Modeling the transmission dynamics and control of hepatitis B virus in China

Preoperative serum total bilirubin-albumin ratio as a prognostic indicator in patients with hepatitis-related cirrhosis after splenectomy

BACKGROUND

Splenectomy is an effective yet invasive intervention for alleviating portal pressure in patients with hepatitis cirrhosis. However, the current prognostic indicators for predicting long-term overall survival of these patients have several limitations.

AIM

To assess the potential of preoperative total bilirubin-albumin (B/A) ratio as a prognostic indicator for patients with hepatitis cirrhosis undergoing splenectomy.

METHODS

A total of 257 patients diagnosed with hepatitis cirrhosis were retrospectively enrolled in the study. Normality test, t-test, Wilcoxon test, χ² test, or Fisher’s exact test was employed to analyze the intraoperative and postoperative conditions of the patients. Receiver operating characteristic (ROC) curve analysis was utilized to depict the 10-year overall survival rate.

RESULTS

During the follow-up period, 85.99% of the patients survived, with a median survival time of 64.6 months. Multivariate analysis revealed that total serum B/A ratio was an independent risk factor for overall survival (P = 0.037). ROC curve analysis demonstrated that a B/A ratio of 0.87 was the optimal cut-off value. Consequently, the patients were categorized into two groups: High B/A group (n = 64) and low B/A group (n = 193). The median follow-up time for the high B/A group and low B/A group was 56.8 months and 67.2 months, respectively (P = 0.045). Notably, the high B/A group exhibited a significantly lower 10-year overall survival compared to the low B/A group (P < 0.001). Patients with hepatocellular carcinoma (HCC) had lower overall survival rates. Patients with a high B/A ratio exhibited a lower overall survival than those with a low B/A rate in the overall cohort and the subgroups of patients with HCC or not, early Child-Pugh grade, low albumin-bilirubin grade, and model for end-stage liver disease score ≥ 10 (log-rank test, P < 0.001 for all).

CONCLUSION

The B/A ratio can serve as an effective prognostic indicator for overall survival in patients with hepatitis B virus-related cirrhosis following splenectomy, and a higher B/A ratio may suggest a poorer prognosis.

Mathematical analysis with control of liver cirrhosis causing from HBV by taking early detection measures and chemotherapy treatment

Reformulating the physical processes associated with the evolution of different ailments in accordance with globally shared objectives is crucial for deeper comprehension. This study aims to investigate the mechanism by which the HB virus induces harmful inflammation of the liver, with a focus on early detection and therapy using corticosteroids or chemotherapy. Based on the developed hypothesis, a new mathematical model has been created for this purpose. The recently developed system for HBV is S E I 1 I 2 R , which is examined both quantitatively and qualitatively to determine its actual effect on stability. Reliable conclusions are ensured by examining the system's boundedness, positivity, existence, uniqueness, and conducting local and global stability analysis-all crucial components of epidemic models. Global stability is tested using Lyapunov first derivative functions to assess the overall impact of asymptomatic persons and chemotherapy treatment. Additionally, the Lipschitz condition is used to confirm the unique solutions for the newly built HBV model using methods from fixed point theory, thus meeting the requirements for uniqueness and existence. Since the population must maintain this property, positivity is confirmed using global derivatives and Lipschitz criteria to calculate the rate of change in each sub-compartment. Applying the Mittag-Leffler kernel with a fractal-fractional operator to continuously monitor the HBV virus for liver cirrhosis infection yields dependable results. Furthermore, the current situation regarding the HBV outbreak pertaining to liver cirrhosis infection, along with the control measures implemented following early diagnosis through asymptomatic measures and chemotherapy treatment under constant observation, are established to prevent chronic stage infections. Simulations have been used to study the true behavior and impact of HBV in asymptomatic persons receiving chemotherapy for liver cirrhosis infection in the community. This research is essential for understanding the spread of viruses and developing control strategies based on our validated findings to mitigate the risk factors associated with liver cirrhosis.

Modeling different infectious phases of hepatitis B with generalized saturated incidence: An analysis and control

Hepatitis B is one of the global health issues caused by the hepatitis B virus (HBV), producing 1.1 million deaths yearly. The acute and chronic phases of HBV are significant because worldwide, approximately 250 million people are infected by chronic hepatitis B. The chronic stage is a long-term, persistent infection that can cause liver damage and increase the risk of liver cancer. In the case of multiple phases of infection, a generalized saturated incidence rate model is more reasonable than a simply saturated incidence because it captures the complex dynamics of the different infection phases. In contrast, a simple saturated incidence rate model assumes a fixed shape for the incidence rate curve, which may not accurately reflect the dynamics of multiple infection phases. Considering HBV and its various phases, we constructed a model to present the dynamics and control strategies using the generalized saturated incidence. First, we proved that the model is well-posed. We then found the reproduction quantity and model equilibria to discuss the time dynamics of the model and investigate the conditions for stabilities. We also examined a control mechanism by introducing various controls to the model with the aim to increase the population of those recovered and minimize the infected people. We performed numerical experiments to check the biological significance and control implementation.

Computational analysis of control of hepatitis B virus disease through vaccination and treatment strategies

Hepatitis B disease is an infection caused by a virus that severely damages the liver. The disease can be both acute and chronic. In this article, we design a new nonlinear SVEICHR model to study dynamics of Hepatitis B Virus (HBV) disease. The aim is to carry out a comprehensive mathematical and computational analysis by exploiting preventive measures of vaccination and hospitalization for disease control. Mathematical properties of proposed model such as boundedness, positivity, and existence and uniqueness of the solutions are proved. We also determine the disease free and endemic equilibrium points. To analyze dynamics of HBV disease, we compute a biologically important quantity known as the reproduction number R0 by using next generation method. We also investigate the stability at both of the equilibrium points. To control the spread of disease due to HBV, two feasible optimal control strategies with three different cases are presented. For this, optimal control problem is constructed and Pontryagin maximum principle is applied with a goal to put down the disease in the population. At the end, we present and discuss effective solutions obtained through a MATLAB code.

