T cell populations are regulated both by signals specific to the T-cell receptor and by signals and resources, such as interleukin 7, IL-7, interleukin 15, IL-15, and space, that act independently of T-cell receptor specificity. We followed four DiGeorge anomaly subjects after thymus transplants, measuring T cell counts, T-cell receptor Vß gene usage and T-cell receptor Vß spectratypes over two years or more. We find, through model-aided data analysis, that the carrying capacity corresponding to T-cell receptor-specific signals is approximately 1000-fold larger than that of T-cell receptor-nonspecific signals, implying that the total size of the peripheral T-cell pool is determined largely by regulation via T-cell receptor-nonspecific signals, but that T-cell receptor-specific regulation is strong enough -and necessary- to maintain robust T-cell receptor repertoire diversity in the face of substantial clonal expansion-induced diversity diminution.
Biological assays have been employed as indirect measures of T cell re- ceptor diversity. Flow cytometry generated data gives information about T-cell receptor Vß gene usage, which can then be used as a surrogate for antigen receptor diversity. In this study, we have used the flow cytometry data and defined a divergence metric that quantifies the deviation from normal of T cell receptor repertoire. We have shown that the divergence measure is dependent on the number of lymphocytes used in generating the flow cytometry data. We have derived two ways to correct for the measurement bias using mathematical and statistical approaches and have predicted a lower bound in the number of lymphocyte needed when using the divergence as a substitute for diversity. We have shown the need to address the dependence of the divergence measure on the sample size before it can be used to make prediction regarding the diversity of the T cell receptor repertoire.
In acute infections, antibody production in response to antigen can occur. Anti-HBs, the antibody to the surface antigen HBsAg is likely present, although it can only be detected after the resolution of infection and therefore its role in viral clearance is unknown. Experiments in ducks suggest that neutralizing antibodies might inhibit the spread of infection. However they can not affect viral replication in cells already infected. In this study, we develop a model that describes the effects of neutralizing antibody during hepatitis B acute infection. We compare the model predictions to patient data in order to predict the dynamics of the humoral immune response and possible reasons for its ineffectiveness.
During acute hepatitis B virus (HBV) infection viral loads reach high levels (~10^(10) HBV DNA per ml), and nearly every hepatocyte becomes infected. Nonetheless, 85 to 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.
Mathematical models have been used to understand the factors that govern infectious disease progression in viral infections. Here we focus on hepatitis B virus (HBV) dynamics during the acute stages of the infection and analyze the immune mechanisms responsible for viral clearance. We start by presenting the basic model used to interpret HBV therapy studies conducted in chronically infected patients. We then introduce additional models to study acute infection where immune responses presumably play an important role in determining whether the infection will be cleared or become chronic. We add complexity incrementally and explain each step of the modeling process. Finally, we validate the model against experimental data to determine how well it represents the biological system and, consequently, how useful are its predictions. In particular, we find that a cell-mediated immune response plays an important role in controlling the virus after the peak in viral load.
Ecologist Peter Turchin and anthropologist Andrey Korotayev (2006) propose that pre-state societies exhibit a deterministic relationship between population size and incidence of internal warfare or sociopolitical instability. We examine their model with data from Southwest Colorado between A.D. 600 and 1300 and find that it fits well during those periods when this area is a more or less closed system. It fits poorly during the time from about A.D. 1000-1200 when this area is heavily influenced first by the spread of the Chacoan system, and then, by its collapse and the local political reorganization that follows. The model is helpful in isolating periods in which the relationship between violence and population size is not as expected. The mechanisms by which it achieves its success need to be elaborated, a task we begin here.
The dynamics of HIV-1 infection consist of three distinct phases starting with primary infection, then latency and finally AIDS or drug therapy. In this paper we model the dynamics of primary infection and the beginning of latency. We show that allowing for time delays in the model better predicts viral load data when compared to models with no time delays. We also find that our model of primary infection predicts the turnover rates for productively infected T cells and viral totals to be much longer than compared to data from patients receiving anti-viral drug therapy. Hence the dynamics of the infection can change dramatically from one stage to the next. However, we also show that with the data available the results are highly sensitive to the chosen model. We compare the results using analysis and Monte Carlo techniques for three different models and show how each predicts rather dramatic differences between the fitted parameters. We show, using a v2 test, that these differences between models are statistically significant and using a jackknifing method, we find the confidence intervals for the parameters. These differences in parameter estimations lead to widely varying conclusions about HIV pathogenesis. For instance, we find in our model with time delays the existence of a Hopf bifurcation that leads to sustained oscillations and that these oscillations could simulate the rapid turnover between viral strains and the appropriate CTL response necessary to control the virus, similar to that of a predator–prey type system.
A nonlinear delay differential equation of van der Pol type is con- sidered. Local stability conditions are derived together with the existence of a sequence of Hopf bifurcations. The direction and stability of the bifurcating periodic solutions is obtained using the center manifold theory. By perturba- tion analysis techniques we obtain periodic solutions for both a weak and a strong feedback equation. The effect of a delay in the promotion or suppression of limit cycle oscillations is investigated.
Local stability and bifurcation analysis is performed in a system of delay differential equations that models the immune response during Hepatitis B infection. Using dynamical systems tools we try to predict the temporal transition to viral persistance during chronic infections.