The dynamics of hepatitis B virus infection

Lyapunov function and global asymptotic stability for a new multiscale viral dynamics model incorporating the immune system response: Implemented upon HCV

In this paper, a new mathematical model is formulated that describes the interaction between uninfected cells, infected cells, viruses, intracellular viral RNA, Cytotoxic T-lymphocytes (CTLs), and antibodies. Hence, the model contains certain biological relations that are thought to be key factors driving this interaction which allow us to obtain precise logical conclusions. Therefore, it improves our perception, that would otherwise not be possible, to comprehend the pathogenesis, to interpret clinical data, to control treatment, and to suggest new relations. This model can be used to study viral dynamics in patients for a wide range of infectious diseases like HIV, HPV, HBV, HCV, and Covid-19. Though, analysis of a new multiscale HCV model incorporating the immune system response is considered in detail, the analysis and results can be applied for all other viruses. The model utilizes a transformed multiscale model in the form of ordinary differential equations (ODE) and incorporates into it the interaction of the immune system. The role of CTLs and the role of antibody responses are investigated. The positivity of the solutions is proven, the basic reproduction number is obtained, and the equilibrium points are specified. The stability at the equilibrium points is analyzed based on the Lyapunov invariance principle. By using appropriate Lyapunov functions, the uninfected equilibrium point is proven to be globally asymptotically stable when the reproduction number is less than one and unstable otherwise. Global stability of the infected equilibrium points is considered, and it has been found that each equilibrium point has a specific domain of stability. Stability regions could be overlapped and a bistable equilibria could be found, which means the coexistence of two stable equilibrium points. Hence, the solution converges to one of them depending on the initial conditions.

Dynamical Analysis of a Multiscale Model of Hepatitis C Virus Infection Using a Transformed ODEs Model

A mathematically identical ordinary differential equations (ODEs) model was derived from a multiscale partial differential equations (PDEs) model of hepatitis c virus infection, which helps to overcome the limitations of the PDE model in clinical data analysis. We have discussed about basic properties of the system and found the basic reproduction number of the system. A condition for the local stability of the uninfected and the infected steady states is presented. The local stability analysis of the model shows that the system is asymptotically stable at the disease-free equilibrium point when the basic reproduction number is less than one. When the basic reproduction number is greater than one endemic equilibrium point exists, and the local stability analysis proves that this point is asymptotically stable. Numerical sensitivity analysis based on model parameters is performed and therefore the result describes the influence of each parameter on the basic reproduction number.

A mathematical model of the intracellular replication and within host evolution of hepatitis type B virus: Understanding the long time course of chronic hepatitis

Hepatitis B virus (HBV) causes acute and chronic liver disease. Especially, chronic hepatitis is a major risk factor of liver cirrhosis and hepatocellular carcinoma. Viral kinetics of HBV observed in peripheral blood is quite different depending on the clinical course of hepatitis. But the relationship between the intracellular replication dynamics and clinical course of HBV infection is unclear. Further it is very difficult to predict the long time course of hepatitis because the nature of HBV is changed by mutation within host with high mutation rate. We investigate the intracellular replication dynamics and within host evolution of HBV by using a mathematical model. Two different intracellular replication patterns of HBV, "explosive" and "arrested", are switched depending on the viral gene expression pattern. In the explosive replication, prominent growth of HBV is observed. On the other hand, the virion production is restricted in the arrested replication. It is suggested that the arrested and explosive replication is associated with chronic hepatitis and exacerbation of hepatitis respectively. It is shown by our evolutionary simulation that the exacerbation of hepatitis is caused by the emergence of explosive genotype of HBV from arrested genotype by mutation during chronic hepatitis. It is also shown that chronic infection without exacerbation is maintained by short waiting time for virion release and superinfection with arrested genotype. It is suggested that extension of waiting time for virion release and existence of uninfected hepatocyte in the liver may become risk factors for the exacerbation of hepatitis.

