Hepatitis-B virus endemicity: heterogeneity, catastrophic dynamics and control

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.

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.

Why Controlling the Asymptomatic Infection Is Important: A Modelling Study with Stability and Sensitivity Analysis

The large proportion of asymptomatic patients is the major cause leading to the COVID-19 pandemic which is still a significant threat to the whole world. A six-dimensional ODE system (SEIAQR epidemical model) is established to study the dynamics of COVID-19 spreading considering infection by exposed, infected, and asymptomatic cases. The basic reproduction number derived from the model is more comprehensive including the contribution from the exposed, infected, and asymptomatic patients. For this more complex six-dimensional ODE system, we investigate the global and local stability of disease-free equilibrium, as well as the endemic equilibrium, whereas most studies overlooked asymptomatic infection or some other virus transmission features. In the sensitivity analysis, the parameters related to the asymptomatic play a significant role not only in the basic reproduction number R0. It is also found that the asymptomatic infection greatly affected the endemic equilibrium. Either in completely eradicating the disease or achieving a more realistic goal to reduce the COVID-19 cases in an endemic equilibrium, the importance of controlling the asymptomatic infection should be emphasized. The three-dimensional phase diagrams demonstrate the convergence point of the COVID-19 spreading under different initial conditions. In particular, massive infections will occur as shown in the phase diagram quantitatively in the case R0>1. Moreover, two four-dimensional contour maps of Rt are given varying with different parameters, which can offer better intuitive instructions on the control of the pandemic by adjusting policy-related parameters.

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.

Maternal age at first childbirth and geographical variation in HBV prevalence in Cameroon: Important role of mother-to-child transmission

BACKGROUND

The prevalence of hepatitis B virus (HBV) infection varies geographically around the world. However, the underlying reasons for this variation are unknown. Using a nationally representative population-based sample from all 58 administrative divisions in Cameroon, we examined the association between median maternal age at first childbirth in a preceding generation, a proxy for the frequency of mother-to-child transmission (MTCT) of HBV in a region, and the risk of chronic HBV infection, defined as positive surface antigen (HBsAg), in the index generation.

METHODS

We estimated a division-specific median maternal age at first childbirth using historical data from Demographic Health Surveys (DHS) in 1991/1998/2004/2011. We tested HBsAg in 2011 DHS participants. We used maps to display spatial variation and spatial models for the analysis.

RESULTS

In 14,150 participants (median 27 years old, 51% females), the overall weighted prevalence of HBsAg was 11.9% (95%CI: 11.0-12.8), with a wide geographical variation across the divisions (range: 6.3-23.7%). After adjusting for confounding factors and spatial dependency, lower maternal age at first childbirth was significantly associated with positive HBsAg at the division level (β: 1.89 [95%CI: 1.26-2.52], p<0.001), and at the individual level (OR: 1.20 [95%CI: 1.04-1.39], p=0.016). A similar ecological correlation was observed across other African countries.

CONCLUSIONS

The significant association between the maternal age at first childbirth and HBsAg-positivity suggests a crucial role of MTCT in maintaining high HBV endemicity in some areas in Cameroon. This underlines an urgent need to effectively prevent MTCT in order to achieve WHO's global hepatitis elimination goals.

Global stability analysis for a model with carriers and non-linear incidence rate

We analysed a epidemiological model with varying populations of susceptible, carriers, infectious and recovered (SCIR) and a general non-linear incidence rate of the form [Formula: see text]. We show that this model exhibits two positive equilibriums: the disease-free and disease equilibrium. We proved using the Lyapunov direct method that these two equilibriums are globally asymptotically stable under some sufficient conditions over the functions f, g, h.

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.

Critical transitions in malaria transmission models are consistently generated by superinfection

The history of modelling vector-borne infections essentially begins with the papers by Ross on malaria. His models assume that the dynamics of malaria can most simply be characterized by two equations that describe the prevalence of malaria in the human and mosquito hosts. This structure has formed the central core of models for malaria and most other vector-borne diseases for the past century, with additions acknowledging important aetiological details. We partially add to this tradition by describing a malaria model that provides for vital dynamics in the vector and the possibility of super-infection in the human host: reinfection of asymptomatic hosts before they have cleared a prior infection. These key features of malaria aetiology create the potential for break points in the prevalence of infected hosts, sudden transitions that seem to characterize malaria's response to control in different locations. We show that this potential for critical transitions is a general and underappreciated feature of any model for vector-borne diseases with incomplete immunity, including the canonical Ross-McDonald model. Ignoring these details of the host's immune response to infection can potentially lead to serious misunderstanding in the interpretation of malaria distribution patterns and the design of control schemes for other vector-borne diseases. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'. This issue is linked with the subsequent theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'.

Hepatitis B prevention: Can we learn from the response to HIV/AIDS?

Mirjam Kretzschmar and Marianne van der Sande discuss the accompanying research study by Anna McNaughton and colleagues on strategies to reduce the burden of hepatitis B in African countries.

