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Updated: Aug 5, 2026
12:00
Vaccinia Virus Infection & Temporal Analysis of Virus Gene Expression: Part 1
Published on: April 8, 2009
Hopf Bifurcation in an Incommensurate Caputo Fractional-Order Computer Virus Epidemic Model with Multiple Time Delays
Ailing Zhong1, Chengqiang Wang2
1School of Computer Science and Technology, Tongji University, Shanghai 201804, China.
Entropy (Basel, Switzerland)
|July 28, 2026
Summary
This study explores complex dynamics in computer virus spread using a fractional-order model with time delays. It reveals that exceeding critical time delays triggers Hopf bifurcations, causing sustained virus oscillations.
Area of Science:
- Complex Systems
- Network Science
- Mathematical Biology
Background:
- Nonlinear dynamical systems and high-entropy time series model intricate phenomena.
- Understanding network-based epidemic processes is crucial for real-world applications.
Purpose of the Study:
- Investigate bifurcation dynamics in a fractional-order computer virus propagation model.
- Analyze the impact of time delays on epidemic spread in complex networks.
Main Methods:
- Developed a fractional-order Susceptible-Latent-Breaking-Out model with two distinct time delays.
- Employed Caputo fractional derivatives of incommensurate orders.
- Linearized the model and analyzed characteristic roots to determine stability and bifurcation conditions.
Main Results:
- Established explicit conditions for bifurcation based on time delays.
- Identified critical delay thresholds that induce Hopf bifurcations.
- Demonstrated that exceeding delay thresholds leads to sustained periodic oscillations in virus prevalence.
Conclusions:
- Fractional-order delay models offer enhanced complexity for studying epidemic dynamics.
- Time delays are critical parameters influencing system stability and triggering oscillations.
- Findings provide insights for containment strategies in interconnected systems.
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