Space and time correlations for diffusion models with prompt and delayed birth-and-death events

Area of Science:

• Statistical physics
• Mathematical biology
• Applied probability

Background:

• Population dynamics models are crucial for understanding systems like nuclear reactors and epidemics.
• Previous studies highlighted non-Poissonian fluctuations and
• critical catastrophes
• in birth-death processes.
• Constant population size can mitigate extinction risks.

Purpose of the Study:

• To extend the understanding of population dynamics by incorporating delayed birth-and-death events.
• To analyze models with and without population control mechanisms.
• To investigate the impact of these factors on population statistics.

Main Methods:

• Developing analytical and semi-analytical solutions for population density and spatial correlations.
• Utilizing Monte Carlo simulations as a benchmark for validation.
• Comparing results from theoretical models with simulation data.

Main Results:

• Characterizing statistical properties like density and pair distance under new conditions.
• Demonstrating how delayed events and population control influence fluctuations.
• Identifying conditions that avert population extinction.

Conclusions:

• Delayed birth-death events and population control mechanisms offer insights into managing population stability.
• The findings have implications for nuclear reactor diagnostics and epidemic modeling.
• This work provides a more comprehensive framework for analyzing complex population dynamics.