Sampling to elucidate the dynamics of infections in reservoir hosts

The risk of zoonotic spillover from reservoir hosts, such as wildlife or domestic livestock, to people is shaped by the spatial and temporal distribution of infection in reservoir populations. Quantifying these distributions is a key challenge in epidemiology and disease ecology that requires researchers to make trade-offs between the extent and intensity of spatial versus temporal sampling. We discuss sampling methods that strengthen the reliability and validity of inferences about the dynamics of zoonotic pathogens in wildlife hosts. This article is part of the theme issue 'Dynamic and integrative approaches to understanding pathogen spillover'.

The potential impact of the demographic transition in the Senegal-Gambia region of sub-Saharan Africa on the burden of infectious disease and its potential synergies with control programmes: the case of hepatitis B

BACKGROUND

Sub-Saharan Africa (SSA) continues to suffer high communicable disease burdens as its demographic transition (DT) proceeds. Although the consequent changes in population structures influence age-specific contact patterns relevant for transmission, the age distribution of immunity, and the disease burden, investigation of the potential of DT to affect infectious disease epidemiology in regions of SSA has hitherto been overlooked. With a substantial disease burden and complex epidemiology, hepatitis B virus (HBV) represents a prime example of an infection whose epidemiology may be significantly influenced by the DT.

METHODS

An age-structured mathematical model for HBV in the Senegal and Gambia (SG) region was set within a demographic framework with varying vital rates mirroring the entire course of the DT there over 1850-2100, to investigate the effects of the DT on HBV epidemiology, with and without the combined action of vaccination. The model was run from its reconstructed ancien régime (old order) demo-epidemiologic equilibrium and calibrated against SG 1950 age-distribution estimates and Gambian pre-vaccination HBV age-prevalence data.

RESULTS

The model, which reproduced well demographic and HBV age-prevalence data, predicted a complex transition of HBV epidemiology over the course of the DT. This included a prolonged epoch of expansion alongside population growth and rejuvenation until 1990-2000, followed by a dramatic retreat, mainly reflecting projected fertility decline during the twenty-first century. This transitional pattern was mostly explained by the underlying demographically driven changes in horizontal transmission resulting from the changes in the age structure of the population. During 2000-2150 the HBV burden is predicted to decline by more than 70% even in the absence of vaccination.

CONCLUSIONS

Demographic change alone may strongly affect HBV disease burden and shape HBV endemicity. The onset of the demographically driven decline in HBV prevalence, aligned with the expansion of HBV vaccination, forms a synergy potentially boosting effectiveness of control. Such a synergy currently appears to be presenting a "window of opportunity" facilitating HBV elimination which it would be important to exploit and which underlines the importance of taking demographic change into account when assessing the potential longer term impact of vaccination and other control measures.

CONTROL STRATEGIES of HEPATITIS B WITH THREE CONTROL VARIABLES

In this paper, we present a compartmental mathematical model of hepatitis B virus with optimal control strategies. First, we formulate the model applying the optimal control techniques which use control variables in the form of isolation, educational campaign and vaccination. We derive the conditions under which it is optimal to eradicate the disease and examine the impact of possible vaccination treatment strategies on disease transmission. When such an elimination is impossible, we use the techniques of Pontryagin’s Maximum Principle to derive the necessary conditions for the optimal control problem. The numerical results show that some effective vaccination and control can reduce the disease spread in the community.

Estimating the impact of test-and-treat strategies on hepatitis B virus infection in China by using an age-structured mathematical model

The potential impact of increasing test-and-treat coverage on hepatitis B virus (HBV) infection remains unclear in China. The objective of this study was to develop a dynamic compartmental model at a population level to estimate the long-term effect of this strategy.Based on the natural history of HBV infection and 3 serosurvey data of hepatitis B in China, we proposed an age- and time-dependent discrete model to predict the number of new HBV infection, the number of chronic HBV infection, and the number of HBV-related deaths for the time from 2018 to 2050 under 5 different test-and-treat coverage and compared them with current intervention policy.Compared with current policy, if the test-and-treat coverage was increased to 100% since 2018, the numbers of chronic HBV infection, new HBV infection, and HBV-related deaths in 2035 would be reduced by 26.60%, 24.88%, 26.55%, respectively, and in 2050 it would be reduced by 44.93%, 43.29%, 43.67%, respectively. In contrast, if the test-and-treat coverage was increased by 10% every year since 2018, then the numbers of chronic HBV infection, new HBV infection, and HBV-related deaths in 2035 would be reduced by 21.81%, 20.10%, 21.40%, respectively, and in 2050 it would be reduced by 41.53%, 39.89%, 40.32%, respectively. In particular, if the test-and-treat coverage was increased to 75% since 2018, then the annual number of HBV-related deaths would begin to decrease from 2018. If the test-and-treat coverage was increased to above 25% since 2018, then the hepatitis B surface antigen (HBsAg) prevalence for population aged 1 to 59 years in China would be reduced to below 2% in 2035. Our model also showed that in 2035, the numbers of chronic HBV infection and HBV-related deaths in 65 to 69 age group would be reduced the most (about 1.6 million and 13 thousand, respectively).Increasing test-and-treat coverage would significantly reduce HBV infection in China, especially in the middle-aged people and older people. The earlier the treatment and the longer the time, the more significant the reduction. Implementation of test-and-treat strategy is highly effective in controlling hepatitis B in China.

