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Delay differential equations for the spatially-resolved simulation of epidemics with specific application to COVID-19
  • Nicola Guglielmi,
  • Elisa Iacomini,
  • Alexander Viguerie
Nicola Guglielmi
Gran Sasso Science Institute
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Elisa Iacomini
RWTH Aachen University
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Alexander Viguerie
Gran Sasso Science Institute
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Abstract

In the wake of the 2020 COVID-19 epidemic, much work has been performed on the development of mathematical models for the simulation of the epidemic, and of disease models generally. Most works follow the susceptible-infected-removed (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.

Peer review status:UNDER REVIEW

14 Apr 2021Submitted to Mathematical Methods in the Applied Sciences
15 Apr 2021Submission Checks Completed
15 Apr 2021Assigned to Editor
19 Apr 2021Reviewer(s) Assigned
06 Aug 2021Review(s) Completed, Editorial Evaluation Pending
07 Aug 2021Editorial Decision: Revise Minor
12 Aug 20211st Revision Received
13 Aug 2021Submission Checks Completed
13 Aug 2021Assigned to Editor
13 Aug 2021Reviewer(s) Assigned