The dynamics analysis of Gompertz virus disease model under impulsive control

Area of Science:

• Mathematical epidemiology
• Agricultural science

Background:

• Gompertz virus disease poses a significant threat to agricultural production.
• Mathematical modeling is a key tool for understanding infectious disease dynamics.

Purpose of the Study:

• To propose and analyze a novel mathematical model for the dynamics of an impulsive Gompertz virus disease system.
• To investigate the conditions for the permanence and global exponential stability of the disease model.

Main Methods:

• Development of a new mathematical model for Gompertz virus disease.
• Theoretical analysis of model dynamics, including permanence and stability.
• Numerical simulations to validate analytical findings.

Main Results:

• The study proves the permanence and globally exponential stability of the proposed Gompertz virus disease model.
• A sufficient condition for the existence of a positive solution under specific parameters was established.
• Numerical simulations confirmed the theoretical conclusions.

Conclusions:

• The developed mathematical model provides a robust framework for understanding Gompertz virus disease dynamics.
• The findings on permanence and stability offer insights for disease control strategies in agriculture.
• The study validates the use of mathematical modeling for analyzing impulsive infectious disease systems.