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Article

Some Dissimilarity Measures of Branching Processes and Optimal Decision Making in the Presence of Potential Pandemics

1
Königinstrasse 75, 80539 Munich, Germany
2
Department of Mathematics, University of Erlangen–Nürnberg, Cauerstrasse 11, 91058 Erlangen, Germany
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(8), 874; https://doi.org/10.3390/e22080874
Received: 26 June 2020 / Revised: 27 July 2020 / Accepted: 28 July 2020 / Published: 8 August 2020
We compute exact values respectively bounds of dissimilarity/distinguishability measures–in the sense of the Kullback-Leibler information distance (relative entropy) and some transforms of more general power divergences and Renyi divergences–between two competing discrete-time Galton-Watson branching processes with immigration GWI for which the offspring as well as the immigration (importation) is arbitrarily Poisson-distributed; especially, we allow for arbitrary type of extinction-concerning criticality and thus for non-stationarity. We apply this to optimal decision making in the context of the spread of potentially pandemic infectious diseases (such as e.g., the current COVID-19 pandemic), e.g., covering different levels of dangerousness and different kinds of intervention/mitigation strategies. Asymptotic distinguishability behaviour and diffusion limits are investigated, too. View Full-Text
Keywords: Galton-Watson branching processes with immigration; Hellinger integrals; power divergences; Kullback-Leibler information distance/divergence; relative entropy; Renyi divergences; epidemiology; COVID-19 pandemic; Bayesian decision making; INARCH(1) model; GLM model; Bhattacharyya coefficient/distance Galton-Watson branching processes with immigration; Hellinger integrals; power divergences; Kullback-Leibler information distance/divergence; relative entropy; Renyi divergences; epidemiology; COVID-19 pandemic; Bayesian decision making; INARCH(1) model; GLM model; Bhattacharyya coefficient/distance
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MDPI and ACS Style

Kammerer, N.B.; Stummer, W. Some Dissimilarity Measures of Branching Processes and Optimal Decision Making in the Presence of Potential Pandemics. Entropy 2020, 22, 874. https://doi.org/10.3390/e22080874

AMA Style

Kammerer NB, Stummer W. Some Dissimilarity Measures of Branching Processes and Optimal Decision Making in the Presence of Potential Pandemics. Entropy. 2020; 22(8):874. https://doi.org/10.3390/e22080874

Chicago/Turabian Style

Kammerer, Niels B., and Wolfgang Stummer. 2020. "Some Dissimilarity Measures of Branching Processes and Optimal Decision Making in the Presence of Potential Pandemics" Entropy 22, no. 8: 874. https://doi.org/10.3390/e22080874

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