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Uncertainty quantification analysis of the biological Gompertz model subject to random fluctuations in all its parameters

Author

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  • Bevia, V.
  • Burgos, C.
  • Cortés, J.-C.
  • Navarro-Quiles, A.
  • Villanueva, R.-J.

Abstract

In spite of its simple formulation via a nonlinear differential equation, the Gompertz model has been widely applied to describe the dynamics of biological and biophysical parts of complex systems (growth of living organisms, number of bacteria, volume of infected cells, etc.). Its parameters or coefficients and the initial condition represent biological quantities (usually, rates and number of individual/particles, respectively) whose nature is random rather than deterministic. In this paper, we present a complete uncertainty quantification analysis of the randomized Gomperz model via the computation of an explicit expression to the first probability density function of its solution stochastic process taking advantage of the Liouville-Gibbs theorem for dynamical systems. The stochastic analysis is completed by computing other important probabilistic information of the model like the distribution of the time until the solution reaches an arbitrary value of specific interest and the stationary distribution of the solution. Finally, we apply all our theoretical findings to two examples, the first of numerical nature and the second to model the dynamics of weight of a species using real data.

Suggested Citation

  • Bevia, V. & Burgos, C. & Cortés, J.-C. & Navarro-Quiles, A. & Villanueva, R.-J., 2020. "Uncertainty quantification analysis of the biological Gompertz model subject to random fluctuations in all its parameters," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    • Handle: RePEc:eee:chsofr:v:138:y:2020:i:c:s0960077920303088
    DOI: 10.1016/j.chaos.2020.109908
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    References listed on IDEAS

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    1. Dorini, F.A. & Cunha, M.C.C., 2011. "On the linear advection equation subject to random velocity fields," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(4), pages 679-690.
    2. Cortés, J.C. & Jódar, L. & Villafuerte, L., 2009. "Random linear-quadratic mathematical models: Computing explicit solutions and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2076-2090.
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    Cited by:

    1. Yan, Donglin & Zheng, Yang & Liu, Wanying & Chen, Tianya & Chen, Qijuan, 2022. "Interval uncertainty analysis of vibration response of hydroelectric generating unit based on Chebyshev polynomial," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    2. Cortés, J.-C. & Moscardó-García, A. & Villanueva, R.-J., 2022. "Uncertainty quantification for hybrid random logistic models with harvesting via density functions," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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