Rich dynamics of a hepatitis B viral infection model with logistic hepatocyte growth

Dynamical analysis of a general delayed HBV infection model with capsids and adaptive immune response in presence of exposed infected hepatocytes

The aim of this paper is to develop and investigate a novel mathematical model of the dynamical behaviors of chronic hepatitis B virus infection. The model includes exposed infected hepatocytes, intracellular HBV DNA-containing capsids, uses a general incidence function for viral infection covering a variety of special cases available in the literature, and describes the interaction of cytotoxic T lymphocytes that kill the infected hepatocytes and the magnitude of B-cells that send antibody immune defense to neutralize free virions. Further, one time delay is incorporated to account for actual capsids production. The other time delays are used to account for maturation of capsids and free viruses. We start with the analysis of the proposed model by establishing the local and global existence, uniqueness, non-negativity and boundedness of solutions. After defined the threshold parameters, we discuss the stability properties of all possible steady state constants by using the crafty Lyapunov functionals, the LaSalle's invariance principle and linearization methods. The impacts of the three time delays on the HBV infection transmission are discussed through local and global sensitivity analysis of the basic reproduction number and of the classes of infected states. Finally, an application is provided and numerical simulations are performed to illustrate and interpret the theoretical results obtained. It is suggested that, a good strategy to eradicate or to control HBV infection within a host should concentrate on any drugs that may prolong the values of the three delays.

Global dynamics of multiple delays within-host model for a hepatitis B virus infection of hepatocytes with immune response and drug therapy

In this paper, a mathematical model describing the hepatitis B virus (HBV) infection of hepatocytes with the intracellular HBV-DNA containing capsids, cytotoxic T-lymphocyte (CTL), antibodies including drug therapy (blocking new infection and inhibiting viral production) with two-time delays is studied. It incorporates the delay in the productively infected hepatocytes and the delay in an antigenic stimulation generating CTL. We verify the positivity and boundedness of solutions and determine the basic reproduction number. The local and global stability of three equilibrium points (infection-free, immune-free, and immune-activated) are investigated. Finally, the numerical simulations are established to show the role of these therapies in reducing viral replication and HBV infection. Our results show that the treatment by blocking new infection gives more significant results than the treatment by inhibiting viral production for infected hepatocytes. Further, both delays affect the number of infections and duration i.e. the longer the delay, the more severe the HBV infection.

Effect of cellular regeneration and viral transmission mode on viral spread

Illness negatively affects all aspects of life and one major cause of illness is viral infections. Some viral infections can last for weeks; others, like influenza (the flu), can resolve quickly. During infections, uninfected cells can replicate in order to replenish the cells that have died due to the virus. Many viral models, especially those for short-lived infections like influenza, tend to ignore cellular regeneration since many think that uncomplicated influenza resolves much faster than cells regenerate. This research accounts for cellular regeneration, using an agent-based framework, and varies the regeneration rate in order to understand how cell regeneration affects viral infection dynamics under assumptions of different modes of transmission. We find that although the general trends in peak viral load, time of viral peak, and chronic viral load as regeneration rate changes are the same for cell-free or cell-to-cell transmission, the changes are more extreme for cell-to-cell transmission due to limited access of infected cells to newly generated cells.

Viral Infection Model with Diffusion and Distributed Delay: Finite-Dimensional Global Attractor

We study a virus dynamics model with reaction-diffusion, logistic growth terms and a general non-linear infection rate functional response. The model has a distributed delay, including the case of state-selective delay. We construct a dynamical system in a Hilbert space and prove the existence of a finite-dimensional global attractor.

