Accuracy of results from mathematical and computer models of biological systems is often complicated by the presence of uncertainties in experimental data that are used to estimate parameter values. Current mathematical modeling approaches typically use either single-parameter or local sensitivity analyses. However, these methods do not accurately assess uncertainty and sensitivity in the system as, by default they hold all other parameters fixed at baseline values. Using techniques described within we demonstrate how a multi-dimensional parameter space can be studied globally so all uncertainties can be identified. Further, uncertainty and sensitivity analysis techniques can help to identify and ultimately control uncertainties. In this work we develop methods for applying existing analytical tools to perform analyses on a variety of mathematical and computer models. We compare two specific types of global sensitivity analysis indexes that have proven to be among the most robust and efficient. Through familiar and new examples of mathematical and computer models, we provide a complete methodology for performing these analyses, both in deterministic and stochastic settings, and propose novel techniques to handle problems encountered during this type of analyses.

A number of lines of evidence suggest that immunotherapy with the cytokine interleukin-2 (IL-2) may boost the immune system to fight tumors. CD4+ T cells, the cells that orchestrate the immune response, use these cytokines as signaling mechanisms for immune-response stimulation as well as lymphocyte stimulation, growth, and differentiation. Because tumor cells begin as 'self', the immune system may not respond in an effective way to eradicate them. Adoptive cellular immunotherapy can potentially restore or enhance these effects. We illustrate through mathematical modeling the dynamics between tumor cells, immune-effector cells, and IL-2. These efforts are able to explain both short tumor oscillations in tumor sizes as well as long-term tumor relapse. We then explore the effects of adoptive cellular immunotherapy on the model and describe under what circumstances the tumor can be eliminated.

We examine a model for the interaction of HIV with CD4 T cells that considers four populations: uninfected T cells, latently infected T cells, actively infected T cells, and free virus. Using this model we show that many of the puzzling quantitative features of HIV infection can be explained simply. We also consider effects of AZT on viral growth and T-cell population dynamics.The Two versions of the model are studied. In one the source of T cells from precursors is constant, whereas in the other the source of T cells decreases with viral load, mimicking the infection and killing of T-cell precursors. The latter gives more realistic predictions than the model with a constant source.

Lung granulomas are the pathologic hallmark of tuberculosis (TB). T cells are a major cellular component of TB lung granulomas and are known to play an important role in containment of Mycobacterium tuberculosis (Mtb) infection. We used cynomolgus macaques, a non-human primate model that recapitulates human TB with clinically active disease, latent infection or early infection, to understand functional characteristics and dynamics of T cells in individual granulomas. We sought to correlate T cell cytokine response and bacterial burden of each granuloma, as well as granuloma and systemic responses in individual animals. Our results support that each granuloma within an individual host is independent with respect to total cell numbers, proportion of T cells, pattern of cytokine response, and bacterial burden. The spectrum of these components overlaps greatly amongst animals with different clinical status, indicating that a diversity of granulomas exists within an individual host. On average only about 8% of T cells from granulomas respond with cytokine production after stimulation with Mtb specific antigens, and few “multi-functional” T cells were observed. However, granulomas were found to be “multi-functional” with respect to the combinations of functional T cells that were identified among lesions from individual animals. Although the responses generally overlapped, sterile granulomas had modestly higher frequencies of T cells making IL-17, TNF and any of T-1 (IFN-γ, IL-2, or TNF) and/or T-17 (IL-17) cytokines than non-sterile granulomas. An inverse correlation was observed between bacterial burden with TNF and T-1/T-17 responses in individual granulomas, and a combinatorial analysis of pair-wise cytokine responses indicated that granulomas with T cells producing both pro- and anti-inflammatory cytokines (e.g. IL-10 and IL-17) were associated with clearance of Mtb. Preliminary evaluation suggests that systemic responses in the blood do not accurately reflect local T cell responses within granulomas.