A Literature Review of Mathematical Models of Hepatitis B Virus Transmission Applied to Immunization Strategies From 1994 to 2015

A mathematical model of the transmission dynamics of infectious disease is an important theoretical epidemiology method, which has been used to simulate the prevalence of hepatitis B and evaluate different immunization strategies. However, differences lie in the mathematical processes of modeling HBV transmission in published studies, not only in the model structure, but also in the estimation of certain parameters. This review reveals that the dynamics model of HBV transmission only simulates the spread of HBV in the population from the macroscopic point of view and highlights several main shortcomings in the model structure and parameter estimation. First, age-dependence is the most important characteristic in the transmission of HBV, but an age-structure model and related age-dependent parameters were not adopted in some of the compartmental models describing HBV transmission. In addition, the numerical estimation of the force of HBV infection did not give sufficient weight to the age and time factors and is not suitable using the incidence data. Lastly, the current mathematical models did not well reflect the details of the factors of HBV transmission, such as migration from high or intermediate HBV endemic areas to low endemic areas and the kind of HBV genotype. All of these shortcomings may lead to unreliable results. When the mathematical model closely reflects the fact of hepatitis B spread, the results of the model fit will provide valuable information for controlling the transmission of hepatitis B.

A periodic disease transmission model with asymptomatic carriage and latency periods

In this paper, the global dynamics of a periodic disease transmission model with two delays in incubation and asymptomatic carriage periods is investigated. We first derive the model system with a general nonlinear incidence rate function by stage-structure. Then, we identify the basic reproduction ratio [Formula: see text] for the model and present numerical algorithm to calculate it. We obtain the global attractivity of the disease-free state when [Formula: see text] and discuss the disease persistence when [Formula: see text]. We also explore the coexistence of endemic state in the nonautonomous system and prove the uniqueness with constants coefficients. Numerical simulations are provided to present a case study regarding the meningococcal meningitis disease transmission and discuss the influence of carriers on [Formula: see text].

Modeling and Control of a Delayed Hepatitis B Virus Model with Incubation Period and Combination Treatment

In this paper, a hepatitis B virus (HBV) model with an incubation period and delayed state and control variables is firstly proposed. Furthermore, the combination treatment is adopted to have a longer-lasting effect than mono-therapy. The equilibrium points and basic reproduction number are calculated, and then the local stability is analyzed on this model. We then present optimal control strategies based on the Pontryagin's minimum principle with an objective function not only to reduce the levels of exposed cells, infected cells and free viruses nearly to zero at the end of therapy, but also to minimize the drug side-effect and the cost of treatment. What's more, we develop a numerical simulation algorithm for solving our HBV model based on the combination of forward and backward difference approximations. The state dynamics of uninfected cells, exposed cells, infected cells, free viruses, CTL and ALT are simulated with or without optimal control, which show that HBV is reduced nearly to zero based on the time-varying optimal control strategies whereas the disease would break out without control. At last, by the simulations, we prove that strategy A is the best among the three kinds of strategies we adopt and further comparisons have been done between model (1) and model (2).

The transmission dynamic and optimal control of acute and chronic hepatitis B

In this article, we present the transmission dynamic of the acute and chronic hepatitis B epidemic problem and develop an optimal control strategy to control the spread of hepatitis B in a community. In order to do this, first we present the model formulation and find the basic reproduction number [Formula: see text]. We show that if [Formula: see text] then the disease-free equilibrium is both locally as well as globally asymptotically stable. Then, we prove that the model is locally and globally asymptotically stable, if [Formula: see text]. To control the spread of this infection, we develop a control strategy by applying three control variables such as isolation of infected and non-infected individuals, treatment and vaccination to minimize the number of acute infected, chronically infected with hepatitis B individuals and maximize the number of susceptible and recovered individuals. Finally, we present numerical simulation to illustrate the feasibility of the control strategy.

Age-specific infectious period shapes dynamics of pneumonia in bighorn sheep

Superspreading, the phenomenon where a small proportion of individuals contribute disproportionately to new infections, has profound effects on disease dynamics. Superspreading can arise through variation in contacts, infectiousness or infectious periods. The latter has received little attention, yet it drives the dynamics of many diseases of critical public health, livestock health and conservation concern. Here, we present rare evidence of variation in infectious periods underlying a superspreading phenomenon in a free-ranging wildlife system. We detected persistent infections of Mycoplasma ovipneumoniae, the primary causative agent of pneumonia in bighorn sheep (Ovis canadensis), in a small number of older individuals that were homozygous at an immunologically relevant genetic locus. Interactions among age-structure, genetic composition and infectious periods may drive feedbacks in disease dynamics that determine the magnitude of population response to infection. Accordingly, variation in initial conditions may explain divergent population responses to infection that range from recovery to catastrophic decline and extirpation.

