Modelling the spatial spread of COVID-19 in a German district using a diffusion model

Area of Science:

• Epidemiology
• Mathematical Biology
• Computational Science

Background:

• Modeling infectious disease spread is crucial, especially during early pandemic stages with limited data.
• Understanding local diffusion dynamics is vital for effective public health interventions.
• Previous spatial spread models often lacked real-world, small-scale data application.

Purpose of the Study:

• To model the local spread of COVID-19 infections using partial differential equation (PDE) models.
• To gain a better understanding of disease diffusion dynamics on smaller scales.
• To estimate key epidemiological parameters using real-world data.

Main Methods:

• Utilized a reaction-diffusion model with compartments for Susceptibles, Exposed, Infected, and Recovered (SEIR).
• Employed numerical methods, including Crank-Nicholson and finite element methods, for solving the PDE system on 2D domains.
• Applied Metropolis algorithm and adjoint method for parameter estimation (transmission, recovery, detection, diffusivity rates) via least squares fitting.

Main Results:

• Successfully modeled spatio-temporal COVID-19 spread in a German district during the second pandemic wave.
• Estimated key epidemiological parameters using real district-level medical data.
• Validated numerical methods, showing comparable results and good approximation of infected cases.

Conclusions:

• Partial differential equation models provide valuable insights into local disease spread dynamics.
• Parameter estimation using real-world data is feasible and crucial for refining epidemiological models.
• The study demonstrates the utility of numerical methods for analyzing spatial disease diffusion.