Aerosol Transport Modeling: The Key Link Between Lung Infections of Individuals and Populations

The recent COVID-19 pandemic has propelled the field of aerosol science to the forefront, particularly the central role of virus-laden respiratory droplets and aerosols. The pandemic has also highlighted the critical need, and value for, an information bridge between epidemiological models (that inform policymakers to develop public health responses) and within-host models (that inform the public and health care providers how individuals develop respiratory infections). Here, we review existing data and models of generation of respiratory droplets and aerosols, their exhalation and inhalation, and the fate of infectious droplet transport and deposition throughout the respiratory tract. We then articulate how aerosol transport modeling can serve as a bridge between and guide calibration of within-host and epidemiological models, forming a comprehensive tool to formulate and test hypotheses about respiratory tract exposure and infection within and between individuals.

Analysis of an initial value problem for an extracellular and intracellular model of hepatitis C virus infection

In this paper, a mathematical analysis of the global dynamics of a viral infection model in vivo is carried out. We study the dynamics of a hepatitis C virus (HCV) model, under therapy, that considers both extracellular and intracellular levels of infection. At present, most mathematical modeling of viral kinetics after treatment only addresses the process of infection of a cell by the virus and the release of virions by the cell, while the processes taking place inside the cell are not included. We prove that the solutions of the new model with positive initial values are positive, exist globally in time and are bounded. The model has two virus-free steady states. They are distinguished by the fact that viral RNA is absent inside the cells in the first state and present inside the cells in the second. There are basic reproduction numbers associated to each of these steady states. If the basic reproduction number of the first steady state is less than one, then that state is asymptotically stable. If the basic reproduction number of the first steady state is greater than one and that of the second less than one, then the second steady state is asymptotically stable. If both basic reproduction numbers are greater than one, then we obtain various conclusions which depend on different restrictions on the parameters of the model. Under increasingly strong assumptions, we prove that there is at least one positive steady state (infected equilibrium), that there is a unique positive steady state and that the positive steady state is stable. We also give a condition under which every positive solution converges to a positive steady state. This is proved by methods of Li and Muldowney. Finally, we illustrate the theoretical results by numerical simulations.

Analysis of a stochastic HBV infection model with delayed immune response

Considering the environmental factors and uncertainties, we propose, in this paper, a higher-order stochastically perturbed delay differential model for the dynamics of hepatitis B virus (HBV) infection with immune system. Existence and uniqueness of an ergodic stationary distribution of positive solution to the system are investigated, where the solution fluctuates around the endemic equilibrium of the deterministic model and leads to the stochastic persistence of the disease. Under some conditions, infection-free can be obtained in which the disease dies out exponentially with probability one. Some numerical simulations, by using Milstein's scheme, are carried out to show the effectiveness of the obtained results. The intensity of white noise plays an important role in the treatment of infectious diseases.

An Explainable Artificial Intelligence Framework for the Deterioration Risk Prediction of Hepatitis Patients

In recent years, artificial intelligence-based computer aided diagnosis (CAD) system for the hepatitis has made great progress. Especially, the complex models such as deep learning achieve better performance than the simple ones due to the nonlinear hypotheses of the real world clinical data. However,complex model as a black box, which ignores why it make a certain decision, causes the model distrust from clinicians. To solve these issues, an explainable artificial intelligence (XAI) framework is proposed in this paper to give the global and local interpretation of auxiliary diagnosis of hepatitis while retaining the good prediction performance. First, a public hepatitis classification benchmark from UCI is used to test the feasibility of the framework. Then, the transparent and black-box machine learning models are both employed to forecast the hepatitis deterioration. The transparent models such as logistic regression (LR), decision tree (DT)and k-nearest neighbor (KNN) are picked. While the black-box model such as the eXtreme Gradient Boosting (XGBoost), support vector machine (SVM), random forests (RF) are selected. Finally, the SHapley Additive exPlanations (SHAP), Local Interpretable Model-agnostic Explanations (LIME) and Partial Dependence Plots (PDP) are utilized to improve the model interpretation of liver disease. The experimental results show that the complex models outperform the simple ones. The developed RF achieves the highest accuracy (91.9%) among all the models. The proposed framework combining the global and local interpretable methods improves the transparency of complex models, and gets insight into the judgments from the complex models, thereby guiding the treatment strategy and improving the prognosis of hepatitis patients. In addition, the proposed framework could also assist the clinical data scientists to design a more appropriate structure of CAD.