Mathematical modeling of cytotoxic lymphocyte-mediated immune response to hepatitis B virus infection

Nowak's model of the human immunodeficiency virus (HIV) infection has been extensively and successfully used to simulate the interaction between HIV and cytotoxic lymphocyte- (CTL-) mediated immune response. However, this model is not available for hepatitis B virus (HBV) infection. As the enhanced recruitment of virus-specific CTLs into the liver has been an important novel concept in the pathogenesis of hepatitis B, we develop a specific mathematical model analyzing the relationship between HBV and the CTL-mediated immune response, and the indicator of the liver cell damage, alanine aminotransferase (ALT). The stability condition of the complete recovery equilibrium point at which HBV will be eliminated entirely from the body is discussed. A different set of parameters is used in the simulation, and the results show that the model can interpret the wide variety of clinical manifestations of HBV infection. The model suggests that a rapid and vigorous CTL response is required for resolution of HBV infection.

Stability analysis of within-host parasite models with delays

We provide a global analysis of systems of within-host parasitic infections. The systems studied have parallel classes of different length of latently infected target cells. These systems can also be thought as systems arising from within-host parasitic systems with distributed continuous delays. We compute the basic reproduction ratio R0 for the systems under consideration. If R0< or =1 the parasite is cleared, if R0>1 and if a sufficient condition is satisfied we conclude to the global asymptotic stability (GAS) of the endemic equilibrium. For some generic class of models this condition reduces to R0>1. These results make possible to revisit some parasitic models including intracellular delays and to study their global stability.

The role of cells refractory to productive infection in acute hepatitis B viral dynamics

During acute hepatitis B virus (HBV) infection viral loads reach high levels ( approximately 10(10) HBV DNA per ml), and nearly every hepatocyte becomes infected. Nonetheless, approximately 85-95% of infected adults clear the infection. Although the immune response has been implicated in mediating clearance, the precise mechanisms remain to be elucidated. As infection clears, infected cells are replaced by uninfected ones. During much of this process the virus remains plentiful but nonetheless does not rekindle infection. Here, we analyze data from a set of individuals identified during acute HBV infection and develop mathematical models to test the role of immune responses in various stages of early HBV infection. Fitting the models to data we are able to separate the kinetics of the noncytolytic and the cytolytic immune responses, thus explaining the relative contribution of these two processes. We further show that we need to hypothesize that newly generated uninfected cells are refractory to productive infection. Without this assumption, viral resurgence is observed as uninfected cells are regenerated. Such protection, possibly mediated by cytokines, may also be important in resolving other acute viral infections.

A probability cellular automaton model for hepatitis B viral infections

The existing models of hepatitis B virus (HBV) infection dynamics are based on the assumption that the populations of viruses and cells are uniformly mixed. However, the real virus infection system is actually not homogeneous and some spatial factors might play a nontrivial role in governing the development of HBV infection and its outcome. For instance, the localized populations of dead cells might adversely affect the spread of infection. To consider this kind of inhomogeneous feature, a simple 2D (dimensional) probability Cellular Automaton model was introduced to study the dynamic process of HBV infection. The model took into account the existence of different types of HBV infectious and non-infectious particles. The simulation results thus obtained showed that the Cellular Automaton model could successfully account for some important features of the disease, such as its wide variety in manifestation and its age dependency. Meanwhile, the effects of the model's parameters on the dynamical process of the infection were also investigated. It is anticipated that the Cellular Automaton model may be extended to serve as a useful vehicle for studying, among many other complicated dynamic biological systems, various persistent infections with replicating parasites.

249(ser) TP53 mutation in plasma DNA, hepatitis B viral infection, and risk of hepatocellular carcinoma

Hepatocellular carcinoma (HCC) from regions with high dietary exposure to aflatoxins and endemic for hepatitis B virus (HBV) often contain a specific mutation at codon 249 in TP53 (249(ser); AGG to AGT, Arg to Ser). This mutation is also detectable in circulating cell-free DNA from the plasma of HCC patients and healthy subjects in these regions. We have examined the joint effect of plasma 249(ser) and HBV infection in a case-control study design involving 348 control, 98 cirrhotic, and 186 HCC participants from The Gambia, West Africa, an area of high HCC incidence. The 249(ser) mutation was detected in 3.5% of controls, 15.3% of cirrhotics, and 39.8% of HCC cases (adjusted odds ratios (OR): 4.83, (95% confidence interval (CI): 1.71-13.7) for cirrhosis and 20.3 (8.19-50.0) for HCC). HBsAg positivity along with plasma 249(ser) was observed in 45/183 (24.6%) HCC cases compared to only one (0.3%) control. Risk for HCC was associated with markers of HBV alone (OR: 10.0, 95% CI: 5.16-19.6), 249(ser) alone (OR: 13.2, 95% CI: 4.99-35.0), and both markers present (OR: 399, 95% CI: 48.6-3270). These results suggest a multiplicative effect on HCC risk resulting from the mutational effect of aflatoxin on TP53, as monitored by detection of plasma 249(ser), with concomitant chronic infection with HBV.

