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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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