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Age-density dependent population dispersal in RN

G E Hernández¹

¹University of Connecticut, Storrs 06269-3009, USA. hernande@math.uconn.edu

Mathematical Biosciences

|June 4, 1998

Summary

This study models age-dependent population diffusion using a directed dispersal model. Researchers analyzed the existence and properties of solutions for a reduced mixed parabolic-hyperbolic system, offering insights into population dynamics.

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Area of Science:

Mathematical Biology
Population Dynamics
Partial Differential Equations

Background:

Population density is influenced by age, spatial position, and time.
Diffusion models are crucial for understanding population dispersal.
Age-dependent factors add complexity to population dynamics.

Purpose of the Study:

To develop and analyze an N-dimensional mathematical model for age-dependent population diffusion.
To investigate a directed dispersal model where diffusion depends on population density gradients.
To examine the existence, regularity, and localization of solutions for a reduced system.

Main Methods:

Formulation of an N-dimensional population density model rho(x, t, a).
Definition of total population u(x, t) as an integral of rho.
Reduction of the system to a mixed parabolic-hyperbolic type, incorporating the Porous Medium equation, under specific birth/death modulus assumptions.

Main Results:

The model is reduced to a mixed parabolic-hyperbolic system.
Analysis of the existence and regularity of the solution for the reduced system.
Investigation into the localization properties of the population distribution.

Conclusions:

The developed model provides a framework for studying age-dependent population diffusion.
The mathematical analysis confirms the existence and properties of solutions.
The findings contribute to understanding population dispersal patterns in complex scenarios.

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