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The aim of this note is to give a new proof to the conjecture, proposed by Gray et al. (2011), on the extinction of a stochastic differential equation SIS epidemic model. The conjecture was proved by Xu (2017). Our proof is much more direct…

We study the problem of optimal control of the stochastic SIR model. Models of this type are used in mathematical epidemiology to capture the time evolution of highly infectious diseases such as COVID-19. Our approach relies on…

In this paper, we study an analytically tractable SIS model with a non-linear incidence rate for the number of infectious individuals described through a stochastic differential equation (SDE). We guarantee the existence of a positive…

In the present article, using a further generalization of the algebraic method of separation of variables, the Dirac equation is separated in a family of space-times where it is not possible to find a complete set of first order commuting…

We show how a rescaling of fractional operators with bounded kernels may help circumvent their documented deficiencies, for example, the inconsistency at zero or the lack of inverse integral operator. On the other hand, we build a novel…

Composed image retrieval (CIR) aims to retrieve a target image that depicts a reference image modified by a textual description. While recent vision-language models (VLMs) achieve promising CIR performance by embedding images and text into…

Evidence-based decision making often relies on meta-analyzing multiple studies, which enables more precise estimation and investigation of generalizability. Integrative analysis of multiple heterogeneous studies is, however, highly…

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…

A study of changes in the transmission of a disease, in particular, a new disease like COVID-19, requires very flexible models which can capture, among others, the effects of non-pharmacological and pharmacological measures, changes in…

This paper presents a new single-source surface integral equation (SS-SIE) to model composite penetrable objects. In the proposed formulation, the surface electric and magnetic fields on all interior boundaries are first eliminated through…

Using a recently developed approach for solving the three dimensional Dirac equation with spherical symmetry, we obtain simple representations for the Green's function of the Dirac-Oscillator and Dirac-Coulomb problems. This is accomplished…

We propose a systematic method of dealing with the canonical constrained structure of reducible systems in the Dirac and symplectic approaches which involves an enlargement of phase and configuration spaces, respectively. It is not…

We propose a simple SIR model in order to investigate the impact of various confinement strategies on a most virulent epidemic. Our approach is motivated by the current COVID-19 pandemic. The main hypothesis is the existence of two…

Surface integral equation (SIE) methods are of great interest for the numerical solution of Maxwell's equations in the presence of homogeneous objects. However, existing SIE algorithms have limitations, either in terms of scalability,…

A symmetry reduction of the Dirac equation is shown to yield the system of ordinary differential equations whose integrability by quadratures is closely connected to the stationary mKdV hierarchy.

We intrinsically characterize separability of the Dirac equation in Kerr-NUT-(A)dS spacetimes in all dimensions. Namely, we explicitly demonstrate that in such spacetimes there exists a complete set of first-order mutually commuting…

The recent COVID-19 pandemic has promoted vigorous scientific activity in an effort to understand, advice and control the pandemic. Data is now freely available at a staggering rate worldwide. Unfortunately, this unprecedented level of…

Infectious diseases spread through human networks. Susceptible-Infected-Removed (SIR) model is one of the epidemic models to describe infection dynamics on a complex network connecting individuals. In the metapopulation SIR model, each node…

This paper utilizes a stochastic Susceptible-Infected-recovered (SIR) model with a non-linear incidence rate to perform a detailed mathematical study of optimal lock-down intensity and vaccination rate under the COVID-19 pandemic…

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…