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.

The high prevalence of occult hepatitis B infections among the partners of chronically infected HBV blood donors emphasizes the potential residual risk to blood safety

A small percentage of couples who regularly donated blood in China tested positive for HBsAg. Although it is well known that blood donors can acquire hepatitis B virus (HBV) infection from a chronically infected sexual partner, the prevalence of occult hepatitis B infections (OBIs) among blood donations from partners of HBV-infected chronically infected spouses and the risk to blood safety remain poorly understood. Among 212 763 blood donors, 54 pairs of couples (108 donations) were enrolled because one partner tested positive for HBsAg. Several molecular and serological examinations were conducted. The origin of HBV transmission between sexual partners was investigated further. Also evaluated was the potential risk of HBV infection with OBIs. We identified 10 (10/54, 18.6%) sexual partners of chronically infected HBV donors who were positive for HBV DNA, including five samples (9.3%) with OBIs, of which 3 (3/54, 5.6%, 1 in 70 921 donations) passed the routine blood screening tests. Seven of the 10 HBV-DNA-positive couples contracted the virus possibly through sexual or close contact. Among infected couples, immune escape mutations were observed. A high prevalence of OBIs was found among the partners of chronically infected HBV blood donors, posing a potential threat to blood safety.

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.

The dynamics of novel corona virus disease via stochastic epidemiological model with vaccination

During the past two years, the novel coronavirus pandemic has dramatically affected the world by producing 4.8 million deaths. Mathematical modeling is one of the useful mathematical tools which has been used frequently to investigate the dynamics of various infectious diseases. It has been observed that the nature of the novel disease of coronavirus transmission differs everywhere, implying that it is not deterministic while having stochastic nature. In this paper, a stochastic mathematical model has been investigated to study the transmission dynamics of novel coronavirus disease under the effect of fluctuated disease propagation and vaccination because effective vaccination programs and interaction of humans play a significant role in every infectious disease prevention. We develop the epidemic problem by taking into account the extended version of the susceptible-infected-recovered model and with the aid of a stochastic differential equation. We then study the fundamental axioms for existence and uniqueness to show that the problem is mathematically and biologically feasible. The extinction of novel coronavirus and persistency are examined, and sufficient conditions resulted from our investigation. In the end, some graphical representations support the analytical findings and present the effect of vaccination and fluctuated environmental variation.

Mathematical Model of Hepatitis B Disease with Optimal Control and Cost-Effectiveness Analysis

In this paper, a mathematical model of hepatitis B disease with a two-dose vaccine series has been formulated and analyzed. We demonstrated that the model’s disease-free equilibrium is globally asymptotically stable when the basic reproduction number $\left(R_0\right)$ is less than one, whereas the model’s endemic equilibrium is locally asymptotically stable when $R_0$ is greater than one. Sensitivity analysis is performed, and based on its results, the model is extended to an optimal control problem by incorporating two control interventions, namely, prevention and enhanced newborn vaccination. Finally, simulation analyses of the model are conducted to illustrate the theoretical findings and effectiveness of each strategy, which indicates that the use of prevention efforts is the most cost-saving strategy.

Critical behavior of the diffusive susceptible-infected-recovered model

The critical behavior of the nondiffusive susceptible-infected-recovered model on lattices had been well established in virtue of its duality symmetry. By performing simulations and scaling analyses for the diffusive variant on the two-dimensional lattice, we show that diffusion for all agents, while rendering this symmetry destroyed, constitutes a singular perturbation that induces asymptotically distinct dynamical and stationary critical behavior from the nondiffusive model. In particular, the manifested crossover behavior in the effective mean-square radius exponents reveals that slow crossover behavior in general diffusive multispecies reaction systems may be ascribed to the interference of multiple length scales and timescales at early times.

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.

Dynamical analysis of a stochastic delayed SIR epidemic model with vertical transmission and vaccination

In order to describe the dynamic process of epidemic transmission with vertical transmission and vaccination in more detail and to better track the factors that lead to the occurrence of epidemics, we construct a stochastic delayed model with a specific functional response to describe its epidemic dynamics. We first prove the existence and uniqueness of the positive solution of the model. Moreover, we analyze the sufficient conditions for the extinction and persistence of the model. Finally, numerical simulations are presented to illustrate our mathematical findings.

Dynamical Behavior of SEIR-SVS Epidemic Models with Nonlinear Incidence and Vaccination

For some infectious diseases such as mumps, HBV, there is evidence showing that vaccinated individuals always lose their immunity at different rates depending on the inoculation time. In this paper, we propose an age-structured epidemic model using a step function to describe the rate at which vaccinated individuals lose immunity and reduce the age-structured epidemic model to the delay differential model. For the age-structured model, we consider the positivity, boundedness, and compactness of the semiflow and study global stability of equilibria by constructing appropriate Lyapunov functionals. Moreover, for the reduced delay differential equation model, we study the existence of the endemic equilibrium and prove the global stability of equilibria. Finally, some numerical simulations are provided to support our theoretical results and a brief discussion is given.