Understanding the antiviral effects of RNAi-based therapy in HBeAg-positive chronic hepatitis B infection

The RNA interference (RNAi) drug ARC-520 was shown to be effective in reducing serum hepatitis B virus (HBV) DNA, hepatitis B e antigen (HBeAg) and hepatitis B surface antigen (HBsAg) in HBeAg-positive patients treated with a single dose of ARC-520 and daily nucleosidic analogue (entecavir). To provide insights into HBV dynamics under ARC-520 treatment and its efficacy in blocking HBV DNA, HBsAg, and HBeAg production we developed a multi-compartmental pharmacokinetic-pharamacodynamic model and calibrated it with frequent measured HBV kinetic data. We showed that the time-dependent single dose ARC-520 efficacies in blocking HBsAg and HBeAg are more than 96% effective around day 1, and slowly wane to 50% in 1-4 months. The combined single dose ARC-520 and entecavir effect on HBV DNA was constant over time, with efficacy of more than 99.8%. The observed continuous HBV DNA decline is entecavir mediated, the strong but transient HBsAg and HBeAg decays are ARC-520 mediated. The modeling framework may help assess ongoing RNAi drug development for hepatitis B virus infection.

Coexistence and extinction in a data-based ratio-dependent model of an insect community

In theory, pure competition often leads to competitive exclusion of species. However, what we often see in nature is a large number of distinct predator or consumer species coexist in a community consisting a smaller number of prey or plant species. In an effort of dissecting how indirect competition and selective predation may have contributed to the coexistence of species in an insect community, according to the replicated cage experiments (two aphid species and a specialist parasitoid that attacks only one of the aphids) and proposed mathematical models, van Veen et. al. [5] conclude that the coexistence of the three species is due to a combination of density-mediated and trait-mediated indirect interactions. In this paper, we formulate an alternative model that observes the conventional law of mass conservation and provides a better fitting to their experimental data sets. Moreover, we present an initial attempt in studying the stabilities of the nonnegative steady states of this model.

Acute hepatitis B virus infection model within the host incorporating immune cells and cytokine responses

We formulate and analyze a within-host hepatitis B viral mathematical model for hepatitis B in the acute phase of infection. The model incorporates hepatocytes, hepatitis B virus, immune system cells and cytokine dynamics using a system of ordinary differential equations. We use the model to demonstrate the trends of the hepatitis B infection qualitatively without the effects of immune cells and cytokines. Using these trends, we tested the effects of incorporating the immune cells only and immune cells with cytokine responses at low and high inhibitions on the hepatitis B virus infection. Our results showed that it is impossible to have the immune cells work independently from cytokines when there is an acute hepatitis B virus infection. Therefore, our results suggest that incorporating immune cells and cytokine dynamics in the acute hepatitis B virus infection stage delays infection in the hepatocytes and excluding such dynamics speeds up infection during this phase. Results from this study are useful in developing strategies for control of hepatocellular carcinoma which is caused by hepatitis B virus infection.

