Two-Type Reducible Age-Dependent Branching Processes With Non-Homogeneous Poisson Immigration.

Area of Science:

• Stochastic processes
• Mathematical biology
• Population dynamics

Background:

• Renewal cell population dynamics are complex and require robust modeling approaches.
• Understanding age-dependent processes is crucial for accurate biological system analysis.
• Immigration significantly impacts population dynamics, necessitating its inclusion in models.

Purpose of the Study:

• To model renewal cell population dynamics using two types of age-dependent branching stochastic processes.
• To investigate the asymptotic behavior of these processes, both with and without non-homogeneous Poisson immigration.
• To identify different classes of asymptotic behaviors for population dynamics.

Main Methods:

• Utilizing reducible age-dependent branching stochastic processes.
• Incorporating non-homogeneous Poisson immigration into the models.
• Analyzing the asymptotic behavior of the first moments of the processes.

Main Results:

• Identified several distinct classes of asymptotic behaviors for the cell population dynamics.
• Characterized the influence of immigration on the long-term population trends.
• Demonstrated the applicability of the models to statistical inference.

Conclusions:

• The developed stochastic models provide a framework for understanding age-dependent cell population dynamics.
• The identified asymptotic behaviors offer insights into population stability and growth patterns.
• The findings facilitate the development of statistical inference methods for population modeling.