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On the therapy effect for a stochastic growth Gompertz-type model.

Giuseppina Albano¹, Virginia Giorno, Patricia Román-Román

¹Dipartimento di Scienze Economiche e Statistiche, Università di Salerno, Italy.

Mathematical Biosciences

|December 7, 2011

Summary

This study introduces a modified Gompertz growth model incorporating population-dependent carrying capacity and a time-dependent therapy function. The research analyzes the therapy

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Area of Science:

Mathematical Biology
Population Dynamics
Stochastic Processes

Background:

Deterministic growth models like Gompertz are foundational but often lack realistic environmental factors.
Incorporating stochasticity and external influences is crucial for accurate population modeling.

Purpose of the Study:

To develop a novel diffusion model for population dynamics.
To investigate the impact of a time-dependent 'therapy' function on population characteristics.
To analyze first-passage-time problems in a time-dependent boundary context.

Main Methods:

Utilizing a generalized Gompertz deterministic growth framework.
Modifying the process drift with a time-dependent therapy function.
Deriving transition probability density functions and moments.
Analyzing first-passage-time problems with time-varying boundaries.

Main Results:

The study successfully derived key probabilistic properties of the modified diffusion model.
Quantified the influence of the therapy function on population dynamics and model characteristics.
Investigated the first-passage-time behavior under dynamic conditions.

Conclusions:

The developed diffusion model provides a flexible framework for studying population dynamics under external interventions.
The 'therapy' function offers a mechanism to model exogenous influences on population growth.
The model's applicability is demonstrated through real-world data analysis.