Dynamic properties of deterministic and stochastic SIIIRS models with multiple viruses and saturation incidences.

The classical compartment model is often used to study the spread of an epidemic with one virus. However, there are few types of research on epidemic models with multiple viruses. The article aims to propose two new deterministic and stochastic SIIIRS models with multiple viruses and saturation incidences. We obtain asymptotic properties of disease-free and several endemic equilibria for the deterministic model. In the stochastic case, we prove the existence and uniqueness of positive global solutions. The extinction and persistence of diseases are obtained under different threshold conditions. We analyze the existence of stationary distribution through a suitable Lyapunov function. The results indicate that the extinction or persistence of the two viruses is closely related to the intensity of white noise interference. Specifically, considerable white noise is beneficial for the extinction of diseases, while slight one can lead to long-term epidemics of diseases. Finally, numerical simulations illustrate our theoretical results and the effect of essential parameters.

Spatio-temporal distribution characteristics of the risk of viral hepatitis B incidence based on INLA in 14 prefectures of Xinjiang from 2004 to 2019.

This study aimed to explore the spatio-temporal distribution characteristics and risk factors of hepatitis B (HB) in 14 prefectures of Xinjiang, China, and to provide a relevant reference basis for the prevention and treatment of HB. Based on HB incidence data and risk factor indicators in 14 prefectures in Xinjiang from 2004 to 2019, we explored the distribution characteristics of the risk of HB incidence using global trend analysis and spatial autocorrelation analysis and established a Bayesian spatiotemporal model to identify the risk factors of HB and their spatio-temporal distribution to fit and extrapolate the Bayesian spatiotemporal model using the Integrated Nested Laplace Approximation (INLA) method. There was spatial autocorrelation in the risk of HB and an overall increasing trend from west to east and north to south. The natural growth rate, per capita GDP, number of students, and number of hospital beds per 10, 000 people were all significantly associated with the risk of HB incidence. From 2004 to 2019, the risk of HB increased annually in 14 prefectures in Xinjiang, with Changji Hui Autonomous Prefecture, Urumqi City, Karamay City, and Bayangol Mongol Autonomous Prefecture having the highest rates.

Spatial age-period-cohort analysis of hepatitis B risk in Xinjiang from 2006 to 2019.

Objective: The objective of this study was to investigate the spatio-temporal distribution and epidemiological characteristics of hepatitis B in 96 districts and counties of Xinjiang and to give useful information for hepatitis B prevention and treatment. Methods: Based on the incidence data of hepatitis B in 96 districts and counties of Xinjiang from 2006 to 2019, the global trend analysis method was used to characterize the spatial variability of the disease, and the spatial autocorrelation and spatio-temporal aggregation analysis were used to explore the spatial clustering of hepatitis B and to identify high-risk areas and periods. The Integrated Nested Laplace Approximation (INLA)-based spatial age-period-cohort model was established to further explore the influence of age, period, birth queue effect, and spatial distribution on the incidence risk of hepatitis B, and sum-to-zero constraint was adopted to avoid the issue of model unrecognition. Results: The risk of hepatitis B in Xinjiang is increasing from west to east and from north to south, with spatial heterogeneity and spatio-temporal scanning statistics yielding five clustering areas. The spatial age-period-cohort model showed two peaks in the average risk of hepatitis B, at [25,30) years old and [50,55) years old, respectively. The mean risk of hepatitis B incidence fluctuated up and down around 1 with time, and the average risk of disease by birth cohort displayed an increasing-decreasing-stabilizing trend. Taking age, period, and cohort effect into consideration, it was found that the areas with a high risk of hepatitis B are Tianshan District, Xinshi District, Shuimogou District, Changji City, Aksu City, Kashi City, Korla City, Qiemo County and Yopurga County in Xinjiang. According to the spatio-temporal effect item, it was found that there are unobserved variables affecting the incidence of hepatitis B in some districts and counties of Xinjiang. Conclusion: The spatio-temporal characteristics of hepatitis B and the high-risk population needed to be taken into attention. It is suggested that the relevant disease prevention and control centers should strengthen the prevention and control of hepatitis B among young people while paying attention to middle-aged and older adult people, and strengthening the prevention and monitoring of high-risk areas.

MCMCINLA estimation of varying coefficient spatial lag model-A study of China's economic development in the context of population aging.

The dominant spatial econometric model in spatial econometrics is the parametric form, while in the realistic context, the variables often do not satisfy the assumption of linearity and have nonlinear relationships with each other. In this paper, we introduce nonparametric terms into spatial econometric models and propose the MCMCINLA estimation method for varying coefficient spatial lag models. The empirical analysis is conducted with the socioeconomic data of mainland China from 2015 to 2020 to discuss the influencing factors and spatial and temporal distribution characteristics of China's economic development under the classical spatial lag model and the varying coefficient spatial lag model with population aging as a special covariate, respectively. The results show that with the gradual aging of the population, foreign trade will inhibit the development of regional economy to a certain extent, while urbanization process, resident income, real estate development and high-tech development will have a driving effect on economic growth, and high-tech development has the strongest mobilization on regional economic development. Compared with the classical spatial lag model, the varying coefficient spatial lag model can more fully exploit the information of variables in a more realistic context and derive the variable evolution process.

