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

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

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 239, issue C, 823-844

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.

Keywords: Ordinary differential equations; Exponential distribution; Linear Chain Trick; Gamma Chain Trick; Erlang distribution; Infectious disease modeling; Numerical solution; MEmilio framework (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:239:y:2026:i:c:p:823-844

DOI: 10.1016/j.matcom.2025.07.045

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