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

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

Applied Mathematics and Computation, 2026, vol. 509, issue C

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.

Keywords: Integro-differential equations; Infectious disease modeling; Numerical analysis; Numerical scheme; Nonexponential stay times; Age-of-infection model; MEmilio framework (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:509:y:2026:i:c:s0096300325003625

DOI: 10.1016/j.amc.2025.129636

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