The global stability investigation of the mathematical design of a fractional-order HBV infection

This work presents approximate solutions of a fractional-order design for hepatitis B virus infection. The numerical solution of the system is given by using an implicit fractional linear multi-step method of the second order. Here, Caputo fractional derivative is considered for fractional derivative. Basic theoretical properties are discussed. We prove the global stability analysis of the fractional-order model. Numerical simulations are demonstrated to display our theoretical results. This current study is to reveal that the order of the fractional derivative β does not affect the regular state's stability concerning both theoretical and numerical results. Besides, if the fractional-order β increases, the solutions converge more rapidly to the regular states. Finally, we note that this study can provide beneficial outcomes for understanding and estimating the dissipation of distinct epidemics.

A study on fractional HBV model through singular and non-singular derivatives

The current study's aim is to evaluate the dynamics of a Hepatitis B virus (HBV) model with the class of asymptomatic carriers using two different numerical algorithms and various values of the fractional-order parameter. We considered the model with two different fractional-order derivatives, namely the Caputo derivative and Atangana-Baleanu derivative in the Caputo sense (ABC). The considered derivatives are the most widely used fractional operators in modeling. We present some mathematical analysis of the fractional ABC model. The fixed-point theory is used to determine the existence and uniqueness of the solutions to the considered fractional model. For numerical results, we show a generalized Adams-Bashforth-Moulton (ABM) method for Caputo derivative and an Adams type predictor-corrector (PC) algorithm for Atangana-Baleanu derivatives. Finally, the models are numerically solved using computational techniques and obtained results graphically illustrated with a wide range of fractional-order values. We compare the numerical results for Caputo and ABC derivatives graphically. In addition, a new variable-order fractional network of the HBV model is proposed. Considering the fact that most communities interact with each other, and the rate of disease spread is affected by this factor, the proposed network can provide more accurate insight for the modeling of the disease.

Diaphragm ultrasound to evaluate the antagonistic effect of sugammadex on rocuronium after liver surgery in patients with different liver Child-Pugh grades: study protocol for a prospective, double-blind, non-randomised controlled trial

INTRODUCTION

The use of muscle relaxants is an indispensable in the general anaesthesia but is prone to accidents, which are often related to residual muscle relaxant. Therefore, how to timely and effectively eliminate the residual effect of muscle relaxants after surgery has become an urgent clinical problem. Rocuronium is a non-depolarising muscle relaxant that is primarily metabolised by the liver. Patients with liver dysfunction can affect the metabolic process of rocuronium, thereby delaying the recovery of muscle relaxation. Sugammadex (SUG) is a novel-specific antagonist of aminosteroidal muscle relaxants, which can effectively antagonise muscle relaxants at different depths. However, whether liver dysfunction affects the antagonistic effect of SUG against rocuronium has not been reported. Therefore, we hypothesise that with the increase of patients' liver Child-Pugh grade, the recovery time of rocuronium antagonised by the same dose of SUG after surgery will be prolonged, and the incidence of muscle relaxation residual will be increased in the short term.

METHODS AND ANALYSIS

This study is a prospective, double-blind, low-intervention, non-randomised controlled clinical trial involving 99 patients with American Society of Anesthesiologists (ASA) Ⅰ-Ⅲ, body mass index 18.5-24.9 kg/m2, who will undergo laparoscopic radical resection of liver cancer under general anaesthesia in the Union Hospital, Tongji Medical College, Huazhong University of Science and Technology. Ultrasonography will be applied to monitor the change rate of diaphragm thickness at different time after extubation to evaluate the occurrence of residual muscle relaxant, which indirectly reflects the dose-effect relationship of SUG antagonising against rocuronium in patients with different liver Child-Pugh grades preoperatively.

ETHICS AND DISSEMINATION

The protocol was reviewed and approved by the Medical Ethics Committee of Union Hospital Affiliated to Tongji Medical College of Huazhong University of Science and Technology (UHCT21012). The findings will be disseminated to the public through peer-reviewed scientific journals.

TRIAL REGISTRATION NUMBER

NCT05028088.

Modelling homosexual and heterosexual transmissions of hepatitis B virus in China

Studies have shown that sexual transmission, both heterosexually and homosexually, is one of the main ways of HBV infection. Based on this fact, we propose a mathematical model to study the sexual transmission of HBV among adults by classifying adults into men and women and considering both same-sex and opposite-sex transmissions of HBV in adults. Firstly, we calculate the basic reproduction number R0 and the disease-free equilibrium point E0. Secondly, by analysing the sensitivity of R0 in terms of model parameters, we find that the infection rate among people who have same-sex partners, the frequency of homosexual contact and the immunity rate of adults play important roles in the transmission of HBV. Moreover, we use our model to fit the reported data in China and forecast the trend of hepatitis B. Our results demonstrate that popularizing the basic knowledge of HBV among residents, advocating healthy and reasonable sexual life style, reducing the number of adult carriers, and increasing the immunization rate of adults are effective measures to prevent and control hepatitis B.

Optimal Voluntary Vaccination of Adults and Adolescents Can Help Eradicate Hepatitis B in China

Hepatitis B (HBV) is one of the most common infectious diseases, with a worldwide annual incidence of over 250 million people. About one-third of the cases are in China. While China made significant efforts to implement a nationwide HBV vaccination program for newborns, a significant number of susceptible adults and teens remain. In this paper, we analyze a game-theoretical model of HBV dynamics that incorporates government-provided vaccination at birth coupled with voluntary vaccinations of susceptible adults and teens. We show that the optimal voluntary vaccination brings the disease incidence to very low levels. This result is robust and, in particular, due to a high HBV treatment cost, essentially independent from the vaccine cost.

