Related papers: Observability, Identifiability and Epidemiology --…
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…
Forecasting transmission of infectious diseases, especially for vector-borne diseases, poses unique challenges for researchers. Behaviors of and interactions between viruses, vectors, hosts, and the environment each play a part in…
Mechanistic dynamic models of biochemical networks such as Ordinary Differential Equations (ODEs) contain unknown parameters like the reaction rate constants and the initial concentrations of the compounds. The large number of parameters as…
Mathematical models are invaluable for understanding and predicting how biological systems behave, although their construction requires specifying mechanisms and relationships that are often not perfectly known. In the presence of multiple…
In this paper, we show that many structured epidemic models may be described using a straightforward product structure. Such products, derived from products of directed graphs, may represent useful refinements including geographic and…
When a missing-data mechanism is NMAR or non-ignorable, missingness is itself vital information and it must be taken into the likelihood, which, however, needs to introduce additional parameters to be estimated. The incompleteness of the…
Mixture models have been widely used in modeling of continuous observations. For the possibility to estimate the parameters of a mixture model consistently on the basis of observations from the mixture, identifiability is a necessary…
Consider an n-dimensional linear system where it is known that there are at most k<n non-zero components in the initial state. The observability problem, that is the recovery of the initial state, for such a system is considered. We obtain…
The aim of this paper is to present an, admittedly somewhat subjective, bird's eye view of the mathematical theory concerning the spread of an infectious disease in a susceptible host population with static structure, culminating in a…
Motivated by our intention to use SIR-type epidemiological models in the context of dynamic networks as provided by large-scale highly interacting inhomogeneous human crowds, we investigate in this framework possibilities to reduce the…
We reformulate models in epidemiology and population dynamics in terms of probability distributions. This allows us to construct the Fisher information, which we interpret as the metric of a one-dimensional differentiable manifold. For…
Interpreting data with mathematical models is an important aspect of real-world industrial and applied mathematical modeling. Often we are interested to understand the extent to which a particular set of data informs and constrains model…
The study of human mobility patterns is a crucially important research field for its impact on several socio-economic aspects and, in particular, the measure of regularity patters of human mobility can provide a across-the-board view of…
We consider a model identification problem in which an outcome variable contains nonignorable missing values. Statistical inference requires a guarantee of the model identifiability to obtain estimators enjoying theoretically reasonable…
This paper deals with the problem of evaluating the causal effect using observational data in the presence of an unobserved exposure/ outcome variable, when cause-effect relationships between variables can be described as a directed acyclic…
We define observability and detectability for linear switching systems as the possibility of reconstructing and respectively of asymptotically reconstructing the hybrid state of the system from the knowledge of the output for a suitable…
Despite the recent development of methods dealing with partially observed epidemic dynamics (unobserved model coordinates, discrete and noisy outbreak data), limitations remain in practice, mainly related to the quantity of augmented data…
Causality plays a central role in understanding interactions between variables in complex systems. These systems often exhibit state-dependent causal relationships, where both the strength and direction of causality vary with the value of…
Standard epidemic models based on compartmental differential equations are investigated under continuous parameter change as external forcing. We show that seasonal modulation of the contact parameter superimposed a monotonic decay needs a…
We consider a living organism as an observer of the evolution of its environment recording sensory information about the state space X of the environment in real time. Sensory information is sampled and then processed on two levels. On the…