Spatial models of virus-immune dynamics

To date, the majority of theoretical models describing the dynamics of infectious diseases in vivo are based on the assumption of well-mixed virus and cell populations. Because many infections take place in solid tissues, spatially structured models represent an important step forward in understanding what happens when the assumption of well-mixed populations is relaxed. Here, we explore models of virus and virus-immune dynamics where dispersal of virus and immune effector cells was constrained to occur locally. The stability properties of our spatial virus-immune dynamics models remained robust under almost all biologically plausible dispersal schemes, regardless of their complexity. The various spatial dynamics were compared to the basic non-spatial dynamics and important differences were identified: When space was assumed to be homogeneous, the dynamics generated by non-spatial and spatially structured models differed substantially at the peak of the infection. Thus, non-spatial models may lead to systematic errors in the estimates of parameters underlying acute infection dynamics. When space was assumed to be heterogeneous, spatial coupling not only changed the equilibrium properties of the uncoupled populations but also equalized the dynamics and thereby reduced the likelihood of dynamic elimination of the infection. In line with experimental and clinical observations, long-lasting oscillation periods were virtually absent. When source-sink dynamics were considered, the long-term outcome of the infection depended critically on the degree of spatial coupling. The infection collapsed when emigration from source sites became too large. Finally, we discuss the implications of spatially structured models on medical treatment of infectious diseases, and note that a huge gap exists in data accurately describing infection dynamics in solid tissues.

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The Gambia Liver Cancer Study: Infection with hepatitis B and C and the risk of hepatocellular carcinoma in West Africa

Hepatocellular carcinoma (HCC) is the most common cancer in The Gambia. Hepatitis B virus (HBV) infection is endemic, with 15% to 20% of the population being chronic carriers, whereas hepatitis C virus (HCV) prevalence is low. We recruited 216 incident cases of HCC and 408 controls from three sites. HBV carriage was present in 61% (129/211) of HCC patients and 16% (64/402) of controls, whereas 19% (36/191) of HCC patients were HCV seropositive compared with 3% (11/382) of controls. HCC patients with HCV were notably older and were more likely to be female than those with HBV. Increased HCC risk was strongly associated with chronic HBV (odds ratio, 16.7; 95% CI, 9.7-28.7), HCV (16.7; 6.9-40.1), and dual infection (35.3; 3.9-323). We interpret the additive nature of risk with coinfection as representative of HBV and HCV acting primarily through shared steps in the multistage process of hepatocarcinogenesis. HCV infection was not observed among younger participants, suggesting a possible cohort effect. Reasons for the striking age and gender differences in HCC associated with HBV compared with HCV are unclear, but transmission patterns and age at exposure may be factors. In conclusion, in a standardized evaluation of well-characterized study participants from The Gambia, most cases of HCC are attributable to HBV (57%), but HCV adds a significant fraction (20%), especially among older patients and females. If HCV transmission is not perpetuated in future cohorts, focusing available resources on HB vaccination efforts could greatly ameliorate a major cause of cancer death in sub-Saharan Africa.

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Dynamics of hepatitis B virus infection

Mathematical models of the dynamics of HIV and hepatitis C virus infection have proven to be of great utility in understanding pathogenesis and designing better treatments. Here, we review the state of the art in modeling and interpreting data obtained from hepatitis B virus infected patients treated with antiviral agents.