Analysis of fractional COVID-19 epidemic model under Caputo operator

The article deals with the analysis of the fractional COVID-19 epidemic model (FCEM) with a convex incidence rate. Keeping in view the fading memory and crossover behavior found in many biological phenomena, we study the coronavirus disease by using the noninteger Caputo derivative (CD). Under the Caputo operator (CO), existence and uniqueness for the solutions of the FCEM have been analyzed using fixed point theorems. We study all the basic properties and results including local and global stability. We show the global stability of disease-free equilibrium using the method of Castillo-Chavez, while for disease endemic, we use the method of geometrical approach. Sensitivity analysis is carried out to highlight the most sensitive parameters corresponding to basic reproduction number. Simulations are performed via first-order convergent numerical technique to determine how changes in parameters affect the dynamical behavior of the system.

An application of a novel geometric criterion to global-stability problems of a nonlinear SEIVS epidemic model

This work applies a novel geometric criterion for nonlinear autonomous differential equations developed by Lu and Lu (NARWA 36:20-43, 2017) to a nonlinear SEIVS epidemic model with temporary immunity and achieves its threshold dynamics. Specifically, global-stability problems for the SEIVS model of Cai and Li (AMM 33:2919-2926, 2009) are effectively solved. The corresponding optimal control system with vaccination, awareness campaigns and treatment is further established and four different control strategies are compared by numerical simulations to contain hepatitis B. It is concluded that joint implementation of these measures can minimize the numbers of exposed and infectious individuals in the shortest time, so it is the most efficient strategy to curb the hepatitis B epidemic. Moreover, vaccination for newborns plays the core role and maintains the high level of population immunity.

Regional differences of hepatitis B discrimination in rural China

Background: Hepatitis B (HB) is the most serious and common viral hepatitis in China. Previous studies on HB discrimination mainly have focussed on stratified analysis, and there has been no consideration of the impact of geographical-environmental factors on HB discrimination from a spatial perspective.Objective: This study conducted a large nationwide village-based survey to test whether there were significant regional differences in HB discrimination, and to explore the relationship between different socio-economic geographical factors and HB discrimination.Methods: The sample comprised 22618 rural adults, aged over 18 years old, from villages in seven provinces, representing central, southern, and eastern coastal regions of China. Using face-to-face interviews, we surveyed participants' discrimination against HB patients or carriers. Chi-square tests were used to analyze the effects of the region on differences in proportions between three discrimination levels (low, medium, and high). A geographical detector was used to explore the relationship between different socio-economic and geographical-environmental factors and HB discrimination.Results: The distribution of HB discrimination levels across the 42 villages was statistically significant. The level of HB discrimination in the central and southern regions was generally low, and the level of HB discrimination in the eastern coastal regions was higher. Both socio-economic and geographic-environmental factors had a significant relationship with HB discrimination. Most of these relationships were not linear.Conclusions: Developing the economy and accelerating urbanization did not automatically eliminate discrimination against HB. We recommend government HB publicity and education campaigns to inform the population of HB causes and effects, and strengthen the education of students so that they can have a clear and correct understanding of HB from a young age, both of which will address HB discrimination.

A numerical and analytical study of SE(Is)(Ih)AR epidemic fractional order COVID-19 model

This article describes the corona virus spread in a population under certain assumptions with the help of a fractional order mathematical model. The fractional order derivative is the well-known fractal fractional operator. We have given the existence results and numerical simulations with the help of the given data in the literature. Our results show similar behavior as the classical order ones. This characteristic shows the applicability and usefulness of the derivative and our numerical scheme.

Stability analysis and optimal control of covid-19 with convex incidence rate in Khyber Pakhtunkhawa (Pakistan)

The dynamic of covid-19 epidemic model with a convex incidence rate is studied in this article. First, we formulate the model without control and study all the basic properties and results including local and global stability. We show the global stability of disease free equilibrium using the method of Lyapunov function theory while for disease endemic, we use the method of geometrical approach. Furthermore, we develop a model with suitable optimal control strategies. Our aim is to minimize the infection in the host population. In order to do this, we use two control variables. Moreover, sensitivity analysis complemented by simulations are performed to determine how changes in parameters affect the dynamical behavior of the system. Taking into account the central manifold theory the bifurcation analysis is also incorporated. The numerical simulations are performed in order to show the feasibility of the control strategy and effectiveness of the theoretical results.

Fractional optimal control of COVID-19 pandemic model with generalized Mittag-Leffler function

In this paper, we consider a fractional COVID-19 epidemic model with a convex incidence rate. The Atangana-Baleanu fractional operator in the Caputo sense is taken into account. We establish the equilibrium points, basic reproduction number, and local stability at both the equilibrium points. The existence and uniqueness of the solution are proved by using Banach and Leray-Schauder alternative type theorems. For the fractional numerical simulations, we use the Toufik-Atangana scheme. Optimal control analysis is carried out to minimize the infection and maximize the susceptible people.

The Complex Dynamics of Hepatitis B Infected Individuals with Optimal Control

This paper proposes various stages of the hepatitis B virus (HBV) besides its transmissibility and nonlinear incidence rate to develop an epidemic model. The authors plan the model, and then prove some basic results for the well-posedness in term of boundedness and positivity. Moreover, the authors find the threshold parameter R ₀, called the basic/effective reproductive number and carry out local sensitive analysis. Furthermore, the authors examine stability and hence condition for stability in terms of R ₀. By using sensitivity analysis, the authors formulate a control problem in order to eradicate HBV from the population and proved that the control problem actually exists. The complete characterization of the optimum system was achieved by using the 4^th-order Runge-Kutta procedure.

Stochastic epidemic dynamics based on the association between susceptible and recovered individuals

In this paper, we propose a new mathematical model based on the association between susceptible and recovered individual. Then, we study the stability of this model with the deterministic case and obtain the conditions for the extinction of diseases. Moreover, in view of the association between susceptible and recovered individual perturbed by white noise, we also give sufficient conditions for the extinction and the permanence in mean of disease with the white noise. Finally, we have numerical simulations to demonstrate the correctness of obtained theoretical results.