Estimating age-related incidence of HBsAg seroclearance in chronic hepatitis B virus infections of China by using a dynamic compartmental model

The age-specific seroclearance pattern of hepatitis B surface antigen (HBsAg) in chronic hepatitis B virus (HBV) infections of China remains unclear. In this study, based on three national serosurvey data of hepatitis B in China, we propose an age- and time-dependent discrete model and use the method of non-linear least squares to estimate the age-specific annual rate of HBsAg seroclearance. We found that the HBsAg seroclearance in chronic HBV infections of China aged 1–59 years occurred at an average annual rate of 1.80% (95% CI, 1.54–2.06%) from 1993 to 2006. The HBsAg seroclearance occurred predominantly in the early childhood, 20–24 and 35–39 year age groups. Moreover, our model estimated that HBsAg seroclearance resulted in 23.38% of the decrease of total HBsAg prevalence for population aged 1–59 years in 2006. It also prevented 9.30% of new HBV infections (about 7.43 million people) and 9.95% of HBV-related deaths (about 0.25 million people) from 1993 to 2006. This study develops a new and efficient method to estimate the age-specific incidence of HBsAg seroclearance at a population-level and evaluate its effect.

Numerical solution of diffusive HBV model in a fractional medium

Evolution systems containing fractional derivatives can result to suitable mathematical models for describing better and important physical phenomena. In this paper, we consider a multi-components nonlinear fractional-in-space reaction–diffusion equations consisting of an improved deterministic model which describe the spread of hepatitis B virus disease in areas of high endemic communities. The model is analyzed. We give some useful biological results to show that the disease-free equilibrium is both locally and globally asymptotically stable when the basic reproduction number is less than unity. Our findings of this paper strongly recommend a combination of effective treatment and vaccination as a good control measure, is important to record the success of HBV disease control through a careful choice of parameters. Some simulation results are presented to support the analytical findings.

Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers

In this paper, an epidemic model is investigated for infectious diseases that can be transmitted through both the infectious individuals and the asymptomatic carriers (i.e., infected individuals who are contagious but do not show any disease symptoms). We propose a dose-structured vaccination model with multiple transmission pathways. Based on the range of the explicitly computed basic reproduction number, we prove the global stability of the disease-free when this threshold number is less or equal to the unity. Moreover, whenever it is greater than one, the existence of the unique endemic equilibrium is shown and its global stability is established for the case where the changes of displaying the disease symptoms are independent of the vulnerable classes. Further, the model is shown to exhibit a transcritical bifurcation with the unit basic reproduction number being the bifurcation parameter. The impacts of the asymptomatic carriers and the effectiveness of vaccination on the disease transmission are discussed through through the local and the global sensitivity analyses of the basic reproduction number. Finally, a case study of hepatitis B virus disease (HBV) is considered, with the numerical simulations presented to support the analytical results. They further suggest that, in high HBV prevalence countries, the combination of effective vaccination (i.e. ≥ 3 doses of HepB vaccine), the diagnosis of asymptomatic carriers and the treatment of symptomatic carriers may have a much greater positive impact on the disease control.

An epidemic model with exposure-dependent severities

We consider a stochastic model for the spread of a susceptible–infective–removed (SIR) epidemic among a closed, finite population, in which there are two types of severity of infectious individuals, namely mild and severe. The type of severity depends on the amount of infectious exposure an individual receives, in that infectives are always initially mild but may become severe if additionally exposed. Large-population properties of the model are derived. In particular, a coupling argument is used to provide a rigorous branching process approximation to the early stages of an epidemic, and an embedding argument is used to derive a strong law and an associated central limit theorem for the final outcome of an epidemic in the event of a major outbreak. The basic reproduction number, which determines whether or not a major outbreak can occur given few initial infectives, depends only on parameters of the mild infectious state, whereas the final outcome in the event of a major outbreak depends also on parameters of the severe state. Moreover, the limiting final size proportions need not even be continuous in the model parameters.

An epidemic model with exposure-dependent severities

We consider a stochastic model for the spread of a susceptible–infective–removed (SIR) epidemic among a closed, finite population, in which there are two types of severity of infectious individuals, namely mild and severe. The type of severity depends on the amount of infectious exposure an individual receives, in that infectives are always initially mild but may become severe if additionally exposed. Large-population properties of the model are derived. In particular, a coupling argument is used to provide a rigorous branching process approximation to the early stages of an epidemic, and an embedding argument is used to derive a strong law and an associated central limit theorem for the final outcome of an epidemic in the event of a major outbreak. The basic reproduction number, which determines whether or not a major outbreak can occur given few initial infectives, depends only on parameters of the mild infectious state, whereas the final outcome in the event of a major outbreak depends also on parameters of the severe state. Moreover, the limiting final size proportions need not even be continuous in the model parameters.

