Xiaofei Yu and Jinyan TianThis email address is being protected from spambots. You need JavaScript enabled to view it.
Dept Basic Courses, Henan Polytechnic Institute, Nanyang, 473000, China
Received: August 19, 2025 Accepted: October 27, 2025 Publication Date: December 27, 2025
Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.
In response to the increasingly random and historical dependence challenges in the spread of infectious diseases, a new dynamic model has been proposed in this study. This model integrates stochastic differential equations and fractional differential equations. Stochastic differential equation terms capture random disturbances caused by environmental fluctuations and emergencies. Fractional differential equation terms precisely characterize long-range memory effects and non-local characteristics during propagation. Numerical simulation verified the advantages of the fusion model in terms of accuracy, stability and computational efficiency. In the comparative verification with the age stratified model and the delay differential model, the average error in a strongly disturbed environment decreased to 0.026 . The running time shortened to 0.45 s , and the convergence rate increased by up to 32.7%. When the basic reproduction number was 2.5 , the prediction accuracy rate reached 92.5±2.1%, precisely matching public health intervention practices. Experiments demonstrate that the SDE-FDE model more effectively captures the complex, dynamic characteristics of infectious diseases. It can simulate transmission trends in multiple scenarios and provide a theoretical basis for precise public health intervention strategies.
Keywords: Stochastic differential equations; Fractional order differential equations; Infectious disease models; Stochastic perturbations; Optimal control
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