Global stability of multi-group SEIQR epidemic models with stochastic perturbation in computer network

In this paper, a class of multi-group SEIQR models with random perturbation in computer network is investigated. The existence and uniqueness of global positive solution with any positive initial value are obtained. The sufficient conditions on the asymptotic behavior of solutions around the disease-free equilibrium and endemic equilibrium of the corresponding deterministic model are established. Furthermore, the existence and uniqueness of stationary distribution are also obtained. Lastly, the analytical results are illustrated by the numerical simulations

The Dynamical Behaviors in a Stochastic SIS Epidemic Model with Nonlinear Incidence

A stochastic SIS-type epidemic model with general nonlinear incidence and disease-induced mortality is investigated. It is proved that the dynamical behaviors of the model are determined by a certain threshold value R~0. That is, when R~0<1 and together with an additional condition, the disease is extinct with probability one, and when R~0>1, the disease is permanent in the mean in probability, and when there is not disease-related death, the disease oscillates stochastically about a positive number. Furthermore, when R~0>1, the model admits positive recurrence and a unique stationary distribution. Particularly, the effects of the intensities of stochastic perturbation for the dynamical behaviors of the model are discussed in detail, and the dynamical behaviors for the stochastic SIS epidemic model with standard incidence are established. Finally, the numerical simulations are presented to illustrate the proposed open problems

Analysis and simulation of a stochastic COVID-19 model with large-scale nucleic acid detection and isolation measures: A case study of the outbreak in Urumqi, China in August 2022

In this paper, a stochastic COVID-19 model with large-scale nucleic acid detection and isolation measures is proposed. Firstly, the existence and uniqueness of the global positive solution is obtained. Secondly, threshold criteria for the stochastic extinction and persistence in the mean with probability one are established. Moreover, a sufficient condition for the existence of unique ergodic stationary distribution for any positive solution is also established. Finally, numerical simulations are carried out in combination with real COVID-19 data from Urumqi, China and the theoretical results are verified

Analysis of spatial characteristics and geographic weighted regression of tuberculosis prevalence in Kashgar, China

Number of cases of tuberculosis (TB) was higher than that of the national level in Kashgar, China. This study aimed to analyze the spatial and temporal distribution of TB and the relationship between TB and social factors, which can provide a reference for the prevention and control of TB. We applied spatial autocorrelation analysis to study the distribution of tuberculosis in Kashgar. We used a geographically weighted regression (GWR) model to analyze the relationship between TB and social factors. A total of 100,330 cases of TB in Kashgar from 2016 to 2021 were analyzed. The number of TB cases in Kashgar was higher in the east, lower in the west, and most elevated in the center. The highest cumulative number of cases was found in Shache county. Global Moran's I ranged from -0.212 to -0.549, and local spatial autocorrelation analysis identified four clusters. According to our analysis, the incidence of tuberculosis was negatively correlated among the regions of Kashgar, and the related causes need to be analyzed in depth in future studies. Per capita gross domestic product (GDP), number of medical institutions per capita, and total population influenced the incidence of tuberculosis in Kashgar. Based on our findings, we suggest some effective measures to reduce the risk of TB infection, such as improving the living standard, developing the regional economy, and distributing health resources rationally