ANALYSIS OF A STOCHASTIC HBV INFECTION MODEL WITH NONLINEAR INCIDENCE RATE

Considering that environmental factors, diet, subconscious mind and other uncertainties play an important role in the process of delaying and treating diseases, we propose, in this paper, an amended Hepatitis B virus (HBV) model with stochastic perturbation, and investigate the longtime dynamics of this stochastic model. First, if the basic reproductive number of the corresponding deterministic model is less than 1, some sufficient conditions for almost surely exponentially stable in the sense of the infected cells and free virus are established, and the stationary probability density function of the uninfected sell is also obtained. Further, some sufficient conditions for the existence of the stationary distribution are obtained for the basic reproductive number more than 1. In addition, oscillatory behaviors of this model about the equilibrium of the corresponding deterministic model are discussed. Finally, numerical simulations demonstrate the main theoretical results and show stochastic virus model has more dynamic behaviors relative to its corresponding deterministic model. Theoretical results and numerical simulations imply that the intensity and “type (divided into positive and negative)” of white noise play very important roles in the treatment of infectious disease, which can make the disease more and more repetitive and unpredictable. Of course, comfortable environment, reasonable diet, optimistic mood and other positive uncertainty factors have active effects on the treatment and delaying of diseases, but not the converse.

The review of differential equation models of HBV infection dynamics

Understanding the infection and pathogenesis mechanism of hepatitis B virus (HBV) is very important for the prevention and treatment of hepatitis B. Mathematical models contribute to illuminate the dynamic process of HBV replication in vivo. Therefore, in this paper we review the viral dynamics in HBV infection, which may help us further understand the dynamic mechanism of HBV infection and efficacy of antiviral treatment. Firstly, we introduce a family of deterministic models by considering different biological mechanisms, such as, antiviral therapy, CTL immune response, multi-types of infected hepatocytes, time delay and spatial diffusion. Particularly, we briefly describe the stochastic models of HBV infection. Secondly, we introduce the commonly used parameter estimation methods for HBV viral dynamic models and briefly discuss how to use these methods to estimate unknown parameters (such as drug efficacy) through two specific examples. We also discuss the idea and method of model identification and use a specific example to illustrate its application. Finally, we propose three new research programs, namely, considering HBV drug-resistant strain, coupling within-host and between-host dynamics in HBV infection and linking population dynamics with evolutionary dynamics of HBV diversity.

Mathematical assessment of the role of Dengvaxia vaccine on the transmission dynamics of dengue serotypes

A new mathematical model is designed and used to assess the impact of the newly-released Dengvaxia vaccine on the transmission dynamics of two co-circulating dengue strains (where strain 1 consists of dengue serotypes 1, 3 and 4; and strain 2 consists of dengue serotype 2). It is shown that the model exhibits the phenomenon of backward bifurcation when the disease-induced mortality in the host population exceeds a certain threshold value or if the vaccine does not provide perfect protection against infection with the two strains. In the absence of backward bifurcation, the disease-free equilibrium of the model is shown to be globally-asymptotically stable whenever the associated reproduction number is less than unity. It is shown that the community-wide use of the vaccine could induce positive, negative or no population-level impact, depending on the sign of a certain epidemiological threshold quantity (known as the vaccine impact factor). Simulations of the model, using data from Oaxaca, Mexico, show that, although the community-wide use of the vaccine will significantly reduce dengue burden in the community, it is unable to lead to the elimination of the two dengue strains. It is further shown that the use of Dengvaxia vaccine in dengue-naive populations may induce increased risk of severe disease in these populations.

Modelling hepatotoxicity and antiretroviral therapeutic effect in HIV/HBV coinfection

Enzyme alanine aminotransferase (ALT) elevation which reflects hepatocellular injury is a current challenge in people infected with human immunodeficiency virus (HIV) on antiretroviral therapy (ART). One of the factors that enhance the risk of hepatotoxicity is underlying diseases such as hepatitis caused by hepatitis B virus (HBV). HIV/HBV coinfected patients stand a greater risk of hepatotoxicity because all ART are toxic and liver cells (hepatocytes) that are responsible for metabolising the toxic ART, support all stages of HIV and HBV viral production. Mathematical models coupled with numerical simulations are used in this study with the aim of investigating the optimal combination of ART in HIV/HBV coinfection. Emtricitabine, tenofovir and efavirenz is the optimal combination that maximises the therapeutic effect of therapy and minimises the toxic response to medication in HIV/HBV coinfection.

