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A fractional-order infectivity SIR model

Author

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  • Angstmann, C.N.
  • Henry, B.I.
  • McGann, A.V.

Abstract

Fractional-order SIR models have become increasingly popular in the literature in recent years, however unlike the standard SIR model, they often lack a derivation from an underlying stochastic process. Here we derive a fractional-order infectivity SIR model from a stochastic process that incorporates a time-since-infection dependence on the infectivity of individuals. The fractional derivative appears in the generalised master equations of a continuous time random walk through SIR compartments, with a power-law function in the infectivity. We show that this model can also be formulated as an infection-age structured Kermack–McKendrick integro-differential SIR model. Under the appropriate limit the fractional infectivity model reduces to the standard ordinary differential equation SIR model.

Suggested Citation

  • Angstmann, C.N. & Henry, B.I. & McGann, A.V., 2016. "A fractional-order infectivity SIR model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 86-93.
    • Handle: RePEc:eee:phsmap:v:452:y:2016:i:c:p:86-93
    DOI: 10.1016/j.physa.2016.02.029
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    Citations

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    Cited by:

    1. Wang, Runzhou & Zhang, Xinsheng & Wang, Minghu, 2024. "A two-layer model with partial mapping: Unveiling the interplay between information dissemination and disease diffusion," Applied Mathematics and Computation, Elsevier, vol. 468(C).
    2. Sk, Tahajuddin & Biswas, Santosh & Sardar, Tridip, 2022. "The impact of a power law-induced memory effect on the SARS-CoV-2 transmission," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    3. Min, Seungsik & Shin, Ki-Hong & Baek, Woonhak & Kim, Kyungsik & You, Cheol-Hwan & Lee, Dong-In & Yum, Seong Soo & Kim, Wonheung & Chang, Ki-Ho, 2020. "Dynamical behavior of combined detrended cross-correlation analysis methods in random walks and Lévy flights," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    4. Byun, Jong Hyuk & Jung, Il Hyo, 2021. "Phase-specific cancer-immune model considering acquired resistance to therapeutic agents," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    5. Akinlar, M.A. & Inc, Mustafa & Gómez-Aguilar, J.F. & Boutarfa, B., 2020. "Solutions of a disease model with fractional white noise," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    6. Angstmann, C.N. & Henry, B.I. & Jacobs, B.A. & McGann, A.V., 2017. "A time-fractional generalised advection equation from a stochastic process," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 175-183.
    7. Babaei, A. & Ahmadi, M. & Jafari, H. & Liya, A., 2021. "A mathematical model to examine the effect of quarantine on the spread of coronavirus," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    8. Tirumalasetty Chiranjeevi & Raj Kumar Biswas, 2017. "Discrete-Time Fractional Optimal Control," Mathematics, MDPI, vol. 5(2), pages 1-12, April.
    9. Wenjia Liu & Jian Wang & Yanfeng Ouyang, 2022. "Rumor Transmission in Online Social Networks Under Nash Equilibrium of a Psychological Decision Game," Networks and Spatial Economics, Springer, vol. 22(4), pages 831-854, December.
    10. Nan Xu & Yaoqun Xu, 2022. "Research on Tacit Knowledge Dissemination of Automobile Consumers’ Low-Carbon Purchase Intention," Sustainability, MDPI, vol. 14(16), pages 1-26, August.
    11. Sene, Ndolane, 2020. "SIR epidemic model with Mittag–Leffler fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    12. DAŞBAŞI, Bahatdin, 2020. "Stability analysis of the hiv model through incommensurate fractional-order nonlinear system," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).

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