Related papers: Identifiability and Observability Analysis for Epi…
In this review, we recall the concepts of Identifiability and Observability of dynamical systems, and analyse them in the framework of Mathematical Epidemiology. We show that, even for simple and well known models of the literature, these…
In this project, identifiability, observability and uncertainty properties of the deterministic and Chain Binomial stochastic SIR, SEIR and SEIAR epidemiological models are studied. Techniques for modeling overdispersion are investigated…
Identifiability is the property in mathematical modelling that determines if model parameters can be uniquely estimated from data. For infectious disease models, failure to ensure identifiability can lead to misleading parameter estimates…
Dynamical systems modeling is a core pillar of scientific inquiry across natural and life sciences. Increasingly, dynamical system models are learned from data, rendering identifiability a paramount concept. For systems that are not…
The Susceptible-Infectious-Recovered (SIR) equations and their extensions comprise a commonly utilized set of models for understanding and predicting the course of an epidemic. In practice, it is of substantial interest to estimate the…
Many disease models focus on characterizing the underlying transmission mechanism but make simple, possibly naive assumptions about how infections are reported. In this note, we use a simple deterministic Susceptible-Infected-Removed (SIR)…
A plethora of prediction models of SARS-CoV-2 pandemic were proposed in the past. Prediction performances not only depend on the structure and features of the model, but also on its parametrization. Official databases are often biased due…
Observability is a modelling property that describes the possibility of inferring the internal state of a system from observations of its output. A related property, structural identifiability, refers to the theoretical possibility of…
Ordinary differential equations (ODEs) are widely used to model dynamical behavior of systems. It is important to perform identifiability analysis prior to estimating unknown parameters in ODEs (a.k.a. inverse problem), because if a system…
Linear causal models are important tools for modeling causal dependencies and yet in practice, only a subset of the variables can be observed. In this paper, we examine the parameter identifiability of these models by investigating whether…
Reliable predictions from systems biology models require knowing whether parameters can be estimated from available data, and with what certainty. Identifiability analysis reveals whether parameters are learnable in principle (structural…
The recent coronavirus disease (COVID-19) outbreak has dramatically increased the public awareness and appreciation of the utility of dynamic models. At the same time, the dissemination of contradictory model predictions has highlighted…
Computational and mathematical models rely heavily on estimated parameter values for model development. Identifiability analysis determines how well the parameters of a model can be estimated from experimental data. Identifiability analysis…
Practical parameter identifiability in ODE-based epidemiological models is a known issue, yet one that merits further study. It is essentially ubiquitous due to noise and errors in real data. In this study, to avoid uncertainty stemming…
Susceptible-Exposed-Infectious-Recovered (SEIR) models with inter-individual variation in susceptibility or exposure to infection were proposed early in the COVID-19 pandemic as a potential element of the mathematical/statistical toolset…
The successful application of epidemic models hinges on our ability to estimate model parameters from limited observations reliably. An often-overlooked step before estimating model parameters consists of ensuring that the model parameters…
The SIR model is one of the most prototypical compartmental models in epidemiology. Generalizing this ordinary differential equation (ODE) framework into a spatially distributed partial differential equation (PDE) model is a considerable…
Compartmental models are popular in the mathematics of epidemiology for their simplicity and wide range of applications. Although they are typically solved as initial value problems for a system of ordinary differential equations, the…
Traditional observer design methods rely on certain properties of the system's nonlinearity, such as Lipschitz continuity, one-sided Lipschitzness, a bounded Jacobian, or quadratic boundedness. These properties are described by…
In this note, we propose a novel approach for a class of autonomous dynamical systems that allows, given some observations of the solutions, to identify its parameters and reconstruct the state vector. This approach relies on proving the…