Mathematical model of antiviral immune response. I. Data analysis, generalized picture construction and parameters evaluation for hepatitis B

Modelling of the Innate and Adaptive Immune Response to SARS Viral Infection, Cytokine Storm and Vaccination

In this work, we develop mathematical models of the immune response to respiratory viral infection, taking into account some particular properties of the SARS-CoV infections, cytokine storm and vaccination. Each model consists of a system of ordinary differential equations that describe the interactions of the virus, epithelial cells, immune cells, cytokines, and antibodies. Conventional analysis of the existence and stability of stationary points is completed by numerical simulations in order to study the dynamics of solutions. The behavior of the solutions is characterized by large peaks of virus concentration specific to acute respiratory viral infections. At the first stage, we study the innate immune response based on the protective properties of interferon secreted by virus-infected cells. Viral infection down-regulates interferon production. This competition can lead to the bistability of the system with different regimes of infection progression with high or low intensity. After that, we introduce the adaptive immune response with antigen-specific T- and B-lymphocytes. The resulting model shows how the incubation period and the maximal viral load depend on the initial viral load and the parameters of the immune response. In particular, an increase in the initial viral load leads to a shorter incubation period and higher maximal viral load. The model shows that a deficient production of antibodies leads to an increase in the incubation period and even higher maximum viral loads. In order to study the emergence and dynamics of cytokine storm, we consider proinflammatory cytokines produced by cells of the innate immune response. Depending on the parameters of the model, the system can remain in the normal inflammatory state specific for viral infections or, due to positive feedback between inflammation and immune cells, pass to cytokine storm characterized by the excessive production of proinflammatory cytokines. Finally, we study the production of antibodies due to vaccination. We determine the dose-response dependence and the optimal interval of vaccine dose. Assumptions of the model and obtained results correspond to the experimental and clinical data.

A quantitative systems pharmacology model for acute viral hepatitis B

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Mechanistic model characterizing acute immune response and HBV system interactions.

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Key role of the cellular and regulatory response triggering hepatitis B chronicity.

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Modelling framework to easily incorporate and explore additional biological mechanisms.

Hepatitis B liver infection is caused by hepatitis B virus (HBV) and represents a major global disease problem when it becomes chronic, as is the case for 80–90% of vertical or early life infections. However, in the vast majority (>95%) of adult exposures, the infected individuals are capable of mounting an effective immune response leading to infection resolution. A good understanding of HBV dynamics and the interaction between the virus and immune system during acute infection represents an essential step to characterize and understand the key biological processes involved in disease resolution, which may help to identify potential interventions to prevent chronic hepatitis B.

In this work, a quantitative systems pharmacology model for acute hepatitis B characterizing viral dynamics and the main components of the innate, adaptive, and tolerant immune response has been successfully developed. To do so, information from multiple sources and across different organization levels has been integrated in a common mechanistic framework. The final model adequately describes the chronology and plausibility of an HBV-triggered immune response, as well as clinical data from acute patients reported in the literature. Given the holistic nature of the framework, the model can be used to illustrate the relevance of the different immune pathways and biological processes to ultimate response, observing the negligible contribution of the innate response and the key contribution of the cellular response on viral clearance. More specifically, moderate reductions of the proliferation of activated cytotoxic CD8+ lymphocytes or increased immunoregulatory effects can drive the system towards chronicity.

Modeling within-Host SARS-CoV-2 Infection Dynamics and Potential Treatments

The goal of this study was to develop a mathematical model to simulate the actions of drugs that target SARS-CoV-2 virus infection. To accomplish that goal, we have developed a mathematical model that describes the control of a SARS-CoV-2 infection by the innate and adaptive immune components. Invasion of the virus triggers the innate immunity, whereby interferon renders some of the target cells resistant to infection, and infected cells are removed by effector cells. The adaptive immune response is represented by plasma cells and virus-specific antibodies. The model is parameterized and then validated against viral load measurements collected in COVID-19 patients. We apply the model to simulate three potential anti-SARS-CoV-2 therapies: (1) Remdesivir, a repurposed drug that has been shown to inhibit the transcription of SARS-CoV-2, (2) an alternative (hypothetical) therapy that inhibits the virus' entry into host cells, and (3) convalescent plasma transfusion therapy. Simulation results point to the importance of early intervention, i.e., for any of the three therapies to be effective, it must be administered sufficiently early, not more than a day or two after the onset of symptoms. The model can serve as a key component in integrative platforms for rapid in silico testing of potential COVID-19 therapies and vaccines.

