Loading…
Dynamical analysis of two fractional-order SIQRA malware propagation models and their discretizations
The aim of this work is to propose and study dynamics of two fractional-order SIQRA malware propagation models and their discretizations. Positivity, boundedness and asymptotic stability properties of the proposed fractional-order models are analyzed rigorously. It is worthy noting that the global a...
Saved in:
Published in: | Rendiconti del Circolo matematico di Palermo 2023-02, Vol.72 (1), p.751-771 |
---|---|
Main Author: | |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Summary: | The aim of this work is to propose and study dynamics of two fractional-order SIQRA malware propagation models and their discretizations. Positivity, boundedness and asymptotic stability properties of the proposed fractional-order models are analyzed rigorously. It is worthy noting that the global and uniform asymptotic stability properties of the fractional-order models are investigated based on appropriate Lyapunov functions. As an important consequence, the global asymptotic stability properties of the original integer-order models are also established completely. In addition, the fractional forward Euler method is utilized to discretize the fractional-order models. By rigorously mathematical analyses, we obtain step size thresholds which guarantee that the positivity, boundedness and asymptotic stability properties of the fractional-order models are preserved correctly by the discrete models. Consequently, simple conditions for reliable approximations for the fractional-order models are determined. Finally, a set of numerical examples is performed to illustrate and support the theoretical findings. The results show that the numerical examples are consistent with the constructed theoretical assertions. |
---|---|
ISSN: | 0009-725X 1973-4409 |
DOI: | 10.1007/s12215-021-00707-6 |