Optimal control for an age-structured model for the transmission of hepatitis B

One of the characteristics of HBV transmission is the age structure of the host population and the vertical transmission of the disease. That is the infection is transmitted directly from infected mother to an embryo, fetus, or baby during pregnancy or childbirth (the perinatal infection). We formulated an age-structured model for the transmission dynamics of HBV with differential infectivity: symptomatic and asymptomatic infections. The model without intervention strategies is completely analyzed. We compute the basic reproduction number which determines the outcome of the disease. We also compute equilibria and study their stability. The sensitivity analysis of the initial model parameters is performed (to determine the impact of control-related parameters on outbreak severity). Using optimal control theory, we determine the cost-effective balance of three interventions methods which minimizes HBV-related deaths as well as the costs associated with intervention.

The independent impact of newborn hepatitis B vaccination on reducing HBV prevalence in China, 1992-2006: A mathematical model analysis

OBJECTIVE

To evaluate the independent impact of newborn hepatitis B vaccination on reducing HBV prevalence in China, from its introduction in 1992 to 2006.

METHODS

An age- and time-dependent discrete dynamic model was developed to simulate HBV transmission in China under the assumptions of no any change in interventions and only with newborn vaccination introduction, respectively. The initial conditions of the model were determined according to the national serosurvey in 1992. The simulated results were compared with the observed results of the national serosurvey in 2006, and the contribution rate of newborn vaccination on reducing HBV prevalence was calculated overall and by birth cohort.

RESULTS

The total HBV prevalence would remain stable through the 14-year period if no any change in interventions, but decrease year by year if only with newborn vaccination introduction. Newborn vaccination could account for more than 50% of the reduction of the total HBV prevalence, although the full 3-dose and timely birth dose vaccination coverage rates were low in the early years. The results by birth cohort showed that the higher the two coverage rates, the higher contribution rate on reducing HBV prevalence. For the 2005 birth cohort which had high levels in the two coverage rates, the contribution rate could reach more than 95%.

CONCLUSION

Newborn hepatitis B vaccination from 1992 to 2006 in China had played the most important role in reducing HBV prevalence. Newborn vaccination with high full 3-dose and timely birth dose coverage rates is the decisive factor in controlling hepatitis B in China.

A THEORETICAL ASSESSMENT OF THE EFFECTS OF DISTRIBUTED DELAY ON THE TRANSMISSION DYNAMICS OF HEPATITIS B

In this paper, we investigate the global dynamics of a system of delay differential equations which describes the interaction of hepatitis B virus (HBV) with both liver and blood cells. The model has two distributed time delays describing the time needed for infection of cell and virus replication. We also include the efficiency of drug therapy in inhibiting viral production and the efficiency of drug therapy in blocking new infection. We compute the basic reproduction number and find that increasing delays will decrease the value of the basic reproduction number. We study the sensitivity analysis on the key parameters that drive the disease dynamics in order to determine their relative importance to disease transmission and prevalence. Our analysis reveals that the model exhibits the phenomenon of backward bifurcation (where a stable disease-free equilibrium (DFE) co-exists with a stable endemic equilibrium when the basic reproduction number is less than unity). Numerical simulations are presented to evaluate the impact of time-delays on the prevalence of the disease.

The impact of vaccination and antiviral therapy on hepatitis B and hepatitis D epidemiology

The major cause of liver cancer around the globe is hepatitis B virus (HBV), which also contributes to a large number of deaths due to liver failure alone. Hepatitis delta virus (HDV) is as potentially alarming as HBV since life threatening cases are 10 times more likely with HBV-HDV dual infection compared to HBV monoinfection. So far, there is no established effective treatment against HDV and the only preventive action suggested by the World Health Organization is to introduce HBV vaccination for children immediately after birth (newborns) and thus reduce the available pool for HDV infection. Here the main objective is to understand the complex dynamics of HBV-HDV infection in a human population that can inform public health policy makers on the level of different preventive measures required to eliminate HBV and HDV infections. Model simulations suggest that HBV vertical transmission and HBV vaccination rates for newborns are instrumental in determining HBV and HDV prevalence. A decrease in HBV prevalence is observed as vaccination coverage increases and it is possible to eradicate both HBV and HDV using high vaccination coverage of ≥80% in the long term. We further found that HDV presence results in lower HBV prevalence. An application of our model to China revealed that vaccinating every newborn in China will further prevent 1.69 million new infections by 2028 as compared to the current 90% vaccination coverage. Although, higher vaccination coverage of newborns should eliminate both HBV and HDV over a long time period, any short term strategy to eradicate HDV must include additional preventive measures such as HBV adult vaccination. Implementation of HBV adult vaccination programs at a rate of 10% per year over 15 years will further prevent 39 thousand new HDV infections in China by 2028 as compared to HBV vaccination programs solely for newborns.

