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A fractional SIS model for a random process about infectivity and recovery

Author

Listed:
  • Hui Chen

    (Department of Mathematics, Yunnan Minzu University, 2929, Yuehua Street, Chenggong District, Kunming 650500, P. R. China)

  • Jia Li

    (Department of Mathematics, Yunnan Minzu University, 2929, Yuehua Street, Chenggong District, Kunming 650500, P. R. China)

  • Xuewen Tan

    (Department of Mathematics, Yunnan Minzu University, 2929, Yuehua Street, Chenggong District, Kunming 650500, P. R. China)

Abstract

This paper establishes a new fractional frSIS model utilizing a continuous time random walk method. There are two main innovations in this paper. On the one hand, the model is analyzed from a mathematical perspective. First, unlike the classic SIS infectious disease model, this model presents the infection rate and cure rate in a fractional order. Then, we proved the basic regeneration number R0 of the model and studied the influence of orders a and b on R0. Second, we found that frSIS has a disease-free equilibrium point E0 and an endemic equilibrium point E∗. Moreover, we proved frSIS global stability of the model using R0. If R0<1, the model of E0 is globally asymptotically stable. If R0>1, the model of E∗ is globally asymptotically stable. On the other hand, from the perspective of infectious diseases, we discovered that appropriately increasing a and decreasing b are beneficial for controlling the spread of diseases and ultimately leading to their disappearance. This can help us provide some dynamic adjustments in prevention and control measures based on changes in the disease.

Suggested Citation

  • Hui Chen & Jia Li & Xuewen Tan, 2025. "A fractional SIS model for a random process about infectivity and recovery," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 36(10), pages 1-29, October.
    • Handle: RePEc:wsi:ijmpcx:v:36:y:2025:i:10:n:s0129183124420051
    DOI: 10.1142/S0129183124420051
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