Resistance of hepatitis B virus to antiviral drugs: current aspects and directions for future investigation

Despite the existence of vaccines, chronic hepatitis B virus (HBV) infection remains a major health problem worldwide. Interferon therapy successfully controls infection in only a small percentage of chronically infected individuals. The recent approval of the nucleoside analogue lamivudine for the treatment of chronic HBV infection has ushered in a new era of antiviral therapy. While lamivudine is highly effective at controlling viral infection short-term, prolonged therapy has been associated with an increasing incidence of viral resistance. Thus, it appears that lamivudine alone will not be sufficient to control chronic viral infection in the majority of individuals. In addition to lamivudine, several new nucleoside and nucleotide analogues that show promising antihepadnaviral activity are in various stages of development. Lamivudine resistance has been found to confer cross-resistance to some of these compounds and it is likely that resistance to newer antivirals may also develop during prolonged use. Drug resistance therefore poses a major threat to nucleoside analogue-based therapies for chronic HBV infection. Fortunately, combination chemotherapy (antiviral therapy with two or more agents) can minimize the chance that resistance will develop and can be expected to achieve sustained reductions in viral load, provided that suitable combinations of agents are chosen. Here we review the basis of drug resistance in HBV, with emphasis on aspects that are likely to affect drug choice in future.

Hepatitis B virus infection in Thai children

We studied hepatitis B virus (HBV) transmission among 7416 Thai children from 148 schools in Kamphaeng Phet province, a rural part of northern Thailand. Their age ranged from 2 to 16 years (median 9 years). Between May 1991 and June 1992, 61 of 2593 (2.4%) in the cohort of susceptible children acquired anti-HBc immunoglobulin. Forty-seven of the 148 schools had children who acquired anti-HBc. School seroconversion rates to anti-HBc varied from 0% to 23%. There was no correlation between percent of carriers in schools and percent of anti-HBc acquisition. Of the 61 children who acquired anti-HBc, eight (13%) became HBsAg carriers but only two were symptomatic, for a clinical to subclinical infection ration of 1 : 30. One of the two symptomatic children became an HBsAg carrier. Three (38%) of the eight who were persistently antigenemic developed antibody to hepatitis B virus e antigen. Males were 2.5 times (95% CI 1.4-4.3) more likely to acquire anti-HBc than females. Risk factors for acquisition of HBc in Thailand over a 9-month period were examined in a subset of 2412 susceptible children and later in a case-control study of 22 children who acquired anti-HBc and 59 age and sex-matched controls. Risks for acquiring anti-HBc were male gender and a history of bleeding gums. In comparing this study to an earlier pilot study among 9848 children from the same area in Thailand, the yearly antibody acquisition rate to anti-HBc among Thai children dropped from 5.7% in 1989 to 2.4% in 1992. A random sample of children in the pilot study showed that 16% were HBsAg positive and 27% had anti-HBc at the beginning of the study. 34% had markers for either anti-HBc or HBsAg. 12% were repeatedly positive for HBsAg a year later.

Combination therapy with lamivudine and famciclovir for chronic hepatitis B-infected Chinese patients: a viral dynamics study

In vitro studies have shown that lamivudine and penciclovir (the active metabolite of famciclovir) act synergistically to inhibit hepatitis B virus (HBV) replication. We compared the effectiveness of HBV viral suppression by lamivudine monotherapy versus lamivudine plus famciclovir combination therapy in Chinese patients with chronic HBV infection. Twenty-one Chinese hepatitis B e antigen (HBeAg)-positive patients, with detectable HBV DNA (Digene Hybrid Capture II), were randomized to receive either lamivudine 150 mg/d orally (group 1, 9 patients) or lamivudine 150 mg/d plus famciclovir 500 mg 3 times a day orally (group 2, 12 patients) for 12 weeks, with a follow-up period of at least 16 weeks. Serial serum HBV-DNA levels were determined and a mathematical model with provision for incomplete inhibition of virus production during therapy was applied to analyze the dynamics of viral clearance. The mean antiviral efficacy was significantly greater in group 2 than in group 1 (0.988 +/- 0.012 vs. 0.94 +/- 0.03, P =.0012). HBV DNA returned to pretreatment level within 16 weeks after the end of initial treatment in 4 patients (66.7%) in group 1 and none in group 2 (P =.08), who remained HBeAg positive and received no further treatment after week 12. Hence, in Chinese chronic HBeAg-positive patients, combination therapy using lamivudine and famciclovir was superior to lamivudine monotherapy in inhibiting HBV replication. Further studies of longer duration are needed to define whether combination therapy will increase the HBeAg seroconversion rate and decrease the rate of emergence of lamivudine-resistant variants.

