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A nonstandard numerical scheme for a novel SECIR integro-differential equation-based model allowing nonexponentially distributed stay times

Author

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  • Wendler, Anna
  • Plötzke, Lena
  • Tritzschak, Hannah
  • Kühn, Martin J.

Abstract

Ordinary differential equations (ODE) are a popular tool to model the spread of infectious diseases, yet they implicitly assume an exponential distribution to describe the flow from one infection state to another. However, scientific experience yields more plausible distributions where the likelihood of disease progression or recovery changes accordingly with the duration spent in a particular state of the disease. Furthermore, transmission dynamics depend heavily on the infectiousness of individuals. The corresponding nonlinear variation with the time individuals have already spent in an infectious state requires more realistic models. The previously mentioned items are particularly crucial when modeling dynamics at change points such as the implementation of nonpharmaceutical interventions. In order to capture these aspects and to enhance the accuracy of simulations, integro-differential equations (IDE) can be used.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:509:y:2026:i:c:s0096300325003625
    DOI: 10.1016/j.amc.2025.129636
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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.
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    1. 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.

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