Computation of random time-shift distributions for stochastic population models

Area of Science:

• Mathematical biology
• Computational modeling
• Stochastic processes

Background:

• Deterministic models fail to capture noise effects from small initial populations in large systems.
• These early-stage noise effects can have persistent, measurable impacts on macroscopic behavior.
• Approximating these effects requires accounting for initial condition variability.

Purpose of the Study:

• To develop an efficient numerical method for computing time-shift distributions in stochastic population models.
• To provide a practical tool for generating macroscopic trajectories without extensive simulations.
• To demonstrate the method's applicability on epidemic and viral dynamics models.

Main Methods:

• Developing a numerical method based on differentiating functional equations.
• Automating the calculation of time-shift distributions by deriving rules for model rates.
• Applying the method to mass-action mixing models.

Main Results:

• An efficient method for computing time-shift distributions was developed.
• The method accurately approximates persistent noise effects in large stochastic systems.
• The approach avoids the computational expense of traditional stochastic simulations.

Conclusions:

• The novel numerical method effectively captures persistent noise effects in stochastic population dynamics.
• This approach offers a computationally efficient alternative to direct stochastic simulations.
• The method is broadly applicable to various population models, including those in epidemiology and virology.