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.

Fractal-Fractional Mathematical Model Addressing the Situation of Corona Virus in Pakistan

This work is the consideration of a fractal fractional mathematical model on the transmission and control of corona virus (COVID-19), in which the total population of an infected area is divided into susceptible, infected and recovered classes. We consider a fractal-fractional order SIR type model for investigation of Covid-19. To realize the transmission and control of corona virus in a much better way, first we study the stability of the corresponding deterministic model using next generation matrix along with basic reproduction number. After this, we study the qualitative analysis using "fixed point theory" approach. Next, we use fractional Adams-Bashforth approach for investigation of approximate solution to the considered model. At the end numerical simulation are been given by matlab to provide the validity of mathematical system having the arbitrary order and fractal dimension.

Is it possible to halve the incidence of liver cancer in China by 2050?

A substantial proportion of liver cancers is attributable to chronic infection with hepatitis B and C (HBV/HCV). Liver cancer could become the second cancer, after cervical, to be effectively controlled globally, if proven interventions such as vaccination can be implemented on a large scale. In 2018, the global mortality rate for liver cancer was estimated to be 8.5 per 100 000 individuals. Given patterns of HBV infection and immigration across countries, liver cancer control requires combined, global action. Liver cancer trends vary between countries, in some Western countries, the incidence rates were relatively low but have increased in recent decades; conversely, in several Asian countries, the incidence rates have decreased over time. China has in the past contributed more than half of the global burden of liver cancer but more recently a national decline in liver cancer incidence has been observed. Here, we review the liver cancer burden and exposure to risk factors in China, compared to other countries. We also review the implementation status for primary and secondary prevention interventions and major outcomes achieved over the past three decades. Using Bayesian age-period-cohort analysis, we examine recent trends and based on these, predict that by 2050, the incidence of liver cancer in China could fall by half. We additionally survey the literature to identify current research needs, and review relevant national policies on liver cancer control in China. A comprehensive set of interventions is proposed to progress toward the long-term goal of liver cancer elimination based on the natural history and evidence-based interventions.

Existence, uniqueness, and stability of fractional hepatitis B epidemic model

This paper describes the existence and stability of the hepatitis B epidemic model with a fractional-order derivative in Atangana-Baleanu sense. Some new results are handled by using the Sumudu transform. The existence and uniqueness of the equilibrium solution are presented using the Banach fixed-point theorem. Moreover, sensitivity analysis complemented by simulations is performed to determine how changes in parameters affect the dynamical behavior of the system. The numerical simulations are carried out using a predictor-corrector scheme to demonstrate the obtained results.

Global dynamics of a model of hepatitis B virus infection in a sub-Saharan African rural area

We formulate and systematically study a deterministic compartmental model of Hepatitis B. This model has some important and novel features compared with the well-known basic model in the literature. Specifically, it takes into account the differential susceptibility that follows the vaccine formulation employing three-doses schedule. It points up the HbeAg status of carriers, their levels of viral replication, the fact that treatment being not curative is recommended only to a small proportion of chronic carriers, and finally the fact that only inactive carriers are able to recover from disease. The model has simple dynamical behavior which has a globally asymptotically stable disease-free equilibrium when the basic reproduction number [Formula: see text] and an endemic equilibrium when [Formula: see text]. By the use of Lyapunov functions, when it exists, we prove the global asymptotic stability of the endemic equilibrium under some conditions. Using data from Tokombere, a rural area in Cameroon, numerical simulations are performed. These numerical simulations first confirm analytical results, second they suggest that a policy based on treatment could not significantly impact the course of the infection. Third, they show as it is well known that vaccination is a very effective measure to control the infection. Furthermore, they show that neonatal vaccination influences more the course of infection than mass vaccination strategy. Nevertheless, they picture how much loss between consecutive doses of vaccine could be harmful. Finally, it is suggested that for a Sub-saharan African rural area, two-thirds of expected incidence of Hepatitis B virus infection and one third of expected prevalence of chronic carriers could be averted by 2030 if the birth dose vaccination becomes systematic and if mass vaccination rate increases to up 10%.

OPTIMAL CONTROL ANALYSIS OF THE EFFECT OF TREATMENT, ISOLATION AND VACCINATION ON HEPATITIS B VIRUS

Hepatitis B infection is a serious health issue and a major cause of deaths worldwide. This infection can be overcome by adopting proper treatment and control strategies. In this paper, we develop and use a mathematical model to explore the effect of treatment on the dynamics of hepatitis B infection. First, we formulate and use a model without control variables to calculate the basic reproduction number and to investigate basic properties of the model such as the existence and stability of equilibria. In the absence of control measures, we prove that the disease free equilibrium is locally asymptotically stable when the basic reproduction number is less than unity. Also, using persistent theorem, it is shown that the infection is uniformly persistent, whenever the basic reproduction number is greater than unity. Using optimal control theory, we incorporate into the model three time-dependent control variables and investigate the conditions required to curtail the spread of the disease. Finally, to illustrate the effectiveness of each of the control strategies on disease control and eradication, we perform numerical simulations. Based on the numerical results, we found that the first two strategies (treatment and isolation strategy) and (vaccination and isolation strategy) are not very effective as a long term control or eradication strategy for HBV. Hence, we recommend that in order to effectively control the disease, all the control measures (isolation, vaccination and treatment) must be implemented at the same time.

