Complex network model for COVID-19: Human behavior, pseudo-periodic solutions and multiple epidemic waves.

Area of Science:

• Epidemiology
• Mathematical Biology
• Public Health

Background:

• The COVID-19 pandemic highlighted the need for dynamic models to understand SARS-CoV-2 transmission.
• Human behavior and policy interventions critically influence epidemic trajectories.
• Previous models often lacked the granularity to capture complex real-world dynamics.

Purpose of the Study:

• To develop and analyze a mathematical model for SARS-CoV-2 transmission dynamics.
• To incorporate human behavior and public health policies using piecewise constant parameters.
• To investigate epidemic waves and the impact of mobility using a complex network model.

Main Methods:

• Developed a mathematical model for SARS-CoV-2 transmission in a non-constant population.
• Analyzed model stability for disease-free and endemic equilibria.
• Simulated a six-region complex network model using real-world COVID-19 data from Portugal.

Main Results:

• Proved the existence of pseudo-oscillations, linked to epidemic waves, in the model with piecewise constant parameters.
• Identified network topologies that minimize active infected individuals.
• Determined topologies that are likely to exacerbate infection levels.

Conclusions:

• The proposed modeling methodology offers a powerful tool for managing COVID-19 outbreaks regionally.
• The approach can inform decisions regarding border control and public health interventions.
• Understanding network topology is crucial for mitigating epidemic spread.