Intrinsic noise in systems with switching environments

Area of Science:

• Mathematical Biology
• Stochastic Processes
• Population Dynamics

Background:

• Models gene regulation, bacterial populations, and epidemic spread involve switching environmental conditions.
• Existing piecewise-deterministic Markov process methods approximate population dynamics in the deterministic limit.

Purpose of the Study:

• To develop a more accurate model for individual-based dynamics in finite populations with randomly switching environments.
• To incorporate intrinsic stochasticity beyond the deterministic limit using the linear-noise approximation.

Main Methods:

• Developed an individual-based modeling framework.
• Applied the linear-noise approximation to include intrinsic stochasticity.
• Derived stationary distributions for model systems.

Main Results:

• Achieved good agreement between derived stationary distributions and simulation results.
• Successfully extended modeling capabilities beyond fast and slow switching regimes.
• Provided a more comprehensive understanding of population dynamics under environmental fluctuations.

Conclusions:

• The linear-noise approximation offers a significant improvement over existing methods for modeling population dynamics with environmental switching.
• This approach enhances the accuracy and applicability of stochastic models in biological systems.
• The derived stationary distributions provide valuable insights into system behavior across various switching rates.