Retreatment of chronic hepatitis B e antigen-positive patients with recombinant interferon alfa-2a. The European Concerted Action on Viral Hepatitis (EUROHEP)

Fifty-seven patients with chronic hepatitis B, hepatitis B virus (HBV) e antigen (HBeAg) and HBV DNA positivity, and aminotransferase elevation despite a previous course of any type of adequate interferon alfa (IFN-alpha) therapy were included in a multicenter prospective randomized controlled trial. The objective of the study was to compare a second course of IFN-alpha therapy (9 million units [MU] of IFN-alpha-2a, Roferon-A, thrice weekly for 6 months) versus no therapy in terms of loss of HBV DNA and HBeAg. At the end of the study, a sustained clearance of HBV DNA and HBeAg was observed in 9 of the 27 (33.3%) patients who had received retreatment with IFN-alpha compared with 3/30 (10%) patients who spontaneously cleared these markers in the untreated control group (chi2 = 4.66, P =.031; odds ratio: 4.5, 95%; confidence interval: 1.1-18.9). None of the responders lost HBsAg. Patients retreated with IFN-alpha were more likely to have biochemical remission in association with HBV clearance (5/27, 18.5%) compared with untreated patients (1/30, 3. 3%; Fisher's exact test P =.09 ). Histological improvement in the liver necroinflammatory activity was observed among sustained responders to IFN-alpha retreatment, consisting of regression of the portal and periportal inflammation and of the piecemeal necrosis; there was no change in the degree of liver fibrosis. Side effects were similar to those previously reported during IFN-alpha treatment; these were mild and reversible on IFN-alpha discontinuation. None of the baseline features were associated with response by Cox's regression analysis. In summary, viremic patients with chronic HBeAg-positive hepatitis may experience disease remission following retreatment with IFN-alpha. Thus, retreatment with IFN-alpha may be considered a therapeutic option.

Biphasic clearance kinetics of hepatitis B virus from patients during adefovir dipivoxil therapy

In a recent phase II clinical study, 13 chronic hepatitis B-infected patients treated daily with 30 mg adefovir dipivoxil for 12 weeks displayed a median 4.1-log10 decrease in plasma hepatitis B virus (HBV)-DNA levels. The decline of viral load during therapy displayed a biphasic kinetic profile that was modeled to determine the efficacy of inhibition of viral production, as well as kinetic constants for the clearance of free virus and the loss of infected cells. Viral production was suppressed with an efficacy of 0.993 +/- 0.008, indicating that only 0.7% of viral production persisted during therapy. The initial, faster phase of viral load decline reflects the clearance of HBV particles from plasma with a half-life of 1.1 +/- 0.3 days, translating to a 48% daily turnover of the free virus. The second, slower phase of viral load decline closely mirrors the rate-limiting process of infected cell loss, with a half-life of 18 +/- 7 days. The duration of therapy required to completely eliminate the virus from plasma or suppress it to levels sufficient to induce seroconversion is a function of the half-life of the free virus, the half-life of infected cells, and the efficacy of inhibition of virus production from infected cells. These quantitative analyses provide a more detailed picture of the dynamics of HBV infection and therapy, and can be used to compare the efficacy of various doses and inhibitors of HBV replication for the treatment of HBV infections.

Clinical and histological outcome after hepatitis B e antigen to antibody seroconversion in children with chronic hepatitis B

Data regarding the outcome of children with chronic hepatitis B after seroconversion are scarce. We describe the long-term evolution of these patients. One hundred and three children with antibody against hepatitis B e antigen and normal alanine aminotransferase (ALT) levels were followed for 0.6 to 12.5 years (mean, 6.3 years). Paired liver biopsies (before and after seroconversion) were available in 83 cases. Final biopsies were obtained 0.5 to 12.5 years (mean, 4.5 years) after seroconversion. ALT levels remained normal in most of the children (79%) throughout the follow-up. All children, except five who lost hepatitis B surface antigen, had serum viral DNA detected by polymerase chain reaction. When comparing baseline and final liver biopsies, a significant improvement (P <.001) was found in the histological activity index and in the necrosis, cytolysis, inflammation, and fibrosis scores. The histological diagnosis improvement in the final biopsy was significantly related (P <.001) to the time from seroconversion to the biopsy performance. All children had viral DNA on their final liver biopsy. In summary, seroconversion and ALT normalization are quite stable findings in children, and no differences in the long-term outcome between treated and untreated children were found. In light of the histological outcome, it seems unnecessary to perform a follow-up liver biopsy in these cases.