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A dynamical systems perspective on rates and transition probabilities

This section explains key concepts at the interface between dynamics and statistics that form the foundation of disease modeling. The guide is designed for researchers, disease modelers, and students who want to understand how mathematical models translate biological processes into results that can be used to inform decision-making.

Key concepts covered

  • Rates as used in linear time-invariant systems
  • Converting from continuous to discrete time, and back
  • Extending from deterministic to stochastic dynamics
  • Simulating state transitions in stochastic disease models
  • Understanding dwell times and the memoryless property
  • Estimating rates and probabilities from data
  • Comparative measures like rate ratios, risk ratios, and odds ratios

Review all topics within this section to cover the foundational concepts that will enable you to understand and use rates, transition probabilities, and dwell times in your disease modeling applications. It explores the mathematical principles that underlie these concepts, how to convert between continuous and discrete time representations, and how to simulate state transitions in disease models.

There's much more that a dynamical systems perspective can teach us, and we encourage you to reach out if anything was unclear or if you'd like to learn more.