Modeling epidemic flow with fluid dynamics

Ziqiang Cheng; Jin Wang; Ziqiang Cheng; Jin Wang

doi:10.3934/mbe.2022388

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 8: 8334-8360. doi: 10.3934/mbe.2022388

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Research article

Modeling epidemic flow with fluid dynamics

Ziqiang Cheng ¹,
Jin Wang ^{2
,
,}

1.
School of Mathematics, Hefei University of Technology, Hefei, Anhui 230009, China
2.
Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA

Academic Editor: Yang Kuang

Received: 07 April 2022 Revised: 27 May 2022 Accepted: 31 May 2022 Published: 09 June 2022

In this paper, a new mathematical model based on partial differential equations is proposed to study the spatial spread of infectious diseases. The model incorporates fluid dynamics theory and represents the epidemic spread as a fluid motion generated through the interaction between the susceptible and infected hosts. At the macroscopic level, the spread of the infection is modeled as an inviscid flow described by the Euler equation. Nontrivial numerical methods from computational fluid dynamics (CFD) are applied to investigate the model. In particular, a fifth-order weighted essentially non-oscillatory (WENO) scheme is employed for the spatial discretization. As an application, this mathematical and computational framework is used in a simulation study for the COVID-19 outbreak in Wuhan, China. The simulation results match the reported data for the cumulative cases with high accuracy and generate new insight into the complex spatial dynamics of COVID-19.
- epidemic modeling,
- computational fluid dynamics,
- COVID-19
Citation: Ziqiang Cheng, Jin Wang. Modeling epidemic flow with fluid dynamics[J]. Mathematical Biosciences and Engineering, 2022, 19(8): 8334-8360. doi: 10.3934/mbe.2022388

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Abstract

In this paper, a new mathematical model based on partial differential equations is proposed to study the spatial spread of infectious diseases. The model incorporates fluid dynamics theory and represents the epidemic spread as a fluid motion generated through the interaction between the susceptible and infected hosts. At the macroscopic level, the spread of the infection is modeled as an inviscid flow described by the Euler equation. Nontrivial numerical methods from computational fluid dynamics (CFD) are applied to investigate the model. In particular, a fifth-order weighted essentially non-oscillatory (WENO) scheme is employed for the spatial discretization. As an application, this mathematical and computational framework is used in a simulation study for the COVID-19 outbreak in Wuhan, China. The simulation results match the reported data for the cumulative cases with high accuracy and generate new insight into the complex spatial dynamics of COVID-19.

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