Exponential growth in age-structured two-sex populations

Area of Science:

• Mathematical biology
• Demography
• Population dynamics

Background:

• Continuous age-structured two-sex population models are essential for understanding population dynamics.
• Existing models often simplify interactions or focus on single-sex populations.
• The Fredrickson-Hoppensteadt model provides a framework, but simpler cases are valuable for analysis.

Purpose of the Study:

• To analyze a simplified continuous age-structured two-sex population model.
• To investigate the role of the marriage function (non-linearity) in population growth.
• To determine if the model supports persistent, growing solutions.

Main Methods:

• Utilizing a semilinear system of partial differential equations.
• Incorporating nonlocal boundary conditions.
• Analyzing the properties of a general marriage function, focusing on homogeneity.

Main Results:

• Demonstrated that the homogeneity property of the marriage function leads to exponentially growing persistent solutions.
• The model supports solutions indicating population growth under specific non-linear conditions.
• Established a connection between the model's behavior and demographic principles.

Conclusions:

• The analyzed two-sex population model can exhibit exponential growth.
• This model offers a potential extension of one-sex stable population theory to monogamous populations.
• The marriage function's properties are crucial for determining population persistence and growth patterns.