Mathematical modeling of transmission dynamics and optimal control of vaccination and treatment for hepatitis B virus

Hepatitis B virus (HBV) infection is a worldwide public health problem. In this paper, we study the dynamics of hepatitis B virus (HBV) infection which can be controlled by vaccination as well as treatment. Initially we consider constant controls for both vaccination and treatment. In the constant controls case, by determining the basic reproduction number, we study the existence and stability of the disease-free and endemic steady-state solutions of the model. Next, we take the controls as time and formulate the appropriate optimal control problem and obtain the optimal control strategy to minimize both the number of infectious humans and the associated costs. Finally at the end numerical simulation results show that optimal combination of vaccination and treatment is the most effective way to control hepatitis B virus infection.

Transmission model of hepatitis B virus with the migration effect

Hepatitis B is a globally infectious disease. Mathematical modeling of HBV transmission is an interesting research area. In this paper, we present characteristics of HBV virus transmission in the form of a mathematical model. We analyzed the effect of immigrants in the model to study the effect of immigrants for the host population. We added the following flow parameters: "the transmission between migrated and exposed class" and "the transmission between migrated and acute class." With these new features, we obtained a compartment model of six differential equations. First, we find the basic threshold quantity Ro and then find the local asymptotic stability of disease-free equilibrium and endemic equilibrium. Furthermore, we find the global stability of the disease-free and endemic equilibria. Previous similar publications have not added the kind of information about the numerical results of the model. In our case, from numerical simulation, a detailed discussion of the parameters and their numerical results is presented. We claim that with these assumptions and by adding the migrated class, the model informs policy for governments, to be aware of the immigrants and subject them to tests about the disease status. Immigrants for short visits and students should be subjected to tests to reduce the number of immigrants with disease.

Infection with hepatitis B and C virus in Europe: a systematic review of prevalence and cost-effectiveness of screening

BACKGROUND

Treatment for chronic hepatitis B virus (HBV) and hepatitis C virus (HCV) infection is improving but not benefiting individuals unaware to be infected. To inform screening policies we assessed (1) the hepatitis B surface antigen (HBsAg) and anti-hepatitis C virus antibody (anti-HCV-Ab) prevalence for 34 European countries; and (2) the cost-effectiveness of screening for chronic HBV and HCV infection.

METHODS

We searched peer-reviewed literature for data on HBsAg and anti-HCV-Ab prevalence and cost-effectiveness of screening of the general population and five subgroups, and used data for people who inject drugs (PWID) and blood donors from two European organizations. Of 1759 and 468 papers found in the prevalence and cost-effectiveness searches respectively, we included 124 and 29 papers after assessing their quality. We used decision rules to calculate weighted prevalence estimates by country.

RESULTS

The HBsAg and anti-HCV-Ab prevalence in the general population ranged from 0.1%-5.6% and 0.4%-5.2% respectively, by country. For PWID, men who have sex with men and migrants, the prevalence of HBsAg and anti-HCV-Ab was higher than the prevalence in the general population in all but 3 countries. There is evidence that HCV screening of PWID and HBsAg screening of pregnant women and migrants is cost-effective.

CONCLUSION

The prevalence of chronic HBV and HCV infection varies widely between European countries. Anti-HCV-Ab screening of PWID and HBsAg screening of pregnant women and migrants have European public health priority. Cost-effectiveness analyses may need to take effect of antiviral treatment on preventing HBV and HCV transmission into account.

Dynamic transmission modeling: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force Working Group-5

The transmissible nature of communicable diseases is what sets them apart from other diseases modeled by health economists. The probability of a susceptible individual becoming infected at any one point in time (the force of infection) is related to the number of infectious individuals in the population, will change over time, and will feed back into the future force of infection. These nonlinear interactions produce transmission dynamics that require specific consideration when modeling an intervention that has an impact on the transmission of a pathogen. Best practices for designing and building these models are set out in this paper.

Dynamic transmission modeling: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force--5

The transmissible nature of communicable diseases is what sets them apart from other diseases modeled by health economists. The probability of a susceptible individual becoming infected at any one point in time (the force of infection) is related to the number of infectious individuals in the population, will change over time, and will feed back into the future force of infection. These nonlinear interactions produce transmission dynamics that require specific consideration when modeling an intervention that has an impact on the transmission of a pathogen. Best practices for designing and building these models are set out in this article.

Reconstruction of the epidemic history of hepatitis B virus genotype D in Albania

Despite a recent decrease in the prevalence of HBsAg in the general population, Albania is still highly endemic for HBV infection. Genotype D is the most prevalent HBV strain in the Mediterranean area. We studied the prevalence and distribution of HBV genotypes and subgenotypes in a total of 73 HBsAg-positive patients living in Albania, and reconstructed the epidemiological history of the most prevalent HBV D subgenotype using a "phylodynamic" framework. A time-scaled genealogy of the Albanian patients' and reference P gene sequences with known sampling dates was reconstructed using an MCMC Bayesian approach that allows population growth to be estimated on the basis of coalescent theory. All of the Albanian subjects were infected with the HBV D genotype, and a percentage varying from 44.4% to 100% (depending on the ethnic or risk group) were infected with subgenotype D2, the most prevalent in the study population (72.4%). The other subgenotypes present in a minority of subjects were D1 (13.8%) and D3 (13.8%). The Bayesian skyline plot population dynamics analysis showed that genotype D2 entered the Albanian population in the late 1960s, and that the effective number of infections grew gradually until the second half of the 1980s and more rapidly until the mid-1990s, when it reached a plateau that still persists today. Our data suggest that political and socio-economic factors played an important role in determining the rapid spread of HBV infection in Albania.