Mathematical model of immune response to hepatitis B

A new detailed mathematical model for dynamics of immune response to hepatitis B is proposed, which takes into account contributions from innate and adaptive immune responses, as well as cytokines. Stability analysis of different steady states is performed to identify parameter regions where the model exhibits clearance of infection, maintenance of a chronic infection, or periodic oscillations. Effects of nucleoside analogues and interferon treatments are analysed, and the critical drug efficiency is determined.

Dynamics of a diffusion-driven HBV infection model with capsids and time delay

In this paper, a diffusive hepatitis B virus (HBV) infection model with a discrete time delay is presented and analyzed, where the spatial mobility of both intracellular capsid covered HBV DNA and HBV and the intracellular delay in the reproduction of infected hepatocytes are taken into account. We define the basic reproduction number [Formula: see text] that determines the dynamical behavior of the model. The local and global stability of the spatially homogeneous steady states are analyzed by using the linearization technique and the direct Lyapunov method, respectively. It is shown that the susceptible uninfected steady state is globally asymptotically stable whenever [Formula: see text] and is unstable whenever [Formula: see text]. Also, the infected steady state is globally asymptotically stable when [Formula: see text]. Finally, numerical simulations are carried out to illustrate the results obtained.

Impact of Population Recruitment on the HIV Epidemics and the Effectiveness of HIV Prevention Interventions

Mechanistic mathematical models are increasingly used to evaluate the effectiveness of different interventions for HIV prevention and to inform public health decisions. By focusing exclusively on the impact of the interventions, the importance of the demographic processes in these studies is often underestimated. In this paper, we use simple deterministic models to assess the effectiveness of pre-exposure prophylaxis in reducing the HIV transmission and to explore the influence of the recruitment mechanisms on the epidemic and effectiveness projections. We employ three commonly used formulas that correspond to constant, proportional and logistic recruitment and compare the dynamical properties of the resulting models. Our analysis exposes substantial differences in the transient and asymptotic behavior of the models which result in 47 % variation in population size and more than 6 percentage points variation in HIV prevalence over 40 years between models using different recruitment mechanisms. We outline the strong influence of recruitment assumptions on the impact of HIV prevention interventions and conclude that detailed demographic data should be used to inform the integration of recruitment processes in the models before HIV prevention is considered.

Stability and Hopf bifurcation for a logistic SIR model with a stage — Structure

A SIR model of epidemiological dynamics with stage-structure and a type of nonlinear incidence rate is considered under the assumption that the susceptible individual satisfy the logistic equation. The global attractivity of the model is studied using Lyapunov functions and LaSalle's invariance principle. By the uniform persistence theories, the permanence of the system and the existence of the positive equilibrium are obtained. Moreover, by the normal form theory and the center manifold presented by Hassard, a stability and Hopf bifurcation analysis of the system around positive equilibrium from a local perspective are performed. Numerical simulation is carried out to illustrate our results.

Mathematical models of the interrelated dynamics of hepatitis D and B

The hepatitis delta virus (HDV) is a rarest form of viral hepatitis, but has the worst outcomes for patients.It is a subviral satellite dependent on coinfection with hepatitis B (HBV) to replicate within the host liver.To date, there has been little to no modeling effort for HDV. Deriving and analyzing such a mathematical model poses difficulty as it requires the inclusion of (HBV). Here we begin with a well-studied HBV model from the literature and expand it to incorporate HDV. We investigate two models, one with and one without infected hepatocyte replication. Additionally, we consider treatment by the drug lamivudine. Comparison of model simulations with experimental results of lamivudine treatment indicate that infected cell proliferation may play a significant role in chronic HDV infection. Our results also shed light on several questions surrounding HDV and illustrate the need for more data.