MATHEMATICAL MODELLING OF IMMUNE PROCESSES AND ITS APPLICATION

The aim of the study was to develop a mathematical model to research hypoxic states in case of simulation of an organism infectious lesions. The model is based on the methods of mathematical modeling and the theory of optimal control of moving objects. The processes of organism damage are simulated with the mathematical model of immune response developed by G.I. Marchuk and the members of his scientific school, adapted to current conditions. This model is based on Burnet’s clone selection theory of the determining role of antigen. Simulation results using the model are presented. The dependencies of infectious courses on the volumetric velocity of systemic blood flow is analyzed on the complex mathematical model of immune response, respiratory and blood circulation systems. The immune system is shown to be rather sensitive to the changes in blood flow via capillaries. Thus, the organ blood flows can be used as parameters for the model by which the respiratory, immune response, and blood circulation systems interact and interplay.

Global Asymptotic Stability and Nonlinear Analysis of the Model of the Square Immunopixels Array Based on Delay Lattice Differential Equations

Biosensors and immunosensors show an increasing attractiveness when developing current cheap and fast monitoring and detecting devices. In this work, a model of immunosensor in a class of delayed lattice differential equations is offered and studied. The spatial operator describes symmetric diffusion processes of antigenes between pixels. The main results are devoted to the qualitative research of the model. The conditions of global asymptotic stability, which are constructed with the help of Lyapunov functionals, determine a lower estimate of the time of immune response. Nonlinear analysis of the model is performed with help of a series of numerical characteristics including autocorrelation function, mutual information, embedding, and correlation dimensions, sample entropy, the largest Lyapunov exponents. We consider the influence of both symmetric and unsymmetric diffusion of antigens between pixels on the qualitative behavior of the system. The outcomes are verified with the help of numerical simulation in cases of 4 × 4 - and 16 × 16 - arrays of immunopixels.

On Nonlinear Reaction-Diffusion Model with Time Delay on Hexagonal Lattice

In the work, a nonlinear reaction-diffusion model in a class of delayed differential equations on the hexagonal lattice is considered. The system includes a spatial operator of diffusion between hexagonal pixels. The main results deal with the qualitative investigation of the model. The conditions of global asymptotic stability, which are based on the Lyapunov function construction, are obtained. An estimate of the upper bound of time delay, which enables stability, is presented. The numerical study is executed with the help of the bifurcation diagram, phase trajectories, and hexagonal tile portraits. It shows the changes in qualitative behavior with respect to the growth of time delay; namely, starting from the stable focus at small delay values, then through Hopf bifurcation to limit cycles, and finally, through period doublings to deterministic chaos.

Sequential infection experiments for quantifying innate and adaptive immunity during influenza infection

Laboratory models are often used to understand the interaction of related pathogens via host immunity. For example, recent experiments where ferrets were exposed to two influenza strains within a short period of time have shown how the effects of cross-immunity vary with the time between exposures and the specific strains used. On the other hand, studies of the workings of different arms of the immune response, and their relative importance, typically use experiments involving a single infection. However, inferring the relative importance of different immune components from this type of data is challenging. Using simulations and mathematical modelling, here we investigate whether the sequential infection experiment design can be used not only to determine immune components contributing to cross-protection, but also to gain insight into the immune response during a single infection. We show that virological data from sequential infection experiments can be used to accurately extract the timing and extent of cross-protection. Moreover, the broad immune components responsible for such cross-protection can be determined. Such data can also be used to infer the timing and strength of some immune components in controlling a primary infection, even in the absence of serological data. By contrast, single infection data cannot be used to reliably recover this information. Hence, sequential infection data enhances our understanding of the mechanisms underlying the control and resolution of infection, and generates new insight into how previous exposure influences the time course of a subsequent infection.

