On the formulation and computer implementation of an age-dependent two-sex demographic model

Area of Science:

• Demography
• Mathematical Biology
• Stochastic Processes

Background:

• Traditional demographic models often simplify populations to a single sex, neglecting crucial interaction dynamics.
• Accurate population projections require models that account for age-dependent processes and couple formation/dissolution.

Purpose of the Study:

• To develop and analyze a comprehensive two-sex age-dependent demographic model within a stochastic framework.
• To investigate the stability properties and long-term projection behavior of this advanced model.
• To demonstrate the unique insights provided by two-sex models compared to one-sex formulations.

Main Methods:

• Formulation of a stochastic, age-dependent, two-sex demographic model with time-homogeneous and time-inhomogeneous evolution laws.
• Inclusion of parametric components for couple formation (using Farlie-Morgenstern distributions) and dissolution.
• Utilizing computer experiments to analyze stability properties and long-term projection convergence.

Main Results:

• Computer experiments suggest that key demographic indicators (crude birth rates, rates of natural increase, age distributions) converge to stable forms in long-term projections, analogous to one-sex models.
• The model demonstrates that variations in couple formation and dissolution parameters significantly impact stable demographic indicators.
• Stability properties, though mathematically challenging to prove due to nonlinearities, appear to hold for the two-sex model.

Conclusions:

• The developed two-sex demographic model provides valuable insights not achievable with simpler one-sex models.
• Couple formation and dissolution dynamics are critical factors influencing population stability and long-term projections.
• The model's parametric components facilitate computer implementation and experimentation, validating its practical utility.