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Spatial and temporal dynamics of SARS-CoV-2: Modeling, analysis and simulation.

Peng Wu1, Xiunan Wang2, Zhaosheng Feng3

  • 1Institute of Mathematics & Interdisciplinary Sciences, Zhejiang University of Finance & Economics, Hangzhou 310018, China.

Applied Mathematical Modelling
|September 20, 2022
PubMed
Summary

This study models severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection dynamics using reaction-diffusion equations. Findings show spatial factors significantly impact viral spread, crucial for effective treatments.

Keywords:
Basic reproduction numberGlobal dynamicsHumoral immunityPermanence,SARS-CoV-2 modelingViral diffusion

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Area of Science:

  • Mathematical Biology
  • Epidemiology
  • Virology

Background:

  • Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection dynamics are complex.
  • Understanding viral spread in heterogeneous environments is crucial for public health.

Purpose of the Study:

  • To formulate and analyze a reaction-diffusion model for SARS-CoV-2 infection.
  • To investigate the impact of spatial heterogeneity and humoral immunity on viral dynamics.
  • To determine key thresholds governing infection equilibria.

Main Methods:

  • Development of a reaction-diffusion model with general rate functions.
  • Analysis of model well-posedness, basic reproduction number, and stability.
  • Investigation of spatial diffusion models with humoral immunity.
  • Numerical simulations to validate theoretical findings.

Main Results:

  • The model characterizes SARS-CoV-2 infection in heterogeneous environments.
  • Humoral immunity and spatial diffusion significantly influence infection outcomes.
  • Two dynamical thresholds determine the global attractivity of different equilibria.
  • Spatial heterogeneity and incidence types demonstrably impact the infection process.

Conclusions:

  • Reaction-diffusion modeling provides insights into SARS-CoV-2 spread.
  • Spatial factors and immune responses are critical for controlling SARS-CoV-2.
  • Model findings have implications for experimental design and clinical interventions.