The impact of cell regeneration on the dynamics of viral coinfection

Many mathematical models of respiratory viral infections do not include regeneration of cells within the respiratory tract, arguing that the infection is resolved before there is significant cellular regeneration. However, recent studies have found that ∼40% of patients hospitalized with influenza-like illness are infected with at least two different viruses, which could potentially lead to longer-lasting infections. In these longer infections, cell regeneration might affect the infection dynamics, in particular, allowing for the possibility of chronic coinfections. Several mathematical models have been used to describe cell regeneration in infection models, though the effect of model choice on the predicted time course of viral coinfections is not clear. We investigate four mathematical models incorporating different mechanisms of cell regeneration during respiratory viral coinfection to determine the effect of cell regeneration on infection dynamics. We perform linear stability analysis for each of the models and find the steady states analytically. The analysis suggests that chronic illness is possible but only with one viral species; chronic coexistence of two different viral species is not possible with the regeneration models considered here.

Modelling cross-reactivity and memory in the cellular adaptive immune response to influenza infection in the host

The cellular adaptive immune response plays a key role in resolving influenza infection. Experiments where individuals are successively infected with different strains within a short timeframe provide insight into the underlying viral dynamics and the role of a cross-reactive immune response in resolving an acute infection. We construct a mathematical model of within-host influenza viral dynamics including three possible factors which determine the strength of the cross-reactive cellular adaptive immune response: the initial naive T cell number, the avidity of the interaction between T cells and the epitopes presented by infected cells, and the epitope abundance per infected cell. Our model explains the experimentally observed shortening of a second infection when cross-reactivity is present, and shows that memory in the cellular adaptive immune response is necessary to protect against a second infection.

Novel methods for quantifying individual host response to infectious pathogens for genetic analyses

We propose two novel approaches for describing and quantifying the response of individual hosts to pathogen challenge in terms of infection severity and impact on host performance. The first approach is a direct extension of the methodology for estimating group tolerance (the change in performance with respect to changes in pathogen burden in a host population) to the level of individuals. The second approach aims to capture the dynamic aspects of individual resistance and tolerance over the entire time course of infections. In contrast to the first approach, which provides a means to disentangle host resistance from tolerance, the second approach focuses on the combined effects of both characteristics. Both approaches provide new individual phenotypes for subsequent genetic analyses and come with specific data requirements. In particular, both approaches rely on the availability of repeated performance and pathogen burden measurements of individuals over the time course of one or several episodes of infection. Consideration of individual tolerance also highlights some of the assumptions hidden within the concept of group tolerance, indicating where care needs to be taken in trait definition and measurement.

A low dimensional dynamical model of the initial pulmonary innate response to infection

In order to gain a deeper understanding of the onset and progression of pulmonary infections we present and analyze a low dimensional, phenomenological model of infection and the innate immune response in the lungs. Because pulmonary innate immunity has features unique to itself, general mathematical models of the immune system may not be appropriate. The differential equations model that we propose is based on current knowledge of the biology of pulmonary innate immunity and accurately reproduces known features of the initial phase of the dynamics of pulmonary innate system as exhibited in recent experiments. Further, we propose to use the model as a starting point for interrogation with clinical data from a new noninvasive technique for sampling alveolar lining fluid.

Using experimental human influenza infections to validate a viral dynamic model and the implications for prediction

The aim of this work was to use experimental infection data of human influenza to assess a simple viral dynamics model in epithelial cells and better understand the underlying complex factors governing the infection process. The developed study model expands on previous reports of a target cell-limited model with delayed virus production. Data from 10 published experimental infection studies of human influenza was used to validate the model. Our results elucidate, mechanistically, the associations between epithelial cells, human immune responses, and viral titres and were supported by the experimental infection data. We report that the maximum total number of free virions following infection is 10(3)-fold higher than the initial introduced titre. Our results indicated that the infection rates of unprotected epithelial cells probably play an important role in affecting viral dynamics. By simulating an advanced model of viral dynamics and applying it to experimental infection data of human influenza, we obtained important estimates of the infection rate. This work provides epidemiologically meaningful results, meriting further efforts to understand the causes and consequences of influenza A infection.

