Multistate Models

TL;DR

Models systems that can occupy multiple states and move between them over time.
Used to analyze and predict behavior by representing transitions or population changes.
Common forms include Markov chains (state transitions) and branching processes (population growth/evolution).

Definition

Multistate models are mathematical models used to analyze complex systems with multiple states or conditions.

Explanation

Multistate models represent systems that can exist in several distinct states and describe how the system moves between those states or how populations change over time. They are used to understand and predict system behavior by quantifying transitions (for example, probabilities of moving from one state to another) or by modeling growth and evolution of populations. Specific forms of multistate models account for relevant factors in their contexts (such as age, history, lifestyle, reproduction rate, or likelihood of death) to compute transitions or population dynamics.

Examples

Markov chain

A Markov chain is a mathematical system that undergoes transitions from one state to another according to certain probabilities. For example, a Markov chain model could be used to analyze the likelihood of a person transitioning from a healthy state to a diseased state over time. The model would take into account factors such as the person’s age, medical history, and lifestyle to calculate the probabilities of transitioning from one state to another.

Branching process

A branching process is a mathematical model used to analyze the growth and evolution of a population over time. For example, a branching process model could be used to analyze the growth of a population of bacteria in a laboratory. The model would take into account factors such as the reproduction rate of the bacteria and the likelihood of death to calculate the growth of the population over time.

Use cases

Actuarial science
Engineering
Biology

Markov chain
Branching process