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.
Keywords: Bayesian decision making; Bhattacharyya coefficient/distance; COVID-19 pandemic; GLM model; Galton-Watson branching processes with immigration; Hellinger integrals; INARCH(1) model; Kullback-Leibler information distance/divergence; Renyi divergences; epidemiology; power divergences; relative entropy.