Survival dynamical systems: individual-level survival analysis from population-level epidemic models

Area of Science:

• Epidemiology
• Mathematical Biology
• Statistical Inference

Background:

• Stochastic epidemic models are crucial for understanding disease spread.
• Analyzing individual infection and recovery times is key for public health.
• Traditional methods may not fully leverage population-level dynamics for individual inference.

Purpose of the Study:

• To demonstrate that solutions to ordinary differential equations from epidemic models can serve as survival functions.
• To introduce the concept of a survival dynamical system (SDS) for individual-level analysis.
• To validate the SDS approach using synthetic and real-world outbreak data.

Main Methods:

• Interpreting ordinary differential equations of large-population epidemic models as survival or cumulative hazard functions.
• Developing the survival dynamical system (SDS) framework for individual-level probability laws.
• Conducting numerical analyses with synthetic data and comparing with maximum-likelihood methods.
• Applying the SDS approach to analyze a 2009 influenza A(H1N1) outbreak dataset.

Main Results:

• Solutions to epidemic ODEs can be directly interpreted as individual survival or hazard functions.
• The SDS framework effectively derives individual infection and recovery time probabilities from population dynamics.
• SDS analysis demonstrated favorable comparison against complete-data maximum-likelihood analysis on synthetic data.
• The SDS approach was successfully applied to real-world influenza A(H1N1) outbreak data.

Conclusions:

• Survival dynamical systems provide a novel bridge between population-level epidemic modeling and individual-level statistical inference.
• The SDS method offers a statistically sound and computationally efficient alternative for analyzing epidemic data.
• This approach enhances our ability to understand and predict disease dynamics at both population and individual levels.