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Information theory unification of epidemiological and population dynamics

Author

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  • Filoche, Baptiste
  • Hohenegger, Stefan
  • Sannino, Francesco

Abstract

We reformulate models in epidemiology and population dynamics in terms of probability distributions. This allows us to construct the Fisher information, which we interpret as the metric of a one-dimensional differentiable manifold. For systems that can be effectively described by a single degree of freedom, we show that their time evolution is fully captured by this metric. In this way, we discover universal features across seemingly very different models. This further motivates a reorganisation of the dynamics around zeroes of the Fisher metric, corresponding to extrema of the probability distribution. Concretely, we propose a simple form of the metric for which we can analytically solve the dynamics of the system that well approximates the time evolution of various established models in epidemiology and population dynamics, thus providing a unifying framework.

Suggested Citation

  • Filoche, Baptiste & Hohenegger, Stefan & Sannino, Francesco, 2024. "Information theory unification of epidemiological and population dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 650(C).
    • Handle: RePEc:eee:phsmap:v:650:y:2024:i:c:s0378437124004795
    DOI: 10.1016/j.physa.2024.129970
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    References listed on IDEAS

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    1. Burbea, Jacob & Rao, C. Radhakrishna, 1982. "Entropy differential metric, distance and divergence measures in probability spaces: A unified approach," Journal of Multivariate Analysis, Elsevier, vol. 12(4), pages 575-596, December.
    2. Cacciapaglia, Giacomo & Cot, Corentin & de Hoffer, Adele & Hohenegger, Stefan & Sannino, Francesco & Vatani, Shahram, 2022. "Epidemiological theory of virus variants," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
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