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This paper is concerned with a stochastic model for the spread of an SEIR (susceptible -> exposed (=latent) -> infective -> removed) epidemic with a contact tracing scheme, in which removed individuals may name some of their infectious…
We consider a single outbreak susceptible-infected-recovered (SIR) model and corresponding estimation procedures for the effective reproductive number $\mathcal{R}(t)$. We discuss the estimation of the underlying SIR parameters with a…
In this article a space-dependent epidemic model equipped with a constant latency period is examined. We construct a delay partial integro-differential equation and show that its solution possesses some biologically reasonable features. We…
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…
Recently, emerging epidemics like COVID-19 and its variants require predictive mathematical models to implement suitable responses in order to limit their negative and profound impact on society. The SIR (Susceptible-InfectedRemoved) system…
Unsupervised medical anomaly detection is severely limited by the scarcity of normal training samples. Existing methods typically train dedicated models for each dataset or disease, requiring hundreds of normal images per task and lacking…
A model of "hot"-dimer deposition in one dimension, introduced by Pereyra and Albano, is modified to have an unbounded dissociation range. The resulting dynamical equations are solved exactly. A related k-mer dissociation model is also…
This paper reinforces numerical iterated integration developed by Muhammad--Mori in the following two points: 1) the approximation formula is modified so that it can achieve a better convergence rate in more general cases, and 2) explicit…
In {\it Set-theoretical solutions to the quantum Yang-Baxter equation} (Duke Math. J. {\bf 100} (1999), 169--209), Etingof, Schedler and Soloviev introduced, for each non-degenerate involutive set-theoretical solution $(X,\sigma,\tau)$ of…
Compressive-sensing-based uncertainty quantification methods have become a pow- erful tool for problems with limited data. In this work, we use the sliced inverse regression (SIR) method to provide an initial guess for the alternating…
New sensitivity-based methods are developed for determining identifiability and observability of nonsmooth input-output systems. More specifically, lexicographic calculus is used to construct nonsmooth sensitivity rank condition (SERC)…
We are currently facing a highly critical case of a world-wide pandemic. The novel coronavirus (SARS-CoV-2, a.k.a. COVID-19) has proved to be extremely contagious and the original outbreak from Asia has now spread to all continents. This…
We present exact solutions of the Dirac equation in static curved space-time using two distinct algebraic approaches. The first method employs $su(1,1)$ algebra operators together with the tilting transformation, enabling the derivation of…
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…
Mathematical models are often regarded as recent innovations in the description and analysis of infectious disease outbreaks and epidemics, but simple models have been in use for projection of epidemic trajectories for more than a century.…
A new method, the Dynamical Systems Method (DSM), justified recently, is applied to solving ill-conditioned linear algebraic system (ICLAS). The DSM gives a new approach to solving a wide class of ill-posed problems. In this paper a new…
The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the…
Modeling epidemic dynamics plays an important role in studying how diseases spread, predicting their future course, and designing strategies to control them. In this letter, we introduce a model of SIR (susceptible-infected-removed) type…
This survey article has two components. The first part gives a gentle introduction to Serre's notion of $G$-complete reducibility, where $G$ is a connected reductive algebraic group defined over an algebraically closed field. The second…
In our previous paper, the logistic curve of the removed number was derived from SIR and SEIR models in the case of the small basic reproduction number. In this paper, we derive various logistic curves of the removed, unsusceptible and…