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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.
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 o
We consider an epidemic model of SIR type set on a homogeneous tree and investigate the spreading properties of the epidemic as a function of the degree of the tree, the intrinsic basic reproduction number and the strength of the interactions within
Inference on unknown quantities in dynamical systems via observational data is essential for providing meaningful insight, furnishing accurate predictions, enabling robust control, and establishing appropriate designs for future experiments. Merging
A generalisation of the Susceptible-Infectious model is made to include a time-dependent transmission rate, which leads to a close analytical expression in terms of a logistic function. The solution can be applied to any continuous function chosen to
Existing strategies for determining the optimal treatment or monitoring strategy typically assume unlimited access to resources. However, when a health system has resource constraints, such as limited funds, access to medication, or monitoring capabi