New insights into the evolutionary rate of hepatitis B virus at different biological scales

The evolutionary rates of hepatitis B virus (HBV) estimated using contemporary sequences are 10(2) to 10(4) times higher than those derived from archaeological and genetic evidence. This discrepancy makes the origin of HBV and the time scale of its spread, both of which are critical for studying the burden of HBV pathogenicity, largely unresolved. To evaluate whether the dual demands (i.e., adaptation within hosts and colonization between hosts) of the viral life cycle affect this conundrum, the HBV quasispecies dynamics within and among hosts from a family consisting of a grandmother, her 5 children, and her 2 granddaughters, all of whom presumably acquired chronic HBV through mother-to-infant transmission, were examined by PCR cloning and next-generation sequencing methods. We found that the evolutionary rate of HBV between hosts was considerably lower than that within hosts. Moreover, the between-host substitution rates of HBV decreased as transmission numbers between individuals increased. Both observations were due primarily to changes at nonsynonymous rather than synonymous sites. There were significantly more multiple substitutions than expected for random mutation processes, and 97% of substitutions were changed from common to rare amino acid residues in the database. Continual switching between colonization and adaptation resulted in a rapid accumulation of mutations at a limited number of positions, which quickly became saturated, whereas substitutions at the remaining regions occurred at a much lower rate. Our study may help to explain the time-dependent HBV substitution rates reported in the literature and provide new insights into the origin of the virus.

IMPORTANCE

It is known that the estimated hepatitis B virus (HBV) substitution rate is time dependent, but the reason behind this observation is still elusive. We hypothesize that owing to the small genome size of HBV, transmission between hosts and adaptation within hosts must exhibit high levels of fitness trade-offs for the virus. By studying the HBV quasispecies dynamics for a chain of sequentially infected transmissions within a family, we found the HBV substitution rate between patients to be negatively correlated with the number of transmissions. Continual switching between hosts resulted in a rapid accumulation of mutations at a limited number of genomic sites, which quickly became saturated in the short term. Nevertheless, substitutions at the remaining regions occurred at a much lower rate. Therefore, the HBV substitution rate decreased as the divergence time increased.

Modeling and simulating dynamics of complete- and poor-response chronic hepatitis B chinese patients for adefovir and traditional chinese medicine plus adefovir therapy

ChiCTR-TRC-11001263 study was the first large-scale double-blind randomized placebo-controlled traditional Chinese medicines (TCMs) and adefovir (ADV) antihepatitis B virus (HBV) infection trial in the world. A total of 560 hepatitis B e antigen- (HBeAg-) positive Chinese patients with chronical HBV were randomly classified, in 1 : 1 ratio, into two groups: experimental group (EXG) receiving TCMs + ADV and controlled group (CTG) receiving ADV + TCM-placebo treatment for 48 weeks. This paper introduces two models to model and simulate the evolutions of dynamics for the complete-response patients and the poor-response patients in EXG and CTG, respectively. The stimulated mean HBV DNA and alanine aminotransferase (ALT) levels were close to the patients' experimental data. Analysis and simulations suggest that the activated patients' immune functions by TCMs + ADV may not only clear infected hepatocytes, but also clear HBV, which made the complete-response patients' mean serum HBV DNA levels in EXG reduce rapidly 12 weeks' earlier than the ones in CTG. One can assume that both the TCMs and ADV have the function of preventing complete-response patients' infected hepatocytes from being injured by cytotoxic T lymphocytes (CTLs); the patients' activated immune cells may also block HBV replications.

Analysis and simulation of an Adefovir anti-hepatitis B virus infection therapy immune model with alanine aminotransferase

Hepatitis B virus (HBV) infection models and anti-HBV infection therapy models have been set up to understand and explain clinical phenomena. Many of these models have been proposed based on Zeuzem et al. and Nowak et al.'s basic virus infection model (BVIM). Some references have pointed out that the basic infection reproductive number of the BVIM is biologically questionable and gave the modified models with standard mass action incidences. This study describes one anti-HBV therapy immune model with alanine aminotransferase (ALT) based on standard mass action incidences. There are two basic infection reproductive numbers R0 and R1 in the model. It is proved that if R0 < 1 and R1 < 1, the disease free equilibrium is locally and globally asymptotically stable, respectively. For the endemic equilibrium, simulation shows that if R1 > 1, it may be also globally asymptotically stable. Simulations based on clinical data of HBV DNA and ALT can explain some clinical phenomena. Simulations of the correlation between liver cells, HBV DNA, cytotoxic T lymphocytes and ALT are also given.