Game-Theoretical Model of Retroactive Hepatitis B Vaccination in China

Hepatitis B (HepB) is one of the most common infectious diseases affecting over two billion people worldwide. About one third of all HepB cases are in China. In recent years, China made significant efforts to implement a nationwide HepB vaccination program and reduced the number of unvaccinated infants from 30 to 10%. However, many individuals still remain unprotected, particularly those born before 2003. Consequently, a catch-up retroactive vaccination is an important and potentially cost-effective way to reduce HepB prevalence. In this paper, we analyze a game theoretical model of HepB dynamics that incorporates government-provided vaccination at birth coupled with voluntary retroactive vaccinations. Given the uncertainty about the long-term efficacy of the HepB vaccinations, we study several scenarios. When the waning rate is relatively high, we show that this retroactive vaccination should be a necessary component of any HepB eradication effort. When the vaccine offers long-lasting protection, the voluntary retroactive vaccination brings the disease incidence to sufficiently low levels. Also, we find that the optimal vaccination rates are almost independent of the vaccination coverage at birth. Moreover, it is in an individual's self-interest to vaccinate (and potentially re-vaccinate) at a rate just slightly above the vaccine waning rate.

A Label-Free Immunosensor Based on Graphene Oxide/Fe3O4/Prussian Blue Nanocomposites for the Electrochemical Determination of HBsAg

In this article, a highly sensitive label-free immunosensor based on a graphene oxide (GO)/Fe3O4/Prussian blue (PB) nanocomposite modified electrode was developed for the determination of human hepatitis B surface antigen (HBsAg). In this electrochemical immunoassay system, PB was used as a redox probe, while GO/Fe3O4/PB nanocomposites and AuNPs were prepared and coated on screen-printed electrodes to enhance the detection sensitivity and to immobilize the hepatitis B surface antibody (HBsAb). The immunosensor was fabricated based on the principle that the decrease in peak currents of PB is proportional to the concentration of HBsAg captured on the modified immunosensor. The experimental results revealed that the immunosensor exhibited a sensitive response to HBsAg in the range of 0.5 pg·mL-1 to 200 ng·mL-1, and with a low detection limit of 0.166 pg·mL-1 (S/N = 3). Furthermore, the proposed immunosensor was used to detect several clinical serum samples with acceptable results, and it also showed good reproducibility, selectivity and stability, which may have a promising potential application in clinical immunoassays.

Ergodic Stationary Distribution of a Stochastic Hepatitis B Epidemic Model with Interval-Valued Parameters and Compensated Poisson Process

Hepatitis B epidemic was and is still a rich subject that sparks the interest of epidemiological researchers. The dynamics of this epidemic is often modeled by a system with constant parameters. In reality, the parameters associated with the Hepatitis B model are not certain, but the interval in which it belongs to can readily be determined. Our paper focuses on an imprecise Hepatitis B model perturbed by Lévy noise due to unexpected environmental disturbances. This model has a global positive solution. Under an appropriate assumption, we prove the existence of a unique ergodic stationary distribution by using the mutually exclusive possibilities lemma demonstrated by Stettner in 1986. Our main effort is to establish an almost perfect condition for the existence of the stationary distribution. Numerical simulations are introduced to illustrate the analytical results.

Stochastic mathematical model for the spread and control of Corona virus

This work is devoted to a stochastic model on the spread and control of corona virus (COVID-19), in which the total population of a corona infected area is divided into susceptible, infected, and recovered classes. In reality, the number of individuals who get disease, the number of deaths due to corona virus, and the number of recovered are stochastic, because nobody can tell the exact value of these numbers in the future. The models containing these terms must be stochastic. Such numbers are estimated and counted by a random process called a Poisson process (or birth process). We construct an SIR-type model in which the above numbers are stochastic and counted by a Poisson process. To understand the spread and control of corona virus in a better way, we first study the stability of the corresponding deterministic model, investigate the unique nonnegative strong solution and an inequality managing of which leads to control of the virus. After this, we pass to the stochastic model and show the existence of a unique strong solution. Next, we use the supermartingale approach to investigate a bound managing of which also leads to decrease of the number of infected individuals. Finally, we use the data of the COVOD-19 in USA to calculate the intensity of Poisson processes and verify our results.

Optimal control strategies for preventing hepatitis B infection and reducing chronic liver cirrhosis incidence

Advanced liver cirrhosis has become life-threatening among non-communicable diseases nowadays. Cirrhosis, the terminal stage of liver diseases in which the liver develops scarring as a result of various long-term continuous damages. Among liver diseases, viral hepatitis is the major risk factor for chronic cirrhosis development. The present paper demonstrates a compartmental model of chronic disease liver cirrhosis describing the transmission dynamics of this disease. Applying the Pontryagin’s maximum principle, the optimal control policies such as vaccination for hepatitis B virus and treatment of other causes of cirrhosis are adopted as control measures. The target of this study is to minimize the number of infected and liver cirrhotic individuals as well as the associated cost of the control. For this purpose, the optimal control strategies are employed according to the underlying causes behind this disease. Our goal is to find the strategy of preventing hepatitis B infection which is considered one of the leading causes of cirrhosis and consequently, reduction of the chronic cirrhosis incidence. Efficiency analysis is also performed to observe the effective control among the two control strategies. The model is investigated both analytically and numerically and the numerical simulations are carried out to illustrate the analytical findings. The analysis reveals that both the vaccination and treatment could be the most fruitful way to reduce the incidence of chronic liver cirrhosis.

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.

Current situation and progress toward the 2030 health-related Sustainable Development Goals in China: A systematic analysis

BACKGROUND

The Sustainable Development Goals (SDGs), adopted by all United Nations (UN) member states in 2015, established a set of bold and ambitious health-related targets to achieve by 2030. Understanding China's progress toward these targets is critical to improving population health for its 1.4 billion people.

