An extension of age-of-infection models: A SECIR model based on integro-differential equations for epidemic outbreaks

Kurzfassung

Ordinary differential equations are a popular tool to model the spread of infectious diseases, yet they implicitly assume an exponential distribution to describe the transition 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 non-pharmaceutical interventions. However, in ordinary differential models these aspects cannot be captured directly. To enhance the accuracy of simulations we propose a generalized model based on integro-differential equations with eight infection states. The model allows for variable stay time distributions and generalizes the concept of age-of-infection models. In this, we include particular infection states for severe and critical cases to allow for surveillance of the clinical sector, avoiding bottle necks and overloads. Messina et al. [1] introduced a non-standard numerical scheme to solve an SIR model based on integrodifferential equations. We adapt this scheme to our more advanced model and validate our approach numerically. We can show that our novel model is intrinsically capable of better assessing disease dynamics upon the introduction of nonpharmaceutical interventions. References [1] E. Messina, M. Pezzella and A. Vecchio, A non-standard numerical scheme for an age-of-infection epidemic model, Journal of Computational Dynamics, 2022.