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

• Main Authors: Niels B. Kammerer, Wolfgang Stummer
• Format: Article
• Language: English
• Published: MDPI AG 2020-08-01
• Series: Entropy
• Subjects: Galton-Watson branching processes with immigration; Hellinger integrals; power divergences; Kullback-Leibler information distance/divergence; relative entropy; Renyi divergences
• Online Access: https://www.mdpi.com/1099-4300/22/8/874

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 <i>Galton-Watson branching processes with immigration</i> 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.