Optimal Antiviral Treatment Strategies of HBV Infection Model with Logistic Hepatocyte Growth

This study considers an optimal therapy strategy for HBV infection by incorporating two controls laws into a previous hepatitis B viral infection model with logistic hepatocyte growth. Our goal is to maximize the number of healthy cells and to minimize the cost of the therapy. In this context, the existence of an optimal control is proved. The optimal control is obtained by solving the optimality system which was composed of three nonlinear ODEs with initial conditions and three nonlinear adjoint ODEs with transversality conditions. The results were analysed and interpreted numerically using MATLAB.

Global analysis of a simple parasite-host model with homoclinic orbits

In this paper, a simple parasite-host model proposed by Ebert et al.(2000) is reconsidered. The basic epidemiological reproduction number of parasite infection (R0) and the basic demographic reproduction number of infected hosts (R1) are given. The global dynamics of the model is completely investigated, and the existence of heteroclinic and homoclinic orbits is theoretically proved, which implies that the outbreak of parasite infection may happen. The thresholds determining the host extinction in the presence of parasite infection and variation in the equilibrium level of the infected hosts with R0 are found. The effects of R0 and R1 on dynamics of the model are considered and we show that the equilibrium level of the infected host may not be monotone with respect to R0. In particular, it is found that full loss of fecundity of infected hosts may lead to appearance of the singular case.

GLOBAL ANALYSIS OF A VIRAL INFECTION MODEL WITH APPLICATION TO HBV INFECTION

The basic models of within-host viral infection, proposed by Nowak and May2 and Perelson and Nelson,5 have been widely used in the studies of HBV and HIV infections. The basic reproduction numbers of the two models are proportional to the number of total cells of the host's organ prior to the infection. In this paper, we formulate an amended Perelson and Nelson's model with standard incidence. The basic reproduction number of the amended model is independent of total cells of the host's organ. If the basic reproduction number R0 < 1, then the infection-free equilibrium is globally asymptotically stable and the virus is cleared; if R0 > 1, then the virus persists in the host, and solutions approach either an endemic equilibrium or a periodic orbit. Numerical simulations of this model agree well with the clinical HBV infection data. This can provide a possible interpretation for the viral oscillation behaviors, which were observed in chronic HBV infection patients.

Numerical diagnoses of superinfection in chronic hepatitis B viral dynamics

OBJECTIVES

Fluctuation profile has been observed in chronic hepatitis B patients who are untreated or interrupt therapy. A mathematical model and its parameters could be used to diagnose the assumption of superinfection of hepatocytes and to understand the causes for the spontaneous fluctuation pattern of HBV DNA loads in chronically infected patients.

METHODS

We propose a new conceptual model in terms of chemical kinetics, which is based on the assumption that hepatocytes can be superinfected with hepatitis B virus (HBV). Minimizing the sum of squares of the deviations, we fitted the model to the HBV DNA trajectories from clinical data and obtained the model parameters.

RESULTS

The model with the fitted parameters can capture the tendency of HBV DNA trajectories. The mean value of the fitted number of virions that enter a single hepatocyte at the beginning stage of an invasion is 2.10 ± 0.18. The dynamics patterns may correlate with the clinical phenotypes of patients and the value of clinical parameters, such as α-fetoprotein, hepatitis B e-antigen, hepatitis B e-antibody, total bilirubin and alanine transaminase.