Understanding original antigenic sin in influenza with a dynamical system

Original antigenic sin is the phenomenon in which prior exposure to an antigen leads to a subsequent suboptimal immune response to a related antigen. Immune memory normally allows for an improved and rapid response to antigens previously seen and is the mechanism by which vaccination works. I here develop a dynamical system model of the mechanism of original antigenic sin in influenza, clarifying and explaining the detailed spin-glass treatment of original antigenic sin. The dynamical system describes the viral load, the quantities of healthy and infected epithelial cells, the concentrations of naïve and memory antibodies, and the affinities of naïve and memory antibodies. I give explicit correspondences between the microscopic variables of the spin-glass model and those of the present dynamical system model. The dynamical system model reproduces the phenomenon of original antigenic sin and describes how a competition between different types of B cells compromises the overall effect of immune response. I illustrate the competition between the naïve and the memory antibodies as a function of the antigenic distance between the initial and subsequent antigens. The suboptimal immune response caused by original antigenic sin is observed when the host is exposed to an antigen which has intermediate antigenic distance to a second antigen previously recognized by the host's immune system.

Viral kinetics and exhaled droplet size affect indoor transmission dynamics of influenza infection

The purpose of this paper was to investigate the effects of viral kinetics and exhaled droplet size on indoor transmission dynamics of influenza infection. The target cell-limited model with delayed virus production was adopted to strengthen the inner mechanisms of virus infection on human epithelial cell. The particle number and volume involved in the viral kinetics were linked with Wells-Riley mathematical equation to quantify the infection risk. We investigated population dynamics in a specific elementary school by using the seasonal susceptible - exposed - infected - recovery (SEIR) model. We found that exhaled pulmonary bioaerosol of sneeze (particle diameter <10 microm) have 10(2)-fold estimate higher than that of cough. Sneeze and cough caused risk probabilities range from 0.075 to 0.30 and 0.076, respectively; whereas basic reproduction numbers (R(0)) estimates range from 4 to 17 for sneeze and nearly 4 for cough, indicating sneeze-posed higher infection risk. The viral kinetics and exhaled droplet size for sneeze affect indoor transmission dynamics of influenza infection since date post-infection 1-7. This study provides direct mechanistic support that indoor influenza virus transmission can be characterized by viral kinetics in human upper respiratory tracts that are modulated by exhaled droplet size. Practical Implications This paper provides a predictive model that can integrate the influenza viral kinetics (target cell-limited model), indoor aerosol transmission potential (Wells-Riley mathematical equation), and population dynamic model [susceptible - exposed - infected - recovery (SEIR) model] in a proposed susceptible population. Viral kinetics expresses the competed results of human immunity ability with influenza virus generation. By linking the viral kinetics and different exposure parameters and environmental factors in a proposed school setting with five age groups, the influenza infection risk can be estimated. On the other hand, we implicated a new simple means of inhaling to mitigate exhaled bioaerosols through an inhaled non-toxic aerosol. The proposed predictive model may serve as a tool for further investigation of specific control measure such as the personal protection masks to alter the particle size and number concentration characteristics and minimize the exhaled bioaerosol droplet to decrease the infection risk in indoor environment settings.

Improving alloreactive CTL immunotherapy for malignant gliomas using a simulation model of their interactive dynamics

Glioblastoma (GBM), a highly aggressive (WHO grade IV) primary brain tumor, is refractory to traditional treatments, such as surgery, radiation or chemotherapy. This study aims at aiding in the design of more efficacious GBM therapies. We constructed a mathematical model for glioma and the immune system interactions, that may ensue upon direct intra-tumoral administration of ex vivo activated alloreactive cytotoxic-T-lymphocytes (aCTL). Our model encompasses considerations of the interactive dynamics of aCTL, tumor cells, major histocompatibility complex (MHC) class I and MHC class II molecules, as well as cytokines, such as TGF-beta and IFN-gamma, which dampen or increase the pro-inflammatory environment, respectively. Computer simulations were used for model verification and for retrieving putative treatment scenarios. The mathematical model successfully retrieved clinical trial results of efficacious aCTL immunotherapy for recurrent anaplastic oligodendroglioma and anaplastic astrocytoma (WHO grade III). It predicted that cellular adoptive immunotherapy failed in GBM because the administered dose was 20-fold lower than required for therapeutic efficacy. Model analysis suggests that GBM may be eradicated by new dose-intensive strategies, e.g., 3 x 10(8) aCTL every 4 days for small tumor burden, or 2 x 10(9) aCTL, infused every 5 days for larger tumor burden. Further analysis pinpoints crucial bio-markers relating to tumor growth rate, tumor size, and tumor sensitivity to the immune system, whose estimation enables regimen personalization. We propose that adoptive cellular immunotherapy was prematurely abandoned. It may prove efficacious for GBM, if dose intensity is augmented, as prescribed by the mathematical model. Re-initiation of clinical trials, using calculated individualized regimens for grade III-IV malignant glioma, is suggested.