Prevalence of hepatitis B virus infection in The Netherlands in 1996 and 2007

We aimed to assess differences in the prevalence of hepatitis B virus (HBV) infection in The Netherlands between 1996 and 2007, and to identify risk factors for HBV infection in 2007. Representative samples of the Dutch population in 1996 and 2007 were tested for antibodies to hepatitis B core antigen (anti-HBc), hepatitis B surface antigen (HBsAg) and HBV-DNA. In 2007, the weighted anti-HBc prevalence was 3·5% (95% CI 2·2-5·5) and the HBsAg prevalence was 0·2% (95% CI 0·1-0·4). In indigenous Dutch participants, the anti-HBc prevalence was lower in 2007 than in 1996 (P=0·06). First-generation migrants (FGMs) had a 13-fold greater risk of being HBsAg- and/or HBV-DNA-positive than indigenous Dutch participants. In indigenous Dutch participants, risk factors for anti-HBc positivity were older age and having received a blood product before 1990. In FGMs, being of Asian origin was a risk factor. In second-generation migrants, having a foreign-born partner and injecting drug use were risk factors. FGMs are the main target group for secondary HBV prevention in The Netherlands.

Phenotypic assay of a hepatitis B virus strain carrying an rtS246T variant using a new strategy

Phenotypic assays of hepatitis B virus (HBV) play an important role in research related to the problem of drug resistance that emerges during long-term nucleot(s)ide therapy in patients with chronic hepatitis B. Most of the phenotypic assay systems that are available currently rely on the transfection of recombinant replication-competent HBV DNA into hepatoma cell lines. Cloning clinical HBV isolates using conventional digestion-and-ligation techniques to generate replication-competent recombinants can be very difficult because of the sequence heterogeneity and unique structure of the HBV genome. In this study, a new strategy for constructing an HBV 1.1× recombinant was developed. The core of this strategy is the "fragment substitution reaction" (FSR). FSR allows PCR fragments to be cloned without digestion or ligation, providing a new tool for cloning fragments or genomes amplified from serum HBV DNA, and therefore making the assay of HBV phenotypes more convenient. Using this strategy, a phenotypic assay was performed on an HBV strain carrying an rtS246T variant isolated from a patient with chronic hepatitis B that was only responsive partially to entecavir therapy. The results indicated that this strain is sensitive to entecavir in vitro.

Mathematical models in the evaluation of health programmes

Modelling is valuable in the planning and evaluation of interventions, especially when a controlled trial is ethically or logistically impossible. Models are often used to calculate the expected course of events in the absence of more formal assessments. They are also used to derive estimates of rare or future events from recorded intermediate points. When developing models, decisions are needed about the appropriate level of complexity to be represented and about model structure and assumptions. The degree of rigor in model development and assessment can vary greatly, and there is a danger that existing beliefs inappropriately influence judgments about model assumptions and results.

Modeling the effects of carriers on transmission dynamics of infectious diseases

An S-Ic-I-R epidemic model is investigated for infectious diseases that can be transmitted through carriers, infected individuals who are contagious but do not show any disease symptoms. Mathematical analysis is carried out that completely determines the global dynamics of the model. The impacts of disease carriers on the transmission dynamics are discussed through the basic reproduction number and through numerical simulations.

HBV vaccine efficacy and detection and genotyping of vaccineé asymptomatic breakthrough HBV infection in Egypt

AIM

To evaluate the impact of mass vaccination against the hepatitis B virus (HBV) in Egypt, and to search for vaccinee asymptomatic breakthrough HBV infection and its genotype.

METHODS

Seven hundred serum samples from vaccinated children and adults (aged 2-47 years) were used for quantitative and qualitative detection of HBsAb by ELISA. Three hundred and sixty serum samples representing undetectable or low or high HBsAb were screened for markers of active HBV infection (HBsAg, HBcAb (IgG) and HBeAb by ELISA, plus HBsAg by AxSYM) and HBV-DNA genotyping by nested multiplex PCR and by DNA sequencing.

RESULTS

It was found that 65% of children aged 2-4 years, and 20.5% aged 4-13 years, as well as 45% adults were good responders to HBV vaccination mounting protective level HBsAb. Poor responders were 28%, 59.5% and 34%, and non-responders were 7%, 20% and 21% respectively, in the three studied groups. Markers of asymptomatic HBV infections were HBsAg detected by ELISA in 2.5% vs 11.39% by AxSYM. Other markers were HBcAb (IgG) in 1.38%, HBeAb in 0.83%, and HBV-DNA in 7.8%. All had HBV genotype E infection.

