Female dominant age-dependent deterministic population dynamics.

Area of Science:

• Mathematical Biology
• Population Dynamics
• Differential Equations

Background:

• Deterministic population models are crucial for understanding population dynamics.
• Age and sex differentiation adds complexity to population modeling.

Purpose of the Study:

• To analyze a nonlinear deterministic model of an age/sex differentiated population.
• To prove the existence and uniqueness of the solution for the governing equation.
• To derive time-dependent upper bounds for population sizes and establish equilibrium conditions.

Main Methods:

• Mathematical analysis of nonlinear differential equations.
• Proof techniques for existence and uniqueness of solutions.
• Derivation of population bounds and equilibrium conditions.

Main Results:

• Existence and uniqueness of the solution to the population model's governing equation are proven.
• Time-dependent upper bounds for both male and female populations are obtained.
• Necessary and sufficient conditions for population equilibrium are established.

Conclusions:

• The study provides a rigorous mathematical foundation for the analyzed population model.
• The findings offer insights into population stability and boundedness.
• This work contributes to the theoretical understanding of age/sex structured population dynamics.