Delay differential equations for the spatially resolved simulation of epidemics with specific application to COVID‐19
Mathematical Methods in the Applied Sciences, vol. 45, pp. 4752–4771
Abstract
(SIR) compartmental framework, modeling the epidemic with a system of ordinary differential equations. Alternative formulations using a partial differential equation (PDE) to incorporate both spatial and temporal resolution have also been introduced, with their numerical results showing potentially powerful descriptive and predictive capacity. In the present work, we introduce a new variation to such models by using delay differential equations (DDEs). The dynamics of many infectious diseases, including COVID-19, exhibit delays due to incubation periods and related phenomena. Accordingly, DDE models allow for a natural representation of the problem dynamics, in addition to offering advantages in terms of computational time and modeling, as they eliminate the need for additional, difficult-to-estimate, compartments (such as exposed individuals) to incorporate time delays. In the present work, we introduce a DDE epidemic model in both an ordinary and partial differential equation framework. We present a series of mathematical results assessing the stability of the formulation. We then perform several numerical experiments, validating both the mathematical results and establishing model's ability to reproduce measured data on realistic problems.
Authors 3
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Affiliation as printed
Division of Mathematics, Gran Sasso Science Institute Viale F. Crispi 7 L'Aquila 67100 Province of L'Aquila Italy
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Affiliation as printed
Institut für Geometrie und Praktische Mathematik (IGPM), RWTH Aachen University Templergraben 55 Aachen 52062 Germany
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Alex Viguerie corresponding
Affiliation as printed
Division of Mathematics, Gran Sasso Science Institute Viale F. Crispi 7 L'Aquila 67100 Province of L'Aquila Italy
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