A dynamical model of human immune response to influenza A virus infection

We present a simplified dynamical model of immune response to uncomplicated influenza A virus (IAV) infection, which focuses on the control of the infection by the innate and adaptive immunity. Innate immunity is represented by interferon-induced resistance to infection of respiratory epithelial cells and by removal of infected cells by effector cells (cytotoxic T-cells and natural killer cells). Adaptive immunity is represented by virus-specific antibodies. Similar in spirit to the recent model of Bocharov and Romanyukha [1994. Mathematical model of antiviral immune response. III. Influenza A virus infection. J. Theor. Biol. 167, 323-360], the model is constructed as a system of 10 ordinary differential equations with 27 parameters characterizing the rates of various processes contributing to the course of disease. The parameters are derived from published experimental data or estimated so as to reproduce available data about the time course of IAV infection in a naïve host. We explore the effect of initial viral load on the severity and duration of the disease, construct a phase diagram that sheds insight into the dynamics of the disease, and perform sensitivity analysis on the model parameters to explore which ones influence the most the onset, duration and severity of infection. To account for the variability and speed of adaptation of the adaptive response to a particular virus strain, we introduce a variable that quantifies the antigenic compatibility between the virus and the antibodies currently produced by the organism. We find that for small initial viral load the disease progresses through an asymptomatic course, for intermediate value it takes a typical course with constant duration and severity of infection but variable onset, and for large initial viral load the disease becomes severe. This behavior is robust to a wide range of parameter values. The absence of antibody response leads to recurrence of disease and appearance of a chronic state with nontrivial constant viral load.

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.

Energy cost of infection burden: an approach to understanding the dynamics of host-pathogen interactions

A mathematical model of long-term immune defense against infection was used to estimate the energy involved in the principal processes of immune resistance during periods of health and infection. From these values, an optimal level of energy was determined for immune response depending on infection burden. The present findings suggest that weak but prevalent pathogens lead to latent or chronic infection, whereas more virulent but less prevalent pathogens result in acute infection. This energy-based approach offers insight into the mechanisms of immune system adaptation leading to the development of chronic infectious diseases and immune deficiencies.

Modelling the dynamics of LCMV infection in mice: II. Compartmental structure and immunopathology

In this study, we develop a mathematical model for analysis of the compartmental aspects and immunopathology of lymphocytic choriomeningitis virus (LCMV) infection in mice. We used sets of original and published data on systemic (extrasplenic) virus distribution to estimate the parameters of virus growth and elimination for spleen and other anatomical compartments, such as the liver, kidney, thymus and lung as well as transfer rates between blood and the above organs. A mathematical model quantitatively integrating the virus distribution kinetics in the host, the specific cytotoxic T lymphocyte (CTL) response in spleen and the re-circulation of effector CTL between spleen, blood and liver is advanced to describe the CTL-mediated immunopathology (hepatitis) in mice infected with LCMV. For intravenous and "peripheral" routes of infection we examine the severity of the liver disease, as a function of the virus dose and the host's immune status characterized by the numbers of precursor and/or cytolytic effector CTL. The model is used to predict the efficacy of protection against virus persistence and disease in a localized viral infection as a function of the composition of CTL population. The modelling analysis suggests quantitative demands to CTL memory for maximal protection against a wide range of doses of infection with a primarily peripheral site of virus replication without the risk of favoring immunopathology. It specifies objectives for CTL vaccination to ensure virus elimination with minimal immunopathology vs. vaccination for disease.

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.

Intranasal vaccination: pharmaceutical evaluation of the vaccine delivery system and immunokinetic characteristics of the immune responses

The purpose of this study was to analyze the effect of some pharmaceutical excipients when used for mucosal vaccine formulations and to characterize the achieved immune response. After conducting various pharmaceutical evaluations of the formulations, immunokinetic studies were performed in mice, guinea pigs, and rabbits. The kinetics and the characteristics (antibody isotypes, etc.) of the immune response were studied, as well as the induced level of toxin neutralizing IgG antibodies, which are usually used as the only measures of the potency of vaccines. Results in mice show that intranasal vaccination results in a potent and rapid immune response, similar to that seen after subcutaneous immunization. In guinea pigs and rabbits, however, the subcutaneous immunization produced significantly stronger response than did intranasal vaccination. The most promising excipients were found to be either Polysorbate 20 or Cremophor EL in an aqueous mixture together with caprylic/capric glyceride. The results indicate that nontoxic and pharmaceutically acceptable excipients can be used for mucosal vaccination, providing an interesting alternative to parenteral vaccination.

