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From networked SIS model to the Gompertz function

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  • Estrada, Ernesto
  • Bartesaghi, Paolo

Abstract

The Gompertz function is one of the most widely used models in the description of growth processes in many different fields. We obtain a networked version of the Gompertz function as a worst-case scenario for the exact solution to the SIS model on networks. This function is shown to be asymptotically equivalent to the classical scalar Gompertz function for sufficiently large times. It proves to be very effective both as an approximate solution of the networked SIS equation within a wide range of the parameters involved and as a fitting curve for the most diverse empirical data. As an instance, we perform some computational experiments, applying this function to the analysis of two real networks of sexual contacts. The numerical results highlight the analogies and the differences between the exact description provided by the SIS model and the upper bound solution proposed here, observing how the latter amplifies some empirically observed behaviors such as the presence of multiple and successive peaks in the contagion curve.

Suggested Citation

  • Estrada, Ernesto & Bartesaghi, Paolo, 2022. "From networked SIS model to the Gompertz function," Applied Mathematics and Computation, Elsevier, vol. 419(C).
  • Handle: RePEc:eee:apmaco:v:419:y:2022:i:c:s0096300321009656
    DOI: 10.1016/j.amc.2021.126882
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    1. Ángel Berihuete & Marta Sánchez-Sánchez & Alfonso Suárez-Llorens, 2021. "A Bayesian Model of COVID-19 Cases Based on the Gompertz Curve," Mathematics, MDPI, vol. 9(3), pages 1-16, January.
    2. Li, Hui-Jia & Xu, Wenzhe & Song, Shenpeng & Wang, Wen-Xuan & Perc, Matjaž, 2021. "The dynamics of epidemic spreading on signed networks," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    3. Cabrales, Luis Enrique Bergues & Montijano, Juan I. & Schonbek, Maria & Castañeda, Antonio Rafael Selva, 2018. "A viscous modified Gompertz model for the analysis of the kinetics of tumors under electrochemical therapy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 151(C), pages 96-110.
    4. Omer Karin & Amit Agrawal & Ziv Porat & Valery Krizhanovsky & Uri Alon, 2019. "Senescent cell turnover slows with age providing an explanation for the Gompertz law," Nature Communications, Nature, vol. 10(1), pages 1-9, December.
    5. Leo Katz, 1953. "A new status index derived from sociometric analysis," Psychometrika, Springer;The Psychometric Society, vol. 18(1), pages 39-43, March.
    6. Nicola Perra & Duygu Balcan & Bruno Gonçalves & Alessandro Vespignani, 2011. "Towards a Characterization of Behavior-Disease Models," PLOS ONE, Public Library of Science, vol. 6(8), pages 1-15, August.
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