Convergence of the split-step θ-method for stochastic age-dependent population equations with Markovian switching and variable delay

We present a stochastic age-dependent population model that accounts for Markovian switching and variable delay. By using the approximate value at the nearest grid-point on the left of the delayed argument to estimate the delay function, we propose a class of split-step θ -method for solving stochastic delay age-dependent population equations (SDAPEs) with Markovian switch- ing. We show that the numerical method is convergent under the given conditions. Numerical examples are provided to illustrate our results

Stationary distribution of stochastic SIRS epidemic model with standard incidence

We study stochastic versions of a deterministic SIRS (Susceptible, Infective, Recovered, Susceptible) epidemic model with standard incidence. We study the existence of a stationary distribution of stochastic system by the theory of integral Markov semigroup. We prove the distribution densities of the solutions can converge to an invariant density in L1. This shows the system is ergodic. The presented results are demonstrated by numerical simulations

Una extensión del precondicionador I + Smax para el método de Gauss-Seidel

Se propone una técnica de precondicionamiento para el método deGauss-Seidel basada en la aplicación de una cantidad de pasos arbitrarios perofijos del precondicionador I + Smax. Se analiza de manera teórica la reducción del radio espectral de la matriz de iteración del método de Gauss-Seidel para Z-matrices diagonalmente dominantes. En particular, se demuestra que después de un número finito de pasos esta matriz se reduce a una matriz nula. Para ilustrar la eficacia de la técnica propuesta se presentan experimentos numéricos para una amplia variedad de matrices. Se estudian numéricamente versiones puntuales y de bloques del precondicionador.

Spectral characterizations of sandglass graphs

a b s t r a c t The sandglass graph is obtained by appending a triangle to each pendant vertex of a path. It is proved that sandglass graphs are determined by their adjacency spectra as well as their Laplacian spectra

Stability of highly nonlinear neutral stochastic differential delay equations

Stability criteria for neutral stochastic differential delay equations (NSDDEs) have been studied intensively for the past several decades. Most of these criteria can only be applied to NSDDEs where their coefficients are either linear or nonlinear but bounded by linear functions. This paper is concerned with the stability of hybrid NSDDEs without the linear growth condition, to which we will refer as highly nonlinear ones. The stability criteria established in this paper will be dependent on delays

The impact of gene polymorphism and hepatic insufficiency on voriconazole dose adjustment in invasive fungal infection individuals

Voriconazole (VRZ) is a broad-spectrum antifungal medication widely used to treat invasive fungal infections (IFI). The administration dosage and blood concentration of VRZ are influenced by various factors, posing challenges for standardization and individualization of dose adjustments. On the one hand, VRZ is primarily metabolized by the liver, predominantly mediated by the cytochrome P450 (CYP) 2C19 enzyme. The genetic polymorphism of CYP2C19 significantly impacts the blood concentration of VRZ, particularly the trough concentration (Ctrough), thereby influencing the drug’s efficacy and potentially causing adverse drug reactions (ADRs). Recent research has demonstrated that pharmacogenomics-based VRZ dose adjustments offer more accurate and individualized treatment strategies for individuals with hepatic insufficiency, with the possibility to enhance therapeutic outcomes and reduce ADRs. On the other hand, the security, pharmacokinetics, and dosing of VRZ in individuals with hepatic insufficiency remain unclear, making it challenging to attain optimal Ctrough in individuals with both hepatic insufficiency and IFI, resulting in suboptimal drug efficacy and severe ADRs. Therefore, when using VRZ to treat IFI, drug dosage adjustment based on individuals’ genotypes and hepatic function is necessary. This review summarizes the research progress on the impact of genetic polymorphisms and hepatic insufficiency on VRZ dosage in IFI individuals, compares current international guidelines, elucidates the current application status of VRZ in individuals with hepatic insufficiency, and discusses the influence of CYP2C19, CYP3A4, CYP2C9, and ABCB1 genetic polymorphisms on VRZ dose adjustments and Ctrough at the pharmacogenomic level. Additionally, a comprehensive summary and analysis of existing studies’ recommendations on VRZ dose adjustments based on CYP2C19 genetic polymorphisms and hepatic insufficiency are provided, offering a more comprehensive reference for dose selection and adjustments of VRZ in this patient population

Analyzing the codes that avoid specified differences by binary tree

The error probability of certain magnetic recording systems can be characterized by the difference patterns between the sequences that may be recorded. In [9] it is shown that the number of these sequences increases exponentially with their length and the capacity, the maximum growth rate of such sequences, is proven to be the logarithm of the joint spectral radius of a set of certain (0, 1) matrces. But approximating the joint spectral radius of a set of (0, 1) matrices is known to be NP-hard [11] (This is also stated in [9]).In this correspondence, we study these sequences using binary tree. Compared with the previous work, we get around the computation of the joint spectral radius. The number of sequences that avoid a certain set of difference patterns is proven to satisfy linear recurrence relations. From this we characterize the codes that have the maximum/minimum capacities. Our computation of capacities is straight-forward and therefore has less complexity than the previous ones