Epidemiological theory of virus variants

Area of Science:

• Mathematical modeling of infectious diseases
• Theoretical physics applications in epidemiology
• Complex systems dynamics

Background:

• Traditional compartmental models (e.g., SIR) are foundational but often lack mechanisms for competing variant dynamics.
• Understanding the temporal evolution of multiple virus strains is crucial for public health interventions.
• Identifying underlying principles governing variant competition can enhance predictive capabilities.

Purpose of the Study:

• To develop a novel physics-inspired mathematical model for the temporal evolution of competing virus variants.
• To incorporate concepts of scale invariance and fixed points into epidemiological models.
• To validate the proposed model using real-world COVID-19 variant data.

Main Methods:

• Modification of SIR-type compartmental models to include competing variants.
• Re-phrasing variant evolution using flow equations that converge to quasi fixed points.
• Application of the epidemic Renormalisation Group framework, leveraging near scale invariance.
• Empirical validation against the observed time evolution of COVID-19 variants.

Main Results:

• A physics-inspired mathematical model was successfully developed to describe competing virus variant dynamics.
• The model utilizes (quasi) fixed points to capture large time scale invariance.
• The epidemic Renormalisation Group framework effectively organizes variant evolution.
• Empirical validation using COVID-19 data confirmed the model's predictive power.

Conclusions:

• The proposed physics-inspired model provides a robust framework for understanding and predicting the evolution of competing virus variants.
• The concepts of scale invariance and fixed points are valuable tools in epidemiological modeling.
• The epidemic Renormalisation Group offers an effective approach for analyzing complex disease dynamics.