Modeling and Analyzing the Transmission Dynamics of HBV Epidemic in Xinjiang, China

Impacts of optimal control strategies on the HBV and COVID-19 co-epidemic spreading dynamics

Different cross-sectional and clinical research studies investigated that chronic HBV infected individuals' co-epidemic with COVID-19 infection will have more complicated liver infection than HBV infected individuals in the absence of COVID-19 infection. The main objective of this study is to investigate the optimal impacts of four time dependent control strategies on the HBV and COVID-19 co-epidemic transmission using compartmental modeling approach. The qualitative analyses of the model investigated the model solutions non-negativity and boundedness, calculated all the models effective reproduction numbers by applying the next generation operator approach, computed all the models disease-free equilibrium point (s) and endemic equilibrium point (s) and proved their local stability, shown the phenomenon of backward bifurcation by applying the Center Manifold criteria. By applied the Pontryagin's Maximum principle, the study re-formulated and analyzed the co-epidemic model optimal control problem by incorporating four time dependent controlling variables. The study also carried out numerical simulations to verify the model qualitative results and to investigate the optimal impacts of the proposed optimal control strategies. The main finding of the study reveals that implementation of protections, COVID-19 vaccine, and treatment strategies simultaneously is the most effective optimal control strategy to tackle the HBV and COVID-19 co-epidemic spreading in the community.

Analysis of HBV and COVID-19 Coinfection Model with Intervention Strategies

Coinfection of hepatitis B virus (HBV) and COVID-19 is a common public health problem throughout some nations in the world. In this study, a mathematical model for hepatitis B virus (HBV) and COVID-19 coinfection is constructed to investigate the effect of protection and treatment mechanisms on its spread in the community. Necessary conditions of the proposed model nonnegativity and boundedness of solutions are analyzed. We calculated the model reproduction numbers and carried out the local stabilities of disease-free equilibrium points whenever the associated reproduction number is less than unity. Using the well-known Castillo-Chavez criteria, the disease-free equilibrium points are shown to be globally asymptotically stable whenever the associated reproduction number is less than unity. Sensitivity analysis proved that the most influential parameters are transmission rates. Moreover, we carried out numerical simulation and shown results: some parameters have high spreading effect on the disease transmission, single infections have great impact on the coinfection transmission, and using protections and treatments simultaneously is the most effective strategy to minimize and also to eradicate the HBV and COVID-19 coinfection spreading in the community. It is concluded that to control the transmission of both diseases in a population, efforts must be geared towards preventing incident infection with either or both diseases.

Modelling the dynamics of acute and chronic hepatitis B with optimal control

This article examines hepatitis B dynamics under distinct infection phases and multiple transmissions. We formulate the epidemic problem based on the characteristics of the disease. It is shown that the epidemiological model is mathematically and biologically meaningful of its well-posedness (positivity, boundedness, and biologically feasible region). The reproductive number is then calculated to find the equilibria and the stability analysis of the epidemic model is performed. A backward bifurcation is also investigated in the proposed epidemic problem. With the help of two control measures (treatment and vaccination), we develop control strategies to minimize the infected population (acute and chronic). To solve the proposed control problem, we utilize Pontryagin's Maximum Principle. Some simulations are conducted to illustrate the investigation of the analytical work and the effect of control analysis.

Modelling of Hepatitis B Virus vertical transmission dynamics in Ethiopia: a compartmental modelling approach

BACKGROUND

Hepatitis B (HB) is a virus which causes a potentially fatal liver infection. It is a DNA virus belonging to the Hepadnaviridae virus family. Africa, after Asia, has the second highest number of chronic HBV carriers and is considered a high-endemic region. Ethiopia is classified as a country with a high prevalence of viral hepatitis and with nations that lack a systematic strategy for viral hepatitis surveillance.

METHODS

S-I-C-R deterministic model was developed and the numerical simulations were done in "R" statistical and programming software. Fixed population assumption was considered so as to develop a simple model which could predict the HBV vertical transmission for the next 5 decades.

RESULTS

The model revealed that significant number of populations will be infected and become carrier till the end the next 49 years even though it has decreasing trend. It was predicted that 271,719 people will die of HBV complications if no intervention will be made on its vertical transmission. The sensitivity analysis result showed that the force of infection has the most important parameter in the vertical transmission dynamics of hepatitis B. Provision of hepatitis B immunoglobulin (HBVIG) and vaccines at the time of delivery could decrease the force of infection by more than half and 51,892 lives will be saved if the intervention is offered for 50% of deliveries in Ethiopia.

