vol. 30, no. 10, pp. 1440–1447, 2014.
  • I. Siekmann, J. Sneyd, and E. J. Crampin, “MCMC can detect nonidentifiable models,” Biophysical Journal, vol. 103, no. 11, pp. 2275–2286, 2012.
  • L. E. Eberly and B. P. Carlin, “Identifiability and convergence issues for Markov chain Monte Carlo fitting of spatial models,” Statistics in Medicine, vol. 19, no. 17–18, pp. 2279–2294, 2000.
  • M. Joshi, A. Seidel-Morgenstern, and A. Kremling, “Exploiting the bootstrap method for quantifying parameter confidence intervals in dynamical systems,” Metabolic Engineering, vol. 8, no. 5, pp. 447–455, 2006.
  • J. A. Jacquez and P. Greif, “Numerical parameter identifiability and estimability: Integrating identifiability, estimability, and optimal sampling design,” Mathematical Biosciences, vol. 77, no. 1–2, pp. 201–227, 1985.
  • “Data2Dynamics software,” 2024. [Online]. Available: https://github.com/Data2Dynamics
  • A. Raue, B. Steiert, M. Schelker, C. Kreutz, T. Maiwald, H. Hass, J. Vanlier, C. Tönsing, L. Adlung, R. Engesser, et al., “Data2Dynamics: a modeling environment tailored to parameter estimation in dynamical systems,” Bioinformatics, vol. 31, no. 21, pp. 3558–3560, 2015.
  • A. Raue, M. Schilling, J. Bachmann, A. Matteson, M. Schelke, D. Kaschek, S. Hug, C. Kreutz, B. D. Harms, F. J. Theis, et al., “Lessons learned from quantitative dynamical modeling in systems biology,” PLOS ONE, vol. 8, no. 9, p. e74335, 2013.
  • G. Pogudin, “Speeding things up via linear first integrals,” 2024. [Online]. Available: https://github.com/SciML/StructuralIdentifiability.jl/issues/63
  • Soulaimani, A. Kaddar, and F. A. Rihan, “Stochastic stability and global dynamics of a mathematical model for drug use: Statistical sensitivity analysis via PRCC,” Partial Differential Equations in Applied Mathematics, vol. 12, p. 100964, 2024.
  • S. Marino, I. B. Hogue, C. J. Ray, and D. E. Kirschner, “A methodology for performing global uncertainty and sensitivity analysis in systems biology,” Journal of Theoretical Biology, vol. 254, no. 1, pp. 178–196, 2008.
  • K. Lab, “Our approach to uncertainty and sensitivity analysis (with R and MATLAB codes for use),” 2020. [Online]. Available: http://malthus.micro.med.umich.edu/lab/usanalysis.html
  • 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 Computational Biology, vol. 17, no. 9, p. e1009334, 2021.
  • C. Elias, A. Sekri, P. Leblanc, M. Cucherat, and P. Vanhems, “The incubation period of COVID-19: A meta-analysis,” International Journal of Infectious Diseases, vol. 104, pp. 708–710, 2021.

Türkiye'de COVID-19'un ilk dalgası için bir matematiksel modelin tanımlanabilirlik analizi

Year 2025, Volume: 14 Issue: 1, 494 - 512, 26.03.2025

Tuğba Akman

https://doi.org/10.17798/bitlisfen.1602308

Abstract

Bu çalışmada, Türkiye'de COVID-19'un birinci zirvesini ele alan yapısal olarak tanımlanabilir bir matematiksel model geliştirilmiştir. Pandemi İzleme Ekranı TURCOVID19'den elde edilen, ilk zirve dönemi boyunca COVID-19 vaka sayıları, ölümler, yoğun bakım ünitesindeki hasta sayısı ve solunum cihazına bağlı hasta sayısı, veri kullanılmıştır. Yapısal tanımlanabilirlik analizi, açık kaynak yazılımı Julia kullanılarak gerçekleştirilmiştir. Modeldeki bazı parametreler literatüre dayalı olarak sabitlenmiş olup, geri kalan parametreler ise Data2Dynamics yazılımı kullanılarak hesaplanmıştır. Sonuçlarımızın, kullanılan veri ile tutarlı olduğu görülmektedir. Parametre değerlerindeki belirsizlikleri incelemek için profil benzerliği yöntemiyle pratik tanımlanabilirlik analizi yapılmıştır. Bu analiz, model parametrelerinden üçünün, yani semptomatik enfekte bireylerin hastaneye yatış hızının, virüse maruz kalan bireylerin ve semptomatik enfekte bireylerin virüs bulaştırma hızlarının, pratik olarak tanımlanabilir olmadığını ortaya koymaktadır. Bu sonuçlar, oluşturulan model aracılığıyla müdahale stratejilerinin dikkatlice uygulanması gerektiği anlamına gelmektedir.

