Related papers: Identifiability, Observability, Uncertainty and Ba…
The problems of observability and identifiability have been of great interest as previous steps to estimating parameters and initial conditions of dynamical systems to which some known data (observations) are associated. While most works…
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…
We consider state and parameter estimation for compartmental models having both time-varying and time-invariant parameters. Though the described Bayesian computational framework is general, we look at a specific application to the…
We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model with a contact rate that fluctuates seasonally. Through the use of a nonlinear, stochastic projection, we are able to analytically determine the…
Identifiability of a mathematical model plays a crucial role in parameterization of the model. In this study, we establish the structural identifiability of a Susceptible-Exposed-Infected-Recovered (SEIR) model given different combinations…
Deterministic compartmental models are predominantly used in the modeling of infectious diseases, though stochastic models are considered more realistic, yet are complicated to estimate due to missing data. In this paper we present a novel…
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…
Assessing the practical identifiability of epidemic models is essential for determining whether parameters can be meaningfully estimated from observed data. Monte Carlo (MC) methods provide an accessible and intuitive framework; however,…
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…
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)…
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…
Global pandemics, such as the recent COVID-19 crisis, highlight the need for stochastic epidemic models that can capture the randomness inherent in the spread of disease. Such models must be accompanied by methods for estimating parameters…
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…
The transmission dynamics of an epidemic are rarely homogeneous. Super-spreading events and super-spreading individuals are two types of heterogeneous transmissibility. Inference of super-spreading is commonly carried out on secondary case…
The ever-changing world of disease study heavily relies on mathematical models. They are key in finding and controlling infectious diseases. We aim to explore these mathematical tools used for studying disease spread in biology. The SEIR…
Pairwise models are used widely to model epidemic spread on networks. These include the modelling of susceptible-infected-removed (SIR) epidemics on regular networks and extensions to SIS dynamics and contact tracing on more exotic networks…
Dynamic properties of spreading infection through a heterogeneous population are studied numerically and analytically using a dynamic variant of Watts and Strogatz Small World Network-based stochastic Susceptible-Exposed-Infectious-Removed…
Epidemics are inherently stochastic, and stochastic models provide an appropriate way to describe and analyse such phenomena. Given temporal incidence data consisting of, for example, the number of new infections or removals in a given time…
Epidemic threshold is one of the most important features of the epidemic dynamics. Through a lot of numerical simulations in classic Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Susceptible (SIS) models on various types of…
Many models in mathematical epidemiology are developed with the aim to provide a framework for parameter estimation and then prediction. It is well-known that parameters are not always uniquely identifiable. In this paper we consider…