Research articles
ScienceAsia 52 (2026): 1-9 |doi:
10.2306/scienceasia1513-1874.2026.020
Bifurcation and spectral entropy complexity of a
fractional-order SVIRS epidemic system
Zhen Wanga, Gongsheng Lib,*, Pingping Lib
ABSTRACT: Thisarticle deals with bifurcation dynamics and complexity of a nonlinear fractional-order SVIRS epidemic
system. Based on the analysis of the disease-free and endemic equilibriums, the forward (supercritical) and backward
(subcritical) bifurcations are observed around the basic reproduction number. The complexity of the fractional epidemic
system is estimated by spectral entropy and numerical simulations, and the relation of the order of the fractional
derivative with dynamicsofthesystemisinvestigated andillustrated by the complexity. Thespectral entropycomplexity
can be regarded as an index to connect oscillatory bifurcations with the order of the fractional derivative for the
fractional-order epidemic system.
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| a |
College of Science, Inner Mongolia University of Technology, Hohhot, Inner Mongolia 010100 China |
| b |
School of Mathematics and Statistics, Shandong University of Technology, Zibo, Shandong 255000 China |
* Corresponding author, E-mail: ligs@sdut.edu.cn
Received 6 Jun 2025, Accepted 2 Mar 2026
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