New approximations, and policy implications, from a delayed dynamic model of a fast pandemic

Vyasarayani, C.P. and Chatterjee, Anindya (2020) New approximations, and policy implications, from a delayed dynamic model of a fast pandemic. Physica D: Nonlinear Phenomena, 414 (132701). p. 132701. ISSN 01672789

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We study an SEIQR (Susceptible–Exposed–Infectious–Quarantined–Recovered) model due to Young et al. (2019) for an infectious disease, with time delays for latency and an asymptomatic phase. For fast pandemics where nobody has prior immunity and everyone has immunity after recovery, the SEIQR model decouples into two nonlinear delay differential equations (DDEs) with five parameters. One parameter is set to unity by scaling time. The simple subcase of perfect quarantining and zero self-recovery before quarantine, with two free parameters, is examined first. The method of multiple scales yields a hyperbolic tangent solution; and a long-wave (short delay) approximation yields a first order ordinary differential equation (ODE). With imperfect quarantining and nonzero self-recovery, the long-wave approximation is a second order ODE. These three approximations each capture the full outbreak, from infinitesimal initiation to final saturation. Low-dimensional dynamics in the DDEs is demonstrated using a six state non-delayed reduced order model obtained by Galerkin projection. Numerical solutions from the reduced order model match the DDE over a range of parameter choices and initial conditions. Finally, stability analysis and numerics show how a well executed temporary phase of social distancing can reduce the total number of people affected. The reduction can be by as much as half for a weak pandemic, and is smaller but still substantial for stronger pandemics. An explicit formula for the greatest possible reduction is given.

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IITH Creators:
IITH CreatorsORCiD
Vyasarayani, Chandrika Prakash
Item Type: Article
Uncontrolled Keywords: First order ordinary differential equations; Galerkin projections; Long-wave approximation; Method of multiple scale; Nonlinear delay differential equation; Policy implications; Reduced order models; Stability analysis
Subjects: Physics > Mechanical and aerospace
Divisions: Department of Mechanical & Aerospace Engineering
Depositing User: . LibTrainee 2021
Date Deposited: 28 Jun 2021 06:56
Last Modified: 04 Mar 2022 05:07
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