Keywords

Yapısal tanımlanabilirlik pratik tanımlanabilirlik COVID-19 matematiksel modelleme Türkiye

References

  • E. Polat, “Using quality control charts for monitoring COVID-19 daily cases and deaths in Türkiye,” Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 13, no. 1, pp. 134–152.
  • A. Şimşek, “Estimating the expected influence capacities of nodes in complex networks under the susceptible-infectious-recovered model,” Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 13, no. 2, pp. 408–417.
  • 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,” Computer Methods and Programs in Biomedicine, vol. 209, p. 106301, 2021.
  • I. Rahimi, F. Chen, and A. H. Gandomi, “A review on COVID-19 forecasting models,” Neural Computing and Applications, vol. 35, no. 33, pp. 23671–23681, 2023.
  • Y. Xiang, Y. Jia, L. Chen, L. Guo, B. Shu, and E. Long, “COVID-19 epidemic prediction and the impact of public health interventions: A review of COVID-19 epidemic models,” Infectious Disease Modelling, vol. 6, pp. 324–342, 2021.
  • S. E. Eikenberry, M. Mancuso, E. Iboi, T. Phan, K. Eikenberry, Y. Kuang, E. Kostelich, and A. B. Gumel, “To mask or not to mask: Modeling the potential for face mask use by the general public to curtail the COVID-19 pandemic,” Infectious Disease Modelling, vol. 5, pp. 293–308, 2020.
  • S. K. Biswas, J. K. Ghosh, S. Sarkar, and U. Ghosh, “COVID-19 pandemic in India: a mathematical model study,” Nonlinear Dynamics, vol. 102, pp. 537–553, 2020.
  • O. Torrealba-Rodriguez, R. Conde-Gutiérrez, and A. Hernández-Javier, “Modeling and prediction of COVID-19 in Mexico applying mathematical and computational models,” Chaos, Solitons & Fractals, vol. 138, p. 109946, 2020.
  • A. J. Kucharski, T. W. Russell, C. Diamond, Y. Liu, J. Edmunds, S. Funk, R. M. Eggo, F. Sun, M. Jit, and J. D. Munday, “Early dynamics of transmission and control of COVID-19: a mathematical modelling study,” The Lancet Infectious Diseases, vol. 20, no. 5, pp. 553–558, 2020.
  • M. Carlsson and C. Söderberg-Nauclér, “COVID-19 modeling outcome versus reality in Sweden,” Viruses, vol. 14, no. 8, p. 1840, 2022.
  • A. R. Tuite, D. N. Fisman, and A. L. Greer, “Mathematical modelling of COVID-19 transmission and mitigation strategies in the population of Ontario, Canada,” CMAJ, vol. 192, no. 19, pp. E497–E505, 2020.
  • T. Akman, E. Köse, and N. Tuncer, “Assessment of vaccination and underreporting on COVID-19 infections in based on effective reproduction number,” International Journal of Biomathematics, pp. 2350102 – Online ready, 2024. [Online]. Available: https://doi.org/10.1142/S1793524523501024
  • S. Moore, E. M. Hill, M. J. Tildesley, L. Dyson, and M. J. Keeling, “Vaccination and non-pharmaceutical interventions for COVID-19: a mathematical modelling study,” The Lancet Infectious Diseases, vol. 21, no. 6, pp. 793–802, 2021.
  • S. S. Musa, S. Qureshi, S. Zhao, A. Yusuf, U. T. Mustapha, and D. He, “Mathematical modeling of COVID-19 epidemic with effect of awareness programs,” Infectious Disease Modelling, vol. 6, pp. 448–460, 2021.
  • S. Gao, P. Binod, C. W. Chukwu, T. Kwofie, S. Safdar, L. Newman, S. Choe, B. K. Datta, W. K. Attipoe, W. Zhang, and B. K. Datta, “A mathematical model to assess the impact of testing and isolation compliance on the transmission of COVID-19,” Infectious Disease Modelling, vol. 8, no. 2, pp. 427–444, 2023.
  • A. Malik, N. Kumar, and K. Alam, “Estimation of parameter of fractional order COVID-19 SIQR epidemic model,” Materials Today: Proceedings, vol. 49, pp. 3265–3269, 2022.
