Nonlocal finite difference discretization of a class of renewal equation models for epidemics.

In this paper we consider a non-standard discretization to a Volterra integro-differential system which includes a number of age-of-infection models in the literature. The aim is to provide a general framework to analyze the proposed scheme for the numerical solution of a class of problems whose continuous dynamic is well known in the literature and allow a deeper analysis in cases where the theory lacks.

Kinetics of in vivo proliferation and death of memory and naive CD8 T cells: parameter estimation based on 5-bromo-2'-deoxyuridine incorporation in spleen, lymph nodes, and bone marrow.

To study naive and memory CD8 T cell turnover, we performed BrdU incorporation experiments in adult thymectomized C57BL/6 mice and analyzed data in a mathematical framework. The following aspects were novel: 1) we examined the bone marrow, in addition to spleen and lymph nodes, and took into account the sum of cells contained in the three organs; 2) to describe both BrdU-labeling and -delabeling phase, we designed a general mathematical model, in which cell populations were distinguished based on the number of divisions; 3) to find parameters, we used the experimentally determined numbers of total and BrdU(+) cells and the BrdU-labeling coefficient. We treated mice with BrdU continuously via drinking water for up to 42 days, measured by flow cytometry BrdU incorporation at different times, and calculated the numbers of BrdU(+) naive (CD44(int/low)) and memory (CD44(high)) CD8 T cells. By fitting the model to data, we determined proliferation and death rates of both subsets. Rates were confirmed using independent sets of data, including the numbers of BrdU(+) cells at different times after BrdU withdrawal. We found that both doubling time and half-life of the memory population were approximately 9 wk, whereas for the naive subset the doubling time was almost 1 year and the half-life was roughly 7 wk. Our findings suggest that the higher turnover of memory CD8 T cells as compared with naive CD8 T cells is mostly attributable to a higher proliferation rate. Our results have implications for interpreting physiological and abnormal T cell kinetics in humans.

Simulating the effect of vaccine-induced immune responses on HIV infection.

The need for anti-HIV-1 vaccines is universally recognized. Although several potential vaccine formulations are being tested in clinical trials, the complexity of the viral system and the length of the experimentation required and its costs makes the goal of obtaining such a vaccine still elusive. We have built a mathematical model for the simulation of HIV-1 infection spreading into the body, which allows us study in silico the effect of hypothetical anti-HIV-1 vaccines having different properties. In particular, vaccines eliciting a cytolytic T-cell response, a humoral response, or both can be simulated. The vaccines considered can be envisaged either as preventive or therapeutic and can have different strength. The kinetic parameters used for solving the model are those of HIV-1 infection obtained from experimental and clinical observations. The vaccines are instead characterized by parameters that can be varied in order to mimic different behaviors: the rate of killing of the single effector cell and the rate of neutralization of the single antibody molecule; and the level of the immune response raised. The model allows us to predict which characteristics of immunogenicity a preventive or therapeutic vaccine should possess to be efficacious, and which are the key factors that most likely will affect its ability to control the spread of the infection. We discuss here the conclusions that can be drawn from a such a model and some of its limitations.