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A viral load-based model for epidemic spread on spatial networks.

Nadia Loy1, Andrea Tosin1

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Summary
This summary is machine-generated.

This study introduces a kinetic model for infectious disease spread across networks, analyzing viral load and social contacts. It examines disease blow-up, eradication, and the impact of containment strategies like quarantine.

Keywords:
Boltzmann-type equationsMarkov-type jump processescommuterslabel switchingquarantine

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Network Science

Background:

  • Infectious disease transmission is complex, influenced by population movement and social interactions.
  • Understanding disease dynamics on interconnected populations (networks) is crucial for public health.
  • Existing models may not fully capture the interplay between viral load, social contacts, and spatial networks.

Purpose of the Study:

  • To develop a Boltzmann-type kinetic model for infectious disease spread on networks.
  • To analyze the long-term behavior of disease density and mean viral load.
  • To investigate the effects of containment measures on disease diffusion.

Main Methods:

  • Formulation of a Boltzmann-type kinetic model.
  • Derivation of hydrodynamic equations for population density and mean viral load.
  • Numerical simulations to analyze disease trends and intervention impacts.

Main Results:

  • The model captures disease spread dynamics, including potential for blow-up (outbreaks) or eradication.
  • Analysis of large-time trends reveals critical factors influencing disease persistence or decline.
  • Numerical tests demonstrate the effectiveness of quarantine and lockdown measures in controlling disease diffusion.

Conclusions:

  • The proposed kinetic model provides a robust framework for studying epidemic dynamics on networks.
  • Understanding viral load and network structure is key to predicting and managing outbreaks.
  • Confinement strategies can significantly mitigate disease spread, highlighting the importance of spatial interventions.