  • A. Malik, K. Alam, and N. Kumar, “Coefficient identification in SIQR model of inverse problem of COVID-19,” European Journal of Molecular and Clinical Medicine, vol. 7, 2020.
  • L. Wanika, J. R. Egan, N. Swaminathan, C. A. Duran-Villalobos, J. Branke, S. Goldrick, and M. Chappell, “Structural and practical identifiability analysis in bioengineering: a beginner’s guide,” Journal of Biological Engineering, vol. 18, no. 1, p. 20, 2024.
  • U. Abdullah, Ş. Arslan, H. S. Manap, T. Gürkan, M. Çalışkan, A. Dayıoğlu, H. N. Efe, M. Yılmaz, A. Z. İbrahimoğlu, E. Gültekin, R. Durna, R. Başar, F. B. Osmanoğlu, and S. Ören, “Türkiye COVID-19 pandemi izleme ekranı,” [Online]. Available: https://turcovid19.com/, August 2020.
  • 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,” Journal of Biological Dynamics, vol. 16, no. 1, pp. 412–438, 2022.
  • A. Raue, C. Kreutz, T. Maiwald, J. Bachmann, M. Schilling, U. Klingmüller, and J. Timmer, “Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood,” Bioinformatics, vol. 25, no. 15, pp. 1923–1929, 2009.
  • J. K. Hale, “Functional differential equations,” in Analytic Theory of Differential Equations: The Proceedings of the Conference at Western Michigan University, Kalamazoo, from 30 April to 2 May 1970. Berlin, Heidelberg: Springer Berlin Heidelberg, Aug. 2006, pp. 9–22.
  • C. Kreutz, A. Raue, and J. Timmer, “Likelihood based observability analysis and confidence intervals for predictions of dynamic models,” BMC Systems Biology, vol. 6, pp. 1–9, 2012.
  • R. Dong, C. Goodbrake, H. Harrington, and P. G., “Differential elimination for dynamical models via projections with applications to structural identifiability,” SIAM Journal on Applied Algebra and Geometry, vol. 7, no. 1, pp. 194–235, 2023.
  • G. Chowell, S. Dahal, Y. R. Liyanage, A. Tariq, and N. Tuncer, “Structural identifiability analysis of epidemic models based on differential equations: a tutorial-based primer,” Journal of Mathematical Biology, vol. 87, no. 6, p. 79, 2023.
  • E. Walter and L. Pronzato, Identifiability of Parametric Models: From Experimental Data. Springer, 1997.
  • U. Abdullah, Ş. Arslan, H. S. Manap, T. Gürkan, M. Çalışkan, A. Dayıoğlu, H. N. Efe, M. Yılmaz, A. Z. İbrahimoğlu, E. Gültekin, R. Durna, R. Başar, F. B. Osmanoğlu, and S. Ören, “Türkiye’de COVID-19 pandemisinin monitorizasyonu için interaktif ve gerçek zamanlı bir web uygulaması: TURCOVID19 (An interactive web-based dashboard for COVID-19 pandemic in real-time monitorization in Türkiye: TURCOVID19),” Anadolu Kliniği Tıp Bilimleri Dergisi, vol. 25, no. Special Issue on COVID-19, pp. 154–155, 2020.
  • N. Tuncer and T. T. Le, “Structural and practical identifiability analysis of outbreak models,” Mathematical Biosciences, vol. 299, pp. 1–18, 2018.
  • H. Pohjanpalo, “System identifiability based on the power series expansion of the solution,” Mathematical Biosciences, vol. 41, no. 1–2, pp. 21–33, 1978.
  • G. Massonis and A. F. Villaverde, “Finding and breaking Lie symmetries: implications for structural identifiability and observability in biological modelling,” Symmetry, vol. 12, no. 3, p. 469, 2020.
  • Y. Lecourtier, F. Lamnabhi-Lagarrigue, and E. Walter, “Volterra and generating power series approaches to identifiability testing,” Identifiability of Parametric Models, pp. 50–66, 1987.
  • L. Ljung and T. Glad, “On global identifiability for arbitrary model parametrizations,” Automatica, vol. 30, no. 2, pp. 265–276, 1994.
  • J. Bezanson, A. Edelman, S. Karpinski, and V. B. Shah, “Julia: A fresh approach to numerical computing,” SIAM Review, vol. 59, no. 1, pp. 65–98, 2017.
