Determining accurate estimates for the characteristics of the severe acute respiratory syndrome coronavirus 2 in the upper and lower respiratory tracts, by fitting mathematical models to data, is made difficult by the lack of measurements early in the infection. To determine the sensitivity of the parameter estimates to the noise in the data, we developed a novel two-patch within-host mathematical model that considered the infection of both respiratory tracts and assumed that the viral load in the lower respiratory tract decays in a density dependent manner and investigated its ability to match population level data. We proposed several approaches that can improve practical identifiability of parameters, including an optimal experimental approach, and found that availability of viral data early in the infection is of essence for improving the accuracy of the estimates. Our findings can be useful for designing interventions.

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.

The relationship between transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and the amount of virus present in the proximity of a susceptible host is not understood. Here, we developed a within-host and aerosol mathematical model and used it to determine the relationship between viral kinetics in the upper respiratory track, viral kinetics in the aerosols, and new transmissions in golden hamsters challenged with SARS-CoV-2. We determined that infectious virus shedding early in infection correlates with transmission events, shedding of infectious virus diminishes late in the infection, and high viral RNA levels late in the infection are a poor indicator of transmission. We further showed that viral infectiousness increases in a density dependent manner with viral RNA and that their relative ratio is time-dependent. Such information is useful for designing interventions.

Combination antiviral drug therapy improves the survival rates of patients chronically infected with hepatitis B virus by controlling viral replication and enhancing immune responses. Some of these drugs have side effects that make them unsuitable for long-term administration. To address the trade-off between the positive and negative effects of the combination therapy, we investigated an optimal control problem for a delay differential equation model of immune responses to hepatitis virus B infection. Our optimal control problem investigates the interplay between virological and immunomodulatory effects of therapy, the control of viremia and the administration of the minimal dosage over a short period of time. Our numerical results show that the high drug levels that induce immune modulation rather than suppression of virological factors are essential for the clearance of hepatitis B virus.

T cell populations are regulated both by signals specific to the T-cell receptor (TCR) and by signals and resources, such as cytokines and space, that act independently of TCR specificity. Although it has been demonstrated that disruption of either of these pathways has a profound effect on T-cell development, we do not yet have an understanding of the dynamical interactions of these pathways in their joint shaping of the T cell repertoire. Complete DiGeorge Anomaly is a developmental abnormality that results in the failure of the thymus to develop, absence of T cells, and profound immune deficiency. After receiving thymic tissue grafts, patients suffering from DiGeorge anomaly develop T cells derived from their own precursors but matured in the donor tissue. We followed three DiGeorge patients after thymus transplantation to utilize the remarkable opportunity these subjects provide to elucidate human T-cell developmental regulation. Our goal is the determination of the respective roles of TCR-specific vs. TCR-nonspecific regulatory signals in the growth of these emerging T-cell populations. During the course of the study, we measured peripheral blood T-cell concentrations, TCRβ V gene-segment usage and CDR3-length spectratypes over two years or more for each of the subjects. We find, through statistical analysis based on a novel stochastic population-dynamic T-cell model, that the carrying capacity corresponding to TCR-specific resources is approximately 1000-fold larger than that of TCR-nonspecific resources, implying that the size of the peripheral T-cell pool at steady state is determined almost entirely by TCR-nonspecific mechanisms. Nevertheless, the diversity of the TCR repertoire depends crucially on TCR-specific regulation. The estimated strength of this TCR-specific regulation is sufficient to ensure rapid establishment of TCR repertoire diversity in the early phase of T cell population growth, and to maintain TCR repertoire diversity in the face of substantial clonal expansion-induced perturbation from the steady state. Protective adaptive immunity depends crucially on the enormous diversity of the T-cell receptor repertoire, the antigen receptors expressed collectively on T-cell populations. T cells develop from T-cell precursors that originate in the bone marrow and migrate to the thymus, where their T cell receptors are constructed stochastically, and tested for autoreactivity against a host of self antigens. Complete DiGeorge anomaly is a rare congenital disease in which the thymus fails to develop, blocking all T cell development and causing profound immunodeficiency. Thymus transplantation, performed in the first two post-natal years, allows the patient's own T cell precursors to develop in the engrafted thymus tissue into normal, functioning T cells. In addition to saving patients' lives, this procedure provides an extraordinary opportunity to study the de novo development of human T cell populations. We have developed a mathematical model to aid in the statistical analysis of the precious data from these patients. In addition to helping elucidate the means by which the size and diversity of T cell populations are jointly regulated, the insights gained from this study hold promise for the development of therapies to promote immune recovery after transplantation.