CONCLUSION

Despite the fact that the incidence of HBV vertical transmission is substantial, it is expected to decline during the next five decades. However, the situation necessitates immediate attention, since it results in thousands of deaths if no action is taken. Offering HBVIG and vaccinations to the 50% of infants can save many lives and reduces the force of infection by more than a half.

Mathematical model analysis of effective intervention strategies on transmission dynamics of hepatitis B virus

Hepatitis B is one of the world's most common and severe infectious diseases. Worldwide, over 350 million people are currently estimated to be persistent carriers of the hepatitis B virus (HBV), with the death of 1 million people from the chronic stage of HBV infection. In this work, developed a nonlinear mathematical model for the transmission dynamics of HBV. We constructed the mathematical model by considering vaccination, treatment, migration, and screening effects. We calculated both disease-free and endemic equilibrium points for our model. Using the next-generation matrix, an effective reproduction number for the model is calculated. We also proved the asymptotic stability of both local and global asymptotically stability of disease-free and endemic equilibrium points. By calculating the sensitivity indices, the most sensitive parameters that are most likely to affect the disease's endemicity are identified. From the findings of this work, we recommend vaccination of the entire population and screening all the exposed and migrants. Additionally, early treatment of both the exposed class after screening and the chronically infected class is vital to decreasing the transmission of HBV in the community.

Modeling the epidemic trend of middle eastern respiratory syndrome coronavirus with optimal control

Since the outbreak of the Middle East Respiratory Syndrome Coronavirus (MERS-CoV) in 2012 in the Middle East, we have proposed a deterministic theoretical model to understand its transmission between individuals and MERS-CoV reservoirs such as camels. We aim to calculate the basic reproduction number ($ \mathcal{R}_{0} $) of the model to examine its airborne transmission. By applying stability theory, we can analyze and visualize the local and global features of the model to determine its stability. We also study the sensitivity of $ \mathcal{R}_{0} $ to determine the impact of each parameter on the transmission of the disease. Our model is designed with optimal control in mind to minimize the number of infected individuals while keeping intervention costs low. The model includes time-dependent control variables such as supportive care, the use of surgical masks, government campaigns promoting the importance of masks, and treatment. To support our analytical work, we present numerical simulation results for the proposed model.

A comparative study of three models to analyze the impact of air pollutants on the number of pulmonary tuberculosis cases in Urumqi, Xinjiang

In this paper, we separately constructed ARIMA, ARIMAX, and RNN models to determine whether there exists an impact of the air pollutants (such as PM2.5, PM10, CO, O3, NO2, and SO2) on the number of pulmonary tuberculosis cases from January 2014 to December 2018 in Urumqi, Xinjiang. In addition, by using a new comprehensive evaluation index DISO to compare the performance of three models, it was demonstrated that ARIMAX (1,1,2) × (0,1,1)12 + PM2.5 (lag = 12) model was the optimal one, which was applied to predict the number of pulmonary tuberculosis cases in Urumqi from January 2019 to December 2019. The predicting results were in good agreement with the actual pulmonary tuberculosis cases and shown that pulmonary tuberculosis cases obviously declined, which indicated that the policies of environmental protection and universal health checkups in Urumqi have been very effective in recent years.

Dynamics of a stochastic hepatitis B virus transmission model with media coverage and a case study of China

Hepatitis B virus (HBV) infection is a global public health problem and there are 257 million people living with chronic HBV infection throughout the world. In this paper, we investigate the dynamics of a stochastic HBV transmission model with media coverage and saturated incidence rate. Firstly, we prove the existence and uniqueness of positive solution for the stochastic model. Then the condition on the extinction of HBV infection is obtained, which implies that media coverage helps to control the disease spread and the noise intensities on the acute and chronic HBV infection play a key role in disease eradication. Furthermore, we verify that the system has a unique stationary distribution under certain conditions, and the disease will prevail from the biological perspective. Numerical simulations are conducted to illustrate our theoretical results intuitively. As a case study, we fit our model to the available hepatitis B data of mainland China from 2005 to 2021.

