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Revisiting the Linear Chain Trick in epidemiological models: Implications of underlying assumptions for numerical solutions

Author

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  • Plötzke, Lena
  • Wendler, Anna
  • Schmieding, René
  • Kühn, Martin J.

Abstract

In order to simulate the spread of infectious diseases, many epidemiological models use systems of ordinary differential equations (ODEs) to describe the underlying dynamics. These models incorporate the implicit assumption, that the stay time in each disease state follows an exponential distribution. However, a substantial number of epidemiological, data-based studies indicate that this assumption is not plausible. One method to alleviate this limitation is to employ the Linear Chain Trick (LCT) for ODE systems, which realizes the use of Erlang distributed stay times. As indicated by data, this approach allows for more realistic models while maintaining the advantages of using ODEs.

Suggested Citation

  • Plötzke, Lena & Wendler, Anna & Schmieding, René & Kühn, Martin J., 2026. "Revisiting the Linear Chain Trick in epidemiological models: Implications of underlying assumptions for numerical solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 239(C), pages 823-844.
    • Handle: RePEc:eee:matcom:v:239:y:2026:i:c:p:823-844
    DOI: 10.1016/j.matcom.2025.07.045
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    References listed on IDEAS

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    1. Helen J Wearing & Pejman Rohani & Matt J Keeling, 2005. "Appropriate Models for the Management of Infectious Diseases," PLOS Medicine, Public Library of Science, vol. 2(7), pages 1-1, July.
    2. Wendler, Anna & Plötzke, Lena & Tritzschak, Hannah & Kühn, Martin J., 2026. "A nonstandard numerical scheme for a novel SECIR integro-differential equation-based model allowing nonexponentially distributed stay times," Applied Mathematics and Computation, Elsevier, vol. 509(C).
    3. Elizabeth Hunter & Brian Mac Namee & John Kelleher, 2020. "A Hybrid Agent-Based and Equation Based Model for the Spread of Infectious Diseases," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 23(4), pages 1-14.
    4. Ganna Rozhnova & Christiaan H. Dorp & Patricia Bruijning-Verhagen & Martin C. J. Bootsma & Janneke H. H. M. Wijgert & Marc J. M. Bonten & Mirjam E. Kretzschmar, 2021. "Model-based evaluation of school- and non-school-related measures to control the COVID-19 pandemic," Nature Communications, Nature, vol. 12(1), pages 1-11, December.
    5. Christopher E Overton & Lorenzo Pellis & Helena B Stage & Francesca Scarabel & Joshua Burton & Christophe Fraser & Ian Hall & Thomas A House & Chris Jewell & Anel Nurtay & Filippo Pagani & Katrina A L, 2022. "EpiBeds: Data informed modelling of the COVID-19 hospital burden in England," PLOS Computational Biology, Public Library of Science, vol. 18(9), pages 1-20, September.
    6. Liu, Jielun & Ong, Ghim Ping & Pang, Vincent Junxiong, 2022. "Modelling effectiveness of COVID-19 pandemic control policies using an Area-based SEIR model with consideration of infection during interzonal travel," Transportation Research Part A: Policy and Practice, Elsevier, vol. 161(C), pages 25-47.
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