Age-structured population models with Applications

TL;DR

This paper develops a comprehensive age-structured population model using semilinear PDEs, analyzing solution properties, stability, and equilibrium conditions to understand population dynamics.

Contribution

It introduces a general age-structured PDE model with nonlinear boundary conditions, proving existence, uniqueness, regularity, and stability of solutions.

Findings

Existence and uniqueness of solutions established.

Intrinsic growth constant linked to equilibrium stability.

Lyapunov function demonstrates global stability of equilibria.

Abstract

A general model of age-structured population dynamics is developed and the fundamental properties of its solutions are analyzed. The model is a semilinear partial differential equation with a nonlinear nonlocal boundary condition. Existence, uniqueness and regularity of solutions to the model equations are proved. An intrinsic growth constant is obtained and linked to the existence and the stability of the trivial and/or the positive equilibrium. Lyapunov function is constructed to show the global stability of the trivial and/or the positive equilibrium. Key words: Lyapunov function, Partial Differential Equation, Stability, Mathematical Model, Uniform Persistence, Reproductive Number (or Reproduction Number)