METHODS AND FINDINGS

We used estimates from the Global Burden of Disease (GBD) Study 2016, national surveys and surveillance data from China, and qualitative data. Twenty-eight of the 37 indicators included in the GBD Study 2016 were analyzed. We developed an attainment index of health-related SDGs, a scale of 0-100 based on the values of indicators. The projection model is adjusted based on the one developed by the GBD Study 2016 SDG collaborators. We found that China has achieved several health-related SDG targets, including decreasing neonatal and under-5 mortality rates and the maternal mortality ratios and reducing wasting and stunting for children. However, China may only achieve 12 out of the 28 health-related SDG targets by 2030. The number of target indicators achieved varies among provinces and municipalities. In 2016, among the seven measured health domains, China performed best in child nutrition and maternal and child health and reproductive health, with the attainment index scores of 93.0 and 91.8, respectively, followed by noncommunicable diseases (NCDs) (69.4), road injuries (63.6), infectious diseases (63.0), environmental health (62.9), and universal health coverage (UHC) (54.4). There are daunting challenges to achieve the targets for child overweight, infectious diseases, NCD risk factors, and environmental exposure factors. China will also have a formidable challenge in achieving UHC, particularly in ensuring access to essential healthcare for all and providing adequate financial protection. The attainment index of child nutrition is projected to drop to 80.5 by 2025 because of worsening child overweight. The index of NCD risk factors is projected to drop to 38.8 by 2025. Regional disparities are substantial, with eastern provinces generally performing better than central and western provinces. Sex disparities are clear, with men at higher risk of excess mortality than women. The primary limitations of this study are the limited data availability and quality for several indicators and the adoption of "business-as-usual" projection methods.

CONCLUSION

The study found that China has made good progress in improving population health, but challenges lie ahead. China has substantially improved the health of children and women and will continue to make good progress, although geographic disparities remain a great challenge. Meanwhile, China faced challenges in NCDs, mental health, and some infectious diseases. Poor control of health risk factors and worsening environmental threats have posed difficulties in further health improvement. Meanwhile, an inefficient health system is a barrier to tackling these challenges among such a rapidly aging population. The eastern provinces are predicted to perform better than the central and western provinces, and women are predicted to be more likely than men to achieve these targets by 2030. In order to make good progress, China must take a series of concerted actions, including more investments in public goods and services for health and redressing the intracountry inequities.

Modeling and qualitative analysis of a hepatitis B epidemic model

We develop an epidemic mathematical model for hepatitis B contagious disease, which is one of the major causes of death among various infectious diseases. We prove the existence, positivity, and biological feasibility of the model. We find the threshold quantity of the model and analyze the sensitivity analysis to show the effect of various parameters on the spread of hepatitis B virus. Exploiting the linear stability approach, we find stability conditions to perform the stability analysis. We use the central manifold theory to discuss the existence of backward bifurcation of the proposed model. Finally, we present numerical simulations to verify the analytical calculations and to analyze the sensitivity of parameters.

Prevalence of Hepatitis B Virus Infection in Shenzhen, China, 2015-2018

China has nearly 10% of the general HBV carrier population in the world; this infection is the most common cause of chronic liver disease. Understanding HBV epidemiology is essential for future infection control, evaluation, and treatment. This study determined the prevalence of HBV infection in Shenzhen by serological testing and analysis in 282,166 HBV screening cases for the following: HBcAb, indicative of previous HBV infection; HBsAg, indicative of chronic (current) infection; HBsAb, indicative of immunity from vaccination; and 34,368 HBV etiological screening cases for HBV-DNA, indicative of virus carriage, in which 1,204 cases were genotyped and mutation analyzed for drug-resistance evaluation. Shenzhen was a highly endemic area of HBV throughout the study period (prevalence 9.69%). HBV infections were almost entirely in the 20 and older age groups with a male-to-female ratio of 1.16:1 which is approximately the same as the male-to-female ratio of the general population in China. However, only 71.25% of the general population retained HBV immune protection. Genotype B and C were identified as the most common agents; recombinant B/C and B/D also existed; some cases, however, could not be genotyped. NAs resistant mutation occurrence patterns were multitudinous; single mutation patterns of rtM204I/V and rtL180M occurrences accounted for majority, followed by the combinational mutation pattern L180M + M204I/V. Drug-resistance was prevalent, mainly occurring in the cross resistance patterns LAM + LdT and LAM + LdT + ETV, and significantly more critical in males. These results demonstrate that all people free from HBV infection should obtain injections of the vaccine or booster shots, and conventional virologic detection in a clinical laboratory center should incorporate genotype and mutation alongside the serological factors for etiology and develop better classification methods, such as sequencing.

Log-Linear Modelling of Effect of Age and Gender on the Spread of Hepatitis B Virus Infection in Lagos State, Nigeria

BACKGROUND:

The effect of age and gender on the transmission of any infectious disease can be of great important because the age at which the host contact the disease may be a determinant on the rate at which the disease will spread.

AIM:

The purpose of this research is to model the significant effect of age and gender on the spread of hepatitis B virus using data collected from Lagos State, Nigeria.

MATERIAL AND METHODS:

The data that was used for this research is a ten years data covering the period of 2006 to 2015, which was collected from Nigeria Institute of Medical Research (NIMR). A log-linear modelling approach was employed using R programming language software. Akaike Information Criterion (AIC) method of model selection was used in selecting the best model.

RESULTS:

It was discovered from the analysis that both factors (age and gender) have a significant effect on the spread of hepatitis B infection. This means that the age at which an individual is tested positive to hepatitis B virus will affect the spread of the disease. In choosing the best model among the four models that were developed, model AY: GY (age & year: gender and year) was found to be the best model.

CONCLUSION:

Age and gender were found to act as a risk influencer that could have a great effect on the transmission of hepatitis B virus infections in Lagos state, Nigeria.

