A nonlinear model for stage-structured population dynamics with nonlocal density-dependent regulation: An application...

Area of Science:

• Mathematical Biology and Ecology
• Population Dynamics Modeling
• Invasive Species Management

Background:

• Insect pest risk assessment and management benefit from physiologically-based demographic models.
• These models simulate stage-structured populations using nonlinear physiological responses to environmental factors.
• Density-dependent factors are crucial regulators of population dynamics.

Purpose of the Study:

• To propose a nonlinear, physiologically-based Kolmogorov model for stage-structured populations.
• To incorporate a time-dependent mortality rate coupled with a nonlocal density-dependent term.
• To apply the model for simulating the population dynamics of the invasive fall armyworm moth (Spodoptera frugiperda).

Main Methods:

• Development of a nonlinear, physiologically-based Kolmogorov partial differential equation.
• Mathematical proof of existence and uniqueness for the model's solution.
• Discretization of the equation using finite volumes in space and a semi-implicit backward Euler scheme in time.

Main Results:

• Existence and uniqueness of the solution for the complex, nonlinear partial differential equation were established.
• The model was successfully discretized for computational simulation.
• The model was applied to simulate the population dynamics of Spodoptera frugiperda.

Conclusions:

• The developed nonlinear, physiologically-based Kolmogorov model provides a robust framework for simulating stage-structured insect populations.
• This modeling approach can significantly support the assessment and management of invasive pests like the fall armyworm moth.
• The study demonstrates the utility of advanced mathematical models in addressing critical agricultural challenges.