CONCLUSION

It is concluded that HBV vaccine is efficient in controlling HBV infection among children and adults. The vaccine breakthrough infection was by HBV genotype E. A booster dose of vaccine is recommended, probably four years after initial vaccination.

A meta-analysis of the effect of dose and age at exposure on shedding of Mycobacterium avium subspecies paratuberculosis (MAP) in experimentally infected calves and cows

A meta-analysis was performed using all published and one unpublished long-term infection-challenge experiments to quantify the age- and dose-dependence of early and late shedding of Mycobacterium avium subsp. paratuberculosis (MAP) in cattle. There were 194 animals from 17 studies that fulfilled the inclusion criteria, of which 173 received a known dose of MAP and 21 were exposed naturally. Results from parametric time-to-event models indicated that challenging older calves or using multiple-exposure experimental systems resulted in a smaller proportion and shorter duration of early shedding as well as slower transition to late shedding from latent compartments. Calves exposed naturally showed variable infection progression rates, not dissimilar to other infection routes. The log-normal distribution was most appropriate for modelling infection-progression events. The infection pattern revealed by the modelling allowed better understanding of low-grade endemicity of MAP in cattle, and the parameter estimates are the basis for future transmission dynamics modelling.

Economic evaluation of infant and adolescent hepatitis B vaccination in the UK

A Markov model of hepatitis B virus (HBV) disease progression in the UK estimated that 81% of predicted HBV-associated morbidity and mortality could be prevented by universal infant vaccination at a cost of approximately £ 260,000 per QALY gained. Universal adolescent vaccination would be less effective (45% prevented) and less cost-effective (£ 493,000 per QALY gained). Higher HBV incidence rates in males and intermediate/high risk ethnic populations meant it was approximately 3 times more cost-effective to vaccinate these groups. At current vaccine costs a selective infant vaccination programme, based on vaccinating intermediate/high risk ethnic populations would not be considered cost effective. The threshold cost per vaccinated child at which the programme would be considered cost-effective was investigated. Universal infant vaccination would be cost-effective if the average cost of vaccinating each child against HBV, including vaccine and administration costs of all doses, was less than £ 4.09. Given the low cost of vaccination required to make a universal programme cost-effective the most feasible policy in the UK would be to use a suitably priced combined vaccine that included the other antigens in the current infant vaccination schedule.

Modelling the epidemiology of hepatitis B in New Zealand

Hepatitis B is a vaccine preventable disease caused by the hepatitis B virus (HBV) that can induce potentially fatal liver damage. It has the second highest mortality rate of all vaccine preventable diseases in New Zealand. Vaccination against HBV was introduced in New Zealand in 1988, and the country is now categorised with overall low endemicity but with areas of both high and medium endemic levels. We present an SECIR compartmental mathematical model, with the population divided into age classes, for the transmission of HBV using local data on incidence of infection and vaccination coverage. We estimate the basic reproduction number, R(0), to be 1.53, and show that the vaccination campaign has substantially reduced this below one. However, a large number of carriers remain in the population acting as a source of infection.

Dynamical behavior of a hepatitis B virus transmission model with vaccination

Hepatitis B virus (HBV) infection is a globally health problem. In 2005, the WHO Western Pacific Regional Office set a goal of reducing chronic HBV infection rate to less than 2% among children five years of age by 2012, as an interim milestone towards the final goal of less than 1%. Many countries made some plans (such as free HBV vaccination program for all neonates in China now) to control the transmission HBV. We develop a model to explore the impact of vaccination and other controlling measures of HBV infection. The model has simple dynamical behavior which has a globally asymptotically stable disease-free equilibrium when the basic reproduction number R(0)< or =1, and a globally asymptotically stable endemic equilibrium when R(0)>1. Numerical simulation results show that the vaccination is a very effective measure to control the infection and they also give some useful comments on controlling the transmission of HBV.

Population collapse to extinction: the catastrophic combination of parasitism and Allee effect

Infectious diseases are responsible for the extinction of a number of species. In conventional epidemic models, the transition from endemic population persistence to extirpation takes place gradually. However, if host demographics exhibits a strong Allee effect (AE) (population decline at low densities), extinction can occur abruptly in a catastrophic population crash. This might explain why species suddenly disappear even when they used to persist at high endemic population levels. Mathematically, the tipping point towards population collapse is associated with a saddle-node bifurcation. The underlying mechanism is the simultaneous population size depression and the increase of the extinction threshold due to parasite pathogenicity and Allee effect. Since highly pathogenic parasites cause their own extinction but not that of their host, there can be another saddle-node bifurcation with the re-emergence of two endemic equilibria. The implications for control interventions are discussed, suggesting that effective management may be possible for ℛ(0)≫1.