Fitting parameters of stochastic birth-death models to metapopulation data

Area of Science:

• Ecology
• Epidemiology
• Mathematical Biology

Background:

• Ecological and epidemiological systems often feature populations structured into small, interconnected local patches.
• These small populations are susceptible to demographic stochasticity, which can impact disease dynamics.
• Previous studies on simple household disease models (SIS models) suggested local stochasticity is negligible for transmission between many connected patches.

Purpose of the Study:

• To develop a parameter estimation framework for metapopulation and household models.
• To leverage the stationary distribution of infected individuals in large connected patch systems.
• To utilize the balancing condition of birth-death processes for parameter inference.

Main Methods:

• Utilized theoretical results from household disease models (SIS models) concerning stationary distributions.
• Applied the balancing condition of birth-death processes.
• Developed a framework to estimate demographic parameters from observed local population size distributions.

Main Results:

• Demonstrated that the stationary distribution of infected individuals in large, connected patch systems can be described by a birth-death process with immigration.
• Showed how this result, combined with the balancing condition, enables demographic parameter estimation.
• Validated the applicability of the framework for both ecological metapopulation models and epidemiological household models.

Conclusions:

• A novel framework is presented for estimating demographic parameters in structured populations.
• The method effectively uses frequency distributions of local population sizes.
• This approach is broadly applicable to disease transmission modeling and metapopulation dynamics.