Survival properties and spread rates in non-autonomous spread models.

Area of Science:

• Epidemiology
• Mathematical Modeling
• Network Theory

Background:

• Disease transmission patterns evolve over time.
• Accurate models are crucial for understanding disease spread dynamics.
• Existing models may not fully capture complex transmission behaviors.

Purpose of the Study:

• To develop and validate non-autonomous topological and random spread models for disease transmission.
• To connect model survival characteristics with mixing properties using ξ-matrices.
• To introduce and provide formulas for calculating spread rates in periodic models.

Main Methods:

• Development of non-autonomous topological and random spread models.
• Validation of model survival characteristics.
• Analysis of model connection with mixing properties via ξ-matrices (spread mean matrices).
• Introduction of spread rate concepts and calculation formulas for periodic models.

Main Results:

• Validated survival characteristics of the developed spread models.
• Established a connection between spread models and mixing properties through ξ-matrices.
• Introduced quantifiable spread rates for periodic topological and random models.
• Numerical examples and simulations supported the theoretical findings.

Conclusions:

• The developed non-autonomous models offer a precise method for determining disease spread behaviors.
• The ξ-matrices effectively elucidate the link between model survival and mixing properties.
• The introduced spread rates provide a new metric for analyzing disease dynamics in periodic scenarios.
• The study offers a robust theoretical framework supported by empirical evidence for disease transmission modeling.