Viral dynamics in vivo: limitations on estimates of intracellular delay and virus decay

Anti-viral drug treatment of human immunodeficiency virus type I (HIV-1) and hepatitis B virus (HBV) infections causes rapid reduction in plasma virus load. Viral decline occurs in several phases and provides information on important kinetic constants of virus replication in vivo and pharmacodynamical properties. We develop a mathematical model that takes into account the intracellular phase of the viral life-cycle, defined as the time between infection of a cell and production of new virus particles. We derive analytic solutions for the dynamics following treatment with reverse transcriptase inhibitors, protease inhibitors, or a combination of both. For HIV-1, our results show that the phase of rapid decay in plasma virus (days 2-7) allows precise estimates for the turnover rate of productively infected cells. The initial quasi-stationary phase (days 0-1) and the transition phase (days 1-2) are explained by the combined effects of pharmacological and intracellular delays, the clearance of free virus particles, and the decay of infected cells. Reliable estimates of the first three quantities are not possible from data on virus load only; such estimates require additional measurements. In contrast with HIV-1, for HBV our model predicts that frequent early sampling of plasma virus will lead to reliable estimates of the free virus half-life and the pharmacological properties of the administered drug. On the other hand, for HBV the half-life of infected cells cannot be estimated from plasma virus decay.

A cellular model to explain the pathogenesis of infection by the hepatitis B virus

The natural history of infection by the hepatitis B virus (HBV) depends on many factors, including the age and immunological status of the patient, and can range from acute transient infection to subclinical chronic hepatitis. Persistent infection often leads to the development of primary hepatocellular carcinoma. We consider a cellular model of HBV infection based on the hypothesis that the liver contains two populations of cells with contrasting responses to the virus. Our findings show that the model can be used to account for the wide variety of clinical manifestations of infection and can explain the observed age dependence of the main different outcomes of the disease.

Mathematical modeling of T-cell proliferation

A mathematical model of the T-lymphocyte proliferation process (in vivo and in vitro) is presented. This model takes into account cell-cycle progression and the regulation by lymphokines (lymphocyte activating factor interleukin 1 and T-cell growth factor interleukin 2). Using data on the generalized picture of the short-term course of viral hepatitis B, the parameter estimation procedure is carried out. The possibility of immunocorrection (by means of injection of a pharmacologic dose of IL-2) during the immune response to viral hepatitis B with T-lymphocyte deficiency is shown.

Analysis of a cellular model to account for the natural history of infection by the hepatitis B virus and its role in the development of primary hepatocellular carcinoma

Infection with the hepatitis B virus (HBV) can have many different outcomes. Transient infection may result in acute hepatitis or may remain subclinical. Persistent infection may also be subclinical, or may involve chronic active hepatitis, and can finally lead to the development of primary hepatocellular carcinoma. A mathematical model is given to account for the many different outcomes of HBV pathogenesis. The model is based on the assumption that the liver contains two cell populations with differing abilities to support active HBV replication and/or viral integration into the genome. The model helps account for the relationship of the different clinical courses of HBV infection to the age when the disease is acquired, together with the state of the immune system of the patient.

Mathematical model of antiviral immune response. II. Parameters identification for acute viral hepatitis B

Considering the mathematical model of antiviral immune response, we describe a method of fitting the model to the data characterizing acute viral hepatitis B. The corresponding procedure employs an idea of sequential parameter estimation to make the problem of fitting manageable. The underlying mechanisms responsible for the quantitative manifestations of the four basic phases of acute hepatitis B are used to select the model parameters. The identified model of acute hepatitis B is then tested with regard to the following situations: the effect of HBsAg-specific antibodies on HBV challenge; the vaccination and the resistance to challenge using live hepatitis B virus; the dose of viruses--the incubation time relationships. The sensitivity of the model with respect to parameters variations is then analysed. The developed model allows us to quantitatively simulate the basic features of the antiviral immune response during acute hepatitis B and some closely related phenomena.