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Open AccessArticle

On the Entropy of Events under Eventually Global Inflated or Deflated Probability Constraints. Application to the Supervision of Epidemic Models under Vaccination Controls

1
Institute of Research and Development of Processes IIDP, University of the Basque Country, Campus of Leioa, 48940 Leioa, Spain
2
Department of Telecommunications and Systems Engineering, Universitat Autònoma de Barcelona (UAB), 08193 Barcelona, Spain
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(3), 284; https://doi.org/10.3390/e22030284
Received: 27 January 2020 / Revised: 18 February 2020 / Accepted: 27 February 2020 / Published: 29 February 2020
This paper extends the formulation of the Shannon entropy under probabilistic uncertainties which are basically established in terms or relative errors related to the theoretical nominal set of events. Those uncertainties can eventually translate into globally inflated or deflated probabilistic constraints. In the first case, the global probability of all the events exceeds unity while in the second one lies below unity. A simple interpretation is that the whole set of events losses completeness and that some events of negative probability might be incorporated to keep the completeness of an extended set of events. The proposed formalism is flexible enough to evaluate the need to introduce compensatory probability events or not depending on each particular application. In particular, such a design flexibility is emphasized through an application which is given related to epidemic models under vaccination and treatment controls. Switching rules are proposed to choose through time the active model, among a predefined set of models organized in a parallel structure, which better describes the registered epidemic evolution data. The supervisory monitoring is performed in the sense that the tested accumulated entropy of the absolute error of the model versus the observed data is minimized at each supervision time-interval occurring in-between each two consecutive switching time instants. The active model generates the (vaccination/treatment) controls to be injected to the monitored population. In this application, it is not proposed to introduce a compensatory event to complete the global probability to unity but instead, the estimated probabilities are re-adjusted to design the control gains. View Full-Text
Keywords: Shannon entropy; complete/incomplete systems of events; probabilistic uncertainty; probabilistic inflated/deflated probability constraints; epidemic model; vaccination controls; treatment controls Shannon entropy; complete/incomplete systems of events; probabilistic uncertainty; probabilistic inflated/deflated probability constraints; epidemic model; vaccination controls; treatment controls
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De la Sen, M.; Ibeas, A.; Nistal, R. On the Entropy of Events under Eventually Global Inflated or Deflated Probability Constraints. Application to the Supervision of Epidemic Models under Vaccination Controls. Entropy 2020, 22, 284.

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