CONCLUSIONS

The superinfection scenario is possible in HBV infection and it may induce HBV DNA fluctuation in the host.

Modeling the adaptive immune response in HBV infection

The aim of this work is to investigate a new mathematical model that describes the interactions between Hepatitis B virus (HBV), liver cells (hepatocytes), and the adaptive immune response. The qualitative analysis of this as cytotoxic T lymphocytes (CTL) cells and the antibodies. These outcomes are (1) a disease free steady state, which its local stability is characterized as usual by R (0) < 1, (2) and the existence of four endemic steady states when R (0) > 1. The local stability of these steady states depends on functions of R (0). Our study shows that although we give conditions of stability of these steady states, not all conditions are feasible. This rules out the local stability of two steady states. The conditions of stability of the two other steady states (which represent the complete failure of the adaptive immunity and the persistence of the disease) are formulated based on the domination of CTL cells response or the antibody response.

Distinct hepatitis B virus dynamics in the immunotolerant and early immunoclearance phases

Little is known about hepatitis B virus (HBV) diversity changes within a host during the immunotolerant phase of chronic HBV infection. Such knowledge, nevertheless, may help in understanding how host immunity and HBV interact at the early stage of infection. In this study, serial serum samples were collected from a long-term (>17 years) follow-up cohort of seven patients, and multiple copies of the full-length viral genome from serially sampled sera were recovered and analyzed. Viral genetic diversity was positively correlated with host immunity, represented by levels of alanine aminotransferase (ALT), but was negatively correlated with the viral copy number. During the immunotolerant phase, when the host immunity was feeble (ALT < 20 U/liter), viral nucleotide diversity decreased while copy numbers increased. Rates of evolutionary change derived for different patients were in a very narrow range (1.6 x 10(-5) to 5.4 x 10(-5)/site/year). As the disease progressed toward the immunoclearance phase (ALT > 20 U/liter), viral diversity increased but copy numbers decreased. Evolutionary rates varied among patients in accordance with their levels of ALT, ranging from 9.6 x 10(-6) to 3.2 x 10(-4)/site/year. More than half (19/32 sites) of positively selected sites resided in immune epitopes, suggesting their possible role in host immunity. Our results demonstrate that host immunity is a dominant factor in HBV evolution. Different selective forces, including immune-mediated positive selection and virus-mediated negative selection, operate in tandem in shaping viral population dynamics within a host.

Distinct hepatitis B virus dynamics in the immunotolerant and early immunoclearance phases

Little is known about hepatitis B virus (HBV) diversity changes within a host during the immunotolerant phase of chronic HBV infection. Such knowledge, nevertheless, may help in understanding how host immunity and HBV interact at the early stage of infection. In this study, serial serum samples were collected from a long-term (>17 years) follow-up cohort of seven patients, and multiple copies of the full-length viral genome from serially sampled sera were recovered and analyzed. Viral genetic diversity was positively correlated with host immunity, represented by levels of alanine aminotransferase (ALT), but was negatively correlated with the viral copy number. During the immunotolerant phase, when the host immunity was feeble (ALT < 20 U/liter), viral nucleotide diversity decreased while copy numbers increased. Rates of evolutionary change derived for different patients were in a very narrow range (1.6 x 10(-5) to 5.4 x 10(-5)/site/year). As the disease progressed toward the immunoclearance phase (ALT > 20 U/liter), viral diversity increased but copy numbers decreased. Evolutionary rates varied among patients in accordance with their levels of ALT, ranging from 9.6 x 10(-6) to 3.2 x 10(-4)/site/year. More than half (19/32 sites) of positively selected sites resided in immune epitopes, suggesting their possible role in host immunity. Our results demonstrate that host immunity is a dominant factor in HBV evolution. Different selective forces, including immune-mediated positive selection and virus-mediated negative selection, operate in tandem in shaping viral population dynamics within a host.