Bayesian spatiotemporal modelling analysis of hemorrhagic fever with renal syndrome outbreaks in China using R-INLA.

Hemorrhagic fever with renal syndrome (HFRS) is a category B infectious disease caused by Hantavirus infection, which can cause acute kidney injury and has a high mortality rate. At present, China is the country most severely afflicted by HFRS in the world, and it is critical to carry out efficient HFRS prevention and management in a scientific and accurate manner. The study used data on the incidence of HFRS in mainland China from 2015 to 2018, built a Bayesian hierarchical spatiotemporal distribution model, and applied the Integrated Nested Laplace Approximation algorithm to analyse the factors influencing the development of HFRS, the spatial and temporal distribution characteristics, and the threshold exceedance locations. The results revealed that the woodland and grassland area (RR = 1.357, 95% CI: 1.005-1.791), economic level (RR = 1.299, 95% CI: 1.007-1.649), and traffic level (RR = 2.442, 95% CI: 1.825-3.199) were all significantly and positively associated with the development of HFRS, with traffic level having the strongest promoting effect. The seasonal cycle was obvious in time, with peaks in May-June and October-December each year, most notably in November. Spatially, there was a south-heavy north-light trend, with a high risk of incidence largely in places rich in mountain and forest vegetation, of which Guizhou, Guangxi, Guangdong, and Jiangxi provinces continuing to have a high incidence in recent years, and the evolution of the epidemic in Hubei and Hunan was becoming more serious. When the early warning threshold was set at 0.2, the detection impact was best, and Guizhou, Guangxi, Guangdong, Jiangxi, Hainan, and Tianjin were positioned near the critical point of the exceedance threshold with the highest risk of incidence. It is recommended that the relevant managers call for active vaccination of outdoor workers, such as those working in agriculture and construction sites, implement rat prevention and extermination before winter arrives, and warn high-risk and medium-high-risk areas to conduct early outbreak surveillance. Move the prevention and control gates forward based on the exceedance threshold for doing preventive and control detection and epidemic research and judgement work.

Analysis of spatial and temporal impact differences of birth rate in mainland China.

The continuing decline in the birth rate has led to a series of problems, such as the disproportion of population structure and severe aging population, which have restricted the country's economic development. To have a deeper understanding of the geographical differences and influencing factors of the birth rate, this paper collects and organizes the birth population data of 31 provinces in mainland China from 2011 to 2019. The national region is divided into seven natural geographical regions to obtain the spatial hierarchy, and a hierarchical Bayesian Spatio-temporal model is established. The INLA algorithm estimates the model parameters. The results show significant spatial and temporal differences in birth rates in mainland China, which are reflected mainly in the combination of spatial, temporal, and Spatio-temporal interaction effects. In the spatial dimension, the northeast is low, the northwest and southwest are high, and the birth rate has an upward trend from east to west. These trends are caused by unbalanced economic development, different fertility attitudes and differences in fertility security, reflecting regional differences in spatial effects. From 2011 to 2019, China's birth rate showed an overall downward trend in the time dimension. However, all regions except the northeast saw a significant but temporary increase in birth rates in 2016 and 2017, reflecting the temporal effect difference in birth rates.

MCMCINLA Estimation of Missing Data and Its Application to Public Health Development in China in the Post-Epidemic Era.

Medical data are often missing during epidemiological surveys and clinical trials. In this paper, we propose the MCMCINLA estimation method to account for missing data. We introduce a new latent class into the spatial lag model (SLM) and use a conditional autoregressive specification (CAR) spatial model-based approach to impute missing values, making the model fit into the integrated nested Laplace approximation (INLA) framework. Combining the advantages of both the Markov chain Monte Carlo (MCMC) and INLA frameworks, the MCMCINLA algorithm is used to implement imputation of the missing data and fit the model to derive estimates of the parameters from the posterior margins. Finally, the economic data and the hemorrhagic fever with renal syndrome (HFRS) disease data of mainland China from 2016-2018 are used as examples to explore the development of public health in China in the post-epidemic era. The results show that compared with expectation maximization (EM) and full information maximum likelihood estimation (FIML), the predicted values of the missing data obtained using our method are closer to the true values, and the spatial distribution of HFRS in China can be inferred from the imputation results with a southern-heavy and northern-light distribution. It can provide some references for the development of public health in China in the post-epidemic era.