Modeling nonlocal behavior in epidemics via a reaction-diffusion system incorporating population movement along a...

Area of Science:

• Epidemiology
• Mathematical Biology
• Computational Science

Background:

• The COVID-19 pandemic highlighted the need for advanced infectious disease modeling.
• Existing reaction-diffusion models excel at spatial-temporal dynamics but struggle with long-distance travel and nonlocal transmission.
• Ordinary differential equation network models can represent nonlocal spread but lack spatial detail.

Purpose of the Study:

• To develop a hybrid mathematical model combining reaction-diffusion PDEs with network structures.
• To incorporate nonlocal population movement and disease transmission into a spatially explicit framework.
• To enhance the accuracy of epidemic modeling by accounting for both local and long-distance contagion dynamics.

Main Methods:

• Introduction of a population-transfer operator to couple distinct geographic regions within a reaction-diffusion system.
• Analytical investigation of the operator's impact on model consistency and well-posedness.
• Numerical simulations to validate the model and its ability to represent nonlocal phenomena.

Main Results:

• The population-transfer operator was shown to be mathematically sound and physically consistent.
• The model successfully integrated nonlocal transmission pathways into a reaction-diffusion framework.
• Simulations demonstrated the model's capability to capture complex epidemic spread patterns, including nonlocal effects.

Conclusions:

• The developed hybrid model offers a more comprehensive approach to infectious disease modeling.
• This technique effectively combines the strengths of reaction-diffusion and network-based models.
• The model provides a valuable tool for understanding and predicting epidemic dynamics in interconnected populations, as shown in the Rio de Janeiro COVID-19 simulation.