Impact of information intervention on stochastic hepatitis B model and its variable-order fractional network

This paper aims at analyzing the dynamical behavior of a SIR hepatitis B epidemic stochastic model via a novel approach by incorporating the effect of information interventions and random perturbations. Initially, we demonstrate the positivity and global existence of the solutions. Afterward, we derive the stochastic threshold parameter R s , followed by the fact that this number concludes the transmission of hepatitis B from the population. By increasing the intensity of noise, we get R s less than one, inferring that ultimately hepatitis B will lapse. While decreasing the intensity of noise to a sufficient level, we have R s > 1 . For the case R s > 1 , adequate results for the presence of stationary distribution are achieved, showing the prevalence of hepatitis B. The present study also involves the derivation of the necessary conditions for the persistence of the epidemic. Finally, the main theoretical solutions are plotted through simulations. Discussion on theoretical and numerical results shows that utilizing random perturbations and information interventions have a pronounced impact on the syndrome's dynamics. Furthermore, since most communities interact with each other, and the disease spread rate is affected by this factor, a new variable-order fractional network of the stochastic hepatitis B model is offered. Subsequently, this study will provide a robust theoretical basis for comprehending worldwide SIR stochastic and variable-order fractional network-related case studies.

Machine learning model for predicting out-of-hospital cardiac arrests using meteorological and chronological data

OBJECTIVES

To evaluate a predictive model for robust estimation of daily out-of-hospital cardiac arrest (OHCA) incidence using a suite of machine learning (ML) approaches and high-resolution meteorological and chronological data.

METHODS

In this population-based study, we combined an OHCA nationwide registry and high-resolution meteorological and chronological datasets from Japan. We developed a model to predict daily OHCA incidence with a training dataset for 2005-2013 using the eXtreme Gradient Boosting algorithm. A dataset for 2014-2015 was used to test the predictive model. The main outcome was the accuracy of the predictive model for the number of daily OHCA events, based on mean absolute error (MAE) and mean absolute percentage error (MAPE). In general, a model with MAPE less than 10% is considered highly accurate.

RESULTS

Among the 1 299 784 OHCA cases, 661 052 OHCA cases of cardiac origin (525 374 cases in the training dataset on which fourfold cross-validation was performed and 135 678 cases in the testing dataset) were included in the analysis. Compared with the ML models using meteorological or chronological variables alone, the ML model with combined meteorological and chronological variables had the highest predictive accuracy in the training (MAE 1.314 and MAPE 7.007%) and testing datasets (MAE 1.547 and MAPE 7.788%). Sunday, Monday, holiday, winter, low ambient temperature and large interday or intraday temperature difference were more strongly associated with OHCA incidence than other the meteorological and chronological variables.

CONCLUSIONS

A ML predictive model using comprehensive daily meteorological and chronological data allows for highly precise estimates of OHCA incidence.

A stochastic SACR epidemic model for HBV transmission

In this article, a stochastic SACR hepatitis B epidemic model is taken to be under consideration. We develop a stochastic epidemic model by considering the effect of environmental fluctuation on the hepatitis B dynamics and distribute the transmission rate by white noise. Using the stochastic Lyapunov function theory, we have shown the existence and uniqueness of the global positive solution. The extinction and persistence for our proposed model are derived with sufficient conditions. The numerical simulations are carried out using first-order Itô-Taylor stochastic scheme in the last section for the verification of our theoretical results.

Disease burden of chronic hepatitis B and complications in China from 2006 to 2050: an individual-based modeling study

Background

Chronic hepatitis B has become a major public health problem in China. An accurate depiction of the disease burden has not yet been thoroughly conducted. We aimed to project the disease burden of chronic hepatitis B virus (HBV) infection and related complications by modeling various scenarios.

Method

An individual-based Markov model was used to predict disease burden from 2006 through 2050. We simulated 5 scenarios with different annual incidences, diagnoses and nucleotide analog (NA) treatment rates as well as treatment eligibility, which included a natural history without diagnosis or NA therapy, a base case, a World Health Organization (WHO)-proposed target case and two ideal cases.

Result

The natural history scenario is projected to have the fewest HBsAg losses (27.59 million) and highest number of HBV-related deaths (27.19 million). With improved diagnosis and treatment rates of NA therapy, ideal cases have fewer HBV-related deaths (14.46–14.77 million) than do WHO-proposed cases (15.13 million) and base cases (16.89 million), but the proportion of HBsAg loss is similar among them. With a reduction in new infections, the prevalence of chronic HBV in 2050 is expected to be a minimum of 27.03–27.49 million under WHO and ideal cases.

