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Register a new userObservability, Identifiability and Epidemiology -- A survey
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In this document we introduce the concepts of Observability and Iden-tifiability in Mathematical Epidemiology. We show that, even for simple and well known models, these properties are not always fulfilled. We also consider the problem of practical observability and identi-fiability which are connected to sensitivity and numerical condition numbers.
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We analyze the identifiability and observability of the well-known SIR epidemic model with an additional compartment Q of the sub-population of infected individuals that are placed in quarantine (SIQR model), considering that the flow of individuals placed in quarantine and the size of the quarantine population are known at any time. Then, we focus on the problem of identification of the model parameters, with the synthesis of an observer.
We provide an overview of the methods that can be used for prediction under uncertainty and data fitting of dynamical systems, and of the fundamental challenges that arise in this context. The focus is on SIR-like models, that are being commonly used when attempting to predict the trend of the COVID-19 pandemic. In particular, we raise a warning flag about identifiability of the parameters of SIR-like models; often, it might be hard to infer the correct values of the parameters from data, even for very simple models, making it non-trivial to use these models for meaningful predictions. Most of the points that we touch upon are actually generally valid for inverse problems in more general setups.
Corporate responses to illness is currently an ad-hoc, subjective process that has little basis in data on how disease actually spreads at the workplace. Additionally, many studies have shown that productivity is not an individual factor but a social one: in any study on epidemic responses this social factor has to be taken into account. The barrier to addressing this problem has been the lack of data on the interaction and mobility patterns of people in the workplace. We have created a wearable Sociometric Badge that senses interactions between individuals using an infra-red (IR) transceiver and proximity using a radio transmitter. Using the data from the Sociometric Badges, we are able to simulate diseases spreading through face-to-face interactions with realistic epidemiological parameters. In this paper we construct a curve trading off productivity with epidemic potential. We are able to take into account impacts on productivity that arise from social factors, such as interaction diversity and density, which studies that take an individual approach ignore. We also propose new organizational responses to diseases that take into account behavioral patterns that are associated with a more virulent disease spread. This is advantageous because it will allow companies to decide appropriate responses based on the organizational context of a disease outbreak.
In this note we recall the importance of the notion of a finitary isomorphism in the classification problem of dynamical systems.
A great variety of complex physical, natural and artificial systems are governed by statistical distributions, which often follow a standard exponential function in the bulk, while their tail obeys the Pareto power law. The recently introduced $kappa$-statistics framework predicts distribution functions with this feature. A growing number of applications in different fields of investigation are beginning to prove the relevance and effectiveness of $kappa$-statistics in fitting empirical data. In this paper, we use $kappa$-statistics to formulate a statistical approach for epidemiological analysis. We validate the theoretical results by fitting the derived $kappa$-Weibull distributions with data from the plague pandemic of 1417 in Florence as well as data from the COVID-19 pandemic in China over the entire cycle that concludes in April 16, 2020. As further validation of the proposed approach we present a more systematic analysis of COVID-19 data from countries such as Germany, Italy, Spain and United Kingdom, obtaining very good agreement between theoretical predictions and empirical observations. For these countries we also study the entire first cycle of the pandemic which extends until the end of July 2020. The fact that both the data of the Florence plague and those of the Covid-19 pandemic are successfully described by the same theoretical model, even though the two events are caused by different diseases and they are separated by more than 600 years, is evidence that the $kappa$-Weibull model has universal features.
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