  • R. Dong, C. Goodbrake, H. A. Harrington, and G. Pogudin, “Differential elimination for dynamical models via projections with applications to structural identifiability,” SIAM Journal on Applied Algebra and Geometry, vol. 7, no. 1, pp. 194–235, 2023.
  • Y. R. Liyanage, N. Heitzman-Breen, N. Tuncer, and S. M. Ciupe, “Identifiability investigation of within-host models of acute virus infection,” 2024. [Online]. Available: https://www.biorxiv.org/content/early/2024/05/10/2024.05.09.593464
  • F.-G. Wieland, A. L. Hauber, M. Rosenblatt, C. Tönsing, and J. Timmer, “On structural and practical identifiability,” Current Opinion in Systems Biology, vol. 25, pp. 60–69, 2021.
  • A. Raue, J. Karlsson, M. P. Saccomani, M. Jirstrand, and J. Timmer, “Comparison of approaches for parameter identifiability analysis of biological systems,” Bioinformatics, vol. 30, no. 10, pp. 1440–1447, 2014.
  • I. Siekmann, J. Sneyd, and E. J. Crampin, “MCMC can detect nonidentifiable models,” Biophysical Journal, vol. 103, no. 11, pp. 2275–2286, 2012.
  • L. E. Eberly and B. P. Carlin, “Identifiability and convergence issues for Markov chain Monte Carlo fitting of spatial models,” Statistics in Medicine, vol. 19, no. 17–18, pp. 2279–2294, 2000.
  • M. Joshi, A. Seidel-Morgenstern, and A. Kremling, “Exploiting the bootstrap method for quantifying parameter confidence intervals in dynamical systems,” Metabolic Engineering, vol. 8, no. 5, pp. 447–455, 2006.
  • J. A. Jacquez and P. Greif, “Numerical parameter identifiability and estimability: Integrating identifiability, estimability, and optimal sampling design,” Mathematical Biosciences, vol. 77, no. 1–2, pp. 201–227, 1985.
  • “Data2Dynamics software,” 2024. [Online]. Available: https://github.com/Data2Dynamics
  • A. Raue, B. Steiert, M. Schelker, C. Kreutz, T. Maiwald, H. Hass, J. Vanlier, C. Tönsing, L. Adlung, R. Engesser, et al., “Data2Dynamics: a modeling environment tailored to parameter estimation in dynamical systems,” Bioinformatics, vol. 31, no. 21, pp. 3558–3560, 2015.
  • A. Raue, M. Schilling, J. Bachmann, A. Matteson, M. Schelke, D. Kaschek, S. Hug, C. Kreutz, B. D. Harms, F. J. Theis, et al., “Lessons learned from quantitative dynamical modeling in systems biology,” PLOS ONE, vol. 8, no. 9, p. e74335, 2013.
  • G. Pogudin, “Speeding things up via linear first integrals,” 2024. [Online]. Available: https://github.com/SciML/StructuralIdentifiability.jl/issues/63
  • Soulaimani, A. Kaddar, and F. A. Rihan, “Stochastic stability and global dynamics of a mathematical model for drug use: Statistical sensitivity analysis via PRCC,” Partial Differential Equations in Applied Mathematics, vol. 12, p. 100964, 2024.
  • S. Marino, I. B. Hogue, C. J. Ray, and D. E. Kirschner, “A methodology for performing global uncertainty and sensitivity analysis in systems biology,” Journal of Theoretical Biology, vol. 254, no. 1, pp. 178–196, 2008.
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Details

Primary Language English
Subjects Biological Mathematics, Dynamical Systems in Applications
Journal Section Research Article
Authors

Tuğba Akman 0000-0003-1206-2287

Publication Date March 26, 2025
Submission Date December 16, 2024
Acceptance Date January 24, 2025
Published in Issue Year 2025 Volume: 14 Issue: 1

Cite

IEEE T. Akman, “Identifiability Analysis of a Mathematical Model for the First Wave of COVID-19 in Türkiye”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 14, no. 1, pp. 494–512, 2025, doi: 10.17798/bitlisfen.1602308.
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