Conclusion

Ideal scenarios 1 and 2 contribute to the lowest disease burden of HBV and its complications in the future, in which new infection control is more effective than increasing diagnosis, treatment rate and treatment eligibility. However, considering the large existing chronic HBV infected population and the low HBsAg loss rate of NA therapy, it is still difficult to avert the increasing trend of cumulative cirrhosis, DC, HCC, LT, and HBV-related death in all scenarios. If new high-potency drugs are not developed, the disease burden of chronic HBV will remain high in the future.

The prevention and control of tuberculosis: an analysis based on a tuberculosis dynamic model derived from the cases of Americans

Background

Tuberculosis (TB), a preventable and curable disease, is claimed as the second largest number of fatalities, and there are 9,025 cases reported in the United States in 2018. Many researchers have done a lot of research and achieved remarkable results, but TB is still a severe problem for human beings. The study is a further exploration of the prevention and control of tuberculosis.

Methods

In the paper, we propose a new dynamic model to study the transmission dynamics of TB, and then use global differential evolution and local sequential quadratic programming (DESQP) optimization algorithm to estimate parameters of the model. Finally, we use Latin hypercube sampling (LHS) and partial rank correlation coefficients (PRCC) to analyze the influence of parameters on the basic reproduction number (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal R_{0}$\end{document}R0) and the total infectious (including the diagnosed, undiagnosed and incomplete treatment infectious), respectively.

Results

According to the research, the basic reproduction number is computed as 2.3597 from 1984 to 2018, which means TB is also an epidemic in the US. The diagnosed rate is 0.6082, which means the undiagnosed will be diagnosed after 1.6442 years. The diagnosed will recover after an average of 1.9912 years. Moreover, some diagnosed will end the treatment after 1.7550 years for some reason. From the study, it’s shown that 2.40% of the recovered will be reactivated, and 13.88% of the newborn will be vaccinated. However, the immune system will be lost after about 19.6078 years.

Conclusion

Through the results of this study, we give some suggestions to help prevent and control the TB epidemic in the United States, such as prolonging the protection period of the vaccine by developing new and more effective vaccines to prevent TB; using the Chemoprophylaxis for incubation patients to prevent their conversion into active TB; raising people’s awareness of the prevention and control of TB and treatment after illness; isolating the infected to reduce the spread of TB. According to the latest report in the announcement that came at the first WHO Global Ministerial Conference on Ending tuberculosis in the Sustainable Development Era, we predict that it is challenging to control TB by 2030.

A stochastic model for the transmission dynamics of hepatitis B virus

In this paper, we formulate a stochastic model for hepatitis B virus transmission with the effect of fluctuation environment. We divide the total population into four different compartments, namely, the susceptible individuals in which the disease transmission rate is distributed by white noise, the acutely infected individuals in which the same perturbation occur, the chronically infected individuals and the recovered individuals. We use the stochastic Lyapunov function theory to construct a suitable stochastic Lyapunov function for the existence of positive solution. We also then establish the sufficient conditions for the hepatitis B extinction and the hepatitis B persistence. At the end numerical simulation is carried out by using the stochastic Runge-Kutta method to support our analytical findings.

Time Prediction Models for Echinococcosis Based on Gray System Theory and Epidemic Dynamics

Echinococcosis, which can seriously harm human health and animal husbandry production, has become an endemic in the Xinjiang Uygur Autonomous Region of China. In order to explore an effective human Echinococcosis forecasting model in Xinjiang, three grey models, namely, the traditional grey GM(1,1) model, the Grey-Periodic Extensional Combinatorial Model (PECGM(1,1)), and the Modified Grey Model using Fourier Series (FGM(1,1)), in addition to a multiplicative seasonal ARIMA(1,0,1)(1,1,0)₄ model, are applied in this study for short-term predictions. The accuracy of the different grey models is also investigated. The simulation results show that the FGM(1,1) model has a higher performance ability, not only for model fitting, but also for forecasting. Furthermore, considering the stability and the modeling precision in the long run, a dynamic epidemic prediction model based on the transmission mechanism of Echinococcosis is also established for long-term predictions. Results demonstrate that the dynamic epidemic prediction model is capable of identifying the future tendency. The number of human Echinococcosis cases will increase steadily over the next 25 years, reaching a peak of about 1250 cases, before eventually witnessing a slow decline, until it finally ends.