Immunomodulatory Effects of Combination Therapy with Bushen Formula plus Entecavir for Chronic Hepatitis B Patients

Aim

To compare the clinical efficacy of the combination therapy with Bushen formula (BSF) plus entecavir (ETV) in naïve chronic hepatitis B (CHB) patients and that in CHB patients with partial virological response to ETV and explore the relevant immunoregulatory mechanism.

Materials and Methods

Two hundred and twenty CHB patients were enrolled in the historical prospective cohort study. Patients were categorized into a treatment group (T-Group: combination therapy with BSF plus ETV) and a control group (C-Group: ETV). Patients in T-Group and C-Group were grouped into T1/C1 (treatment-naïve patients) and T2/C2 (patients with partial virological response to ETV). Biochemical assessment, viral load quantitation, and HBV markers were tested. Chinese medicine symptom complex score was evaluated and recorded as well. In addition, peripheral blood mononuclear cells were separated from blood samples in 56 patients and 11 healthy donors. The frequencies of Th1, Treg, and dendritic cells (DCs) and expression levels of PD-1/PD-L1 were examined by flow cytometry.

Results

In treatment-naïve CHB patients, complete viral suppression rates in HBeAg(−) patients were higher than those in HBeAg(+) patients in both T and C groups. In patients with partial virological response to ETV, the rate of HBsAg decline ≥ 20% in HBeAg(+) patients of T2-Group was higher than that in HBeAg(+) patients of C2-Group. A significant reduction of Chinese medicine symptom complex score was only observed in T-Group. The study of mechanism showed that, compared with healthy controls, Th1 and DC frequencies were decreased in all CHB patients, while Treg frequency was increased only in treatment-naïve patients. In addition, compared with healthy controls, PD-1 expression levels on Th1 and Treg were increased in all patients and PD-L1 expression levels on DCs were increased only in treatment-naïve patients. In treatment-naïve patients, the combination therapy with BSF plus ETV increased Th1 and DC frequencies and decreased Treg frequency, which was correlated with HBsAg decline. In addition, in patients with partial virological response to ETV, the combination therapy downregulated PD-L1 levels on DCs and the frequency of Treg, which was related with HBsAg decline.

Conclusions

In patients with partial virological response to ETV, HBeAg(+) patients tend to achieve ideal effects after the combination therapy with BSF plus ETV, which may correlate with the decrease of Treg frequency and the downregulation of PD-L1 levels on DCs.

The transmission dynamic of different hepatitis B-infected individuals with the effect of hospitalization

We propose an epidemic model for the transmission of hepatitis B virus along with the classification of different infection phases and hospitalized class. We formulate the model and discuss its basic mathematical properties, e.g. existence, positivity, and biological feasibility. Exploiting the next generation matrix approach, we find the basic reproductive number of the model. We perform sensitivity analysis to illustrate the effect of various parameters on the transmission of the disease. We investigate stability of the equilibria of the model in terms of the basic reproduction number. Conditions for the stability of the proposed model are obtained using various approaches. Finally, we perform the numerical simulations to discuss sensitivity analysis and to support our analytical work.

Efficacy and safety of laparoscopic splenectomy and esophagogastric devascularization for portal hypertension: A single-center experience

Many patients in China have portal hypertension secondary to liver cirrhosis. Splenectomy and devascularization have become an efficacious surgical procedure for portal hypertension, and has been recommended in China as the first choice for the treatment of portal hypertension for a long time. As a result of advances in laparoscopic equipment and techniques, splenectomy and esophagogastric devascularization have been carried out with laparoscope.From January 2012 to December 2017, 453 patients who were diagnosed with portal hypertension and serious gastroesophageal varices received surgical management in our institution. 250 patients chose laparoscopic splenectomy and esophagogastric devascularization and 203 underwent open splenectomy and esophagogastric devascularization.We retrospectively analyzed the perioperative data and follow-up data of these patients. The operation time of laparoscopic group was longer than open group (P ≤ .001). Intraoperative blood loss was less (P ≤ .001), the passing of flatus was earlier (P = .042), and postoperative hospital stay was shorter (P = .001) in the laparoscopic group. During postoperative follow-up of 4 to 75 months, the incidence of esophagogastric variceal rebleeding, encephalopathy, and secondary liver cancer showed no significant differences.Laparoscopic splenectomy and esophagogastric devascularization were safe and more effective than open surgery for portal hypertension and gastroesophageal varices.

Hepatitis B vaccination among 1997-2011 birth cohorts in rural China: the potential for further catch-up vaccination and factors associated with infant coverage rates

Hepatitis B vaccination rates in China have recently increased. This study aimed to investigate infant vaccination coverage for birth cohorts from 1997 to 2011 in rural regions and to assess catch-up vaccination potential. We used questionnaire-based interviews from a cross-section of 6,529 individuals from seven provinces. Logistic regression analyses were used to model two measures of infant vaccination status, namely, birth dose within 24 hours and three doses within the first year of life. During interviews, individuals' vaccination status and vaccination plan were recorded. Unvaccinated individuals without plans for future vaccination were presented with a hypothetical offer of free vaccination and indirect cost compensation. Institutional birth rates were higher than vaccination rates, but both increased over time. Vaccination coverage rates were not significantly associated with sex. Infant vaccination coverage was positively associated with a mother's educational level, household income level, knowledge of transmission routes, and perceived duration of protection obtained through vaccination. Vaccination status at the time of the survey showed the occurrence of catch-up vaccinations, but a notable percentage of individuals remained unvaccinated and had no plans for future vaccination. Of these individuals, approximately 50% were prepared to accept vaccination if offered free of charge.