A silent bomb: the risk of anthrax as a weapon of mass destruction.
Explore the source record for details and available documents.
Anthrax↗
Biomedical subjects
G F Webb
Publications and source records attributed to G F Webb.
Dynamics of bacterial phenotype selection in a colonized host.
The population dynamics of Helicobacter pylori during colonization in an infected animal host provide a quantifiable experimental model of in vivo microbial phenotype evolution. Phenotype variability in H. pylori populations can be typed as polymorphic expression of Lewis antigens on their cell surfaces. The high mutational frequency of H. pylori for Lewis expression provides substrate for differential selection by the host. Experimental challenge and successful colonization of mice and gerbils allows tracking of H. pylori phenotype variability from the initial inoculation to the ultimate establishment of a quasispecies. Colonization data provide a quantitative experimental model of phenotype evolution in a relatively large population (>10(4) individuals) over a relatively long evolutionary time scale (>10(3) generations). A mathematical model is developed to interpret the data in terms of the dynamic processes occurring during colonization. The mathematical model distinguishes the roles of selection and mutation; quantifies the effects of initial phenotype diversity, mutational frequency, and selective advantage; and applies generally to phenotype evolution in biological populations.
Animals↗
Model of HIV-1 disease progression based on virus-induced lymph node homing and homing-induced apoptosis of CD4+ lymphocytes.
Several proposed theories have described the progression of HIV infection. Even so, no concrete evidence supports any as comprehensive, including, for example, why the CD4+ T-cell counts fall from 1000/mm3 of blood to roughly 100/mm3 over an average 10-year period, whereas concomitant viral loads are relatively constant, increasing by several orders of magnitude in late-stage disease. Here, we develop and validate a theoretical model that altered lymphocyte circulation patterns between the lymph system and blood due to HIV-induced enhanced lymph-node homing and subsequent apoptosis of resting CD4+ T cells can explain many aspects of HIV-1 disease progression. These results lead to a recalculation of the CD4+ lymphocyte dynamics during highly active antiretroviral therapy, and also suggest new targets for therapy.
Anti-HIV Agents↗
Understanding drug resistance for monotherapy treatment of HIV infection.
The purpose of this study was to investigate strategies in the monotherapy treatment of HIV infection in the presence of drug-resistant (mutant) strains. A mathematical system is developed to model resistance in HIV chemotherapy. It includes the key players in the immune response to HIV infection: virus and both uninfected CD4+ and infected CD4+ T-cell populations. We model the latent and progressive stages of the disease, and then introduce monotherapy treatment. The model is a system of differential equations describing the interaction of two distinct classes of HIV--drug-sensitive (wild type) and drug-resistant (mutant)--with lymphocytes in the peripheral blood. We then introduce chemotherapy effects. In the absence of treatment, the model produces the three types of qualitative clinical behavior--an uninfected steady state, an infected steady state (latency), and progression to AIDS. Simulation of treatment is provided for monotherapy, during the progression to AIDS state, in the consideration of resistance effects. Treatment benefit is based on an increase or retention in CD4+ T-cell counts together with a low viral titer. We explore the following treatment approaches: an antiviral drug which reduces viral infectivity that is administered early--when the CD4+ T-cell count is > or = 300/mm3, and the late--when the CD4+ T-cell count is less than 300/mm3. We compare all results with data. When treatment is initiated during the progression to AIDS state, treatment prevents T-cell collapse, but gradually loses effectiveness due to drug resistance. We hypothesize that it is the careful balance of mutant and wild-type HIV strains which provides the greatest prolonged benefit from treatment. This is best achieved when treatment is initiated when the CD4+ T-cell counts are greater than 250/mm3, but less than 400/mm3 in this model (i.e. not too early, not too late). These results are supported by clinical data. The work is novel in that it is the first model to accurately simulate data before, during and after monotherapy treatment. Our model also provides insight into recent clinical results, as well as suggests plausible guidelines for clinical testing in the monotherapy of HIV infection.
Anti-HIV Agents↗
A model for treatment strategy in the chemotherapy of AIDS.
Mathematical models are developed for the chemotherapy of AIDS. The models are systems of differential equations describing the interaction of the HIV infected immune system with AZT chemotherapy. The models produce the three types of qualitative clinical behavior: an uninfected steady state, an infected steady state (latency) and a progression to AIDS state. The effect of treatment is to perturb the system from progression to AIDS back to latency. Simulation of treatment schedules is provided for the consideration of treatment regimes. The following issues of chemotherapy are addressed: (i) daily frequency of treatment, (ii) early versus late initiation of treatment and (iii) intermittent treatment with intervals of no treatment. The simulations suggest the following properties of AZT chemotherapy: (i) the daily period of treatment does not affect the outcome of the treatment, (ii) treatment should not begin until after the final decline of T cells begins (not until the T cell population falls below approximately 300 mm-3) and then, it should be administered immediately and (iii) a possible strategy for treatment which may cope with side effects and/or resistance, is to treat intermittently with chemotherapy followed by interruptions in the treatment during which either a different drug or no treatment is administered. These properties are revealed in the simulations, as the model equations incorporate AZT chemotherapy as a weakly effective treatment process. We incorporate into the model the fact that AZT treatment does not eliminate HIV, but only restrains its progress. The mathematical model, although greatly simplified as a description of an extremely complex process, offers a means to pose hypotheses concerning treatment protocols, simulate alternative strategies and guide the qualitative understanding of AIDS chemotherapy.
Acquired Immunodeficiency Syndrome↗
Mathematical modeling of the loss of telomere sequences.
hortening of telomeres is one of the supposed mechanisms of cellular aging and death. An important question related to this so-called "end-replication" hypothesis is whether it can explain in quantitative detail the dynamic of cell sensescence in vitro and in vivo. A natural way to answer this question is to use mathematical modeling. In this paper, the models were successfully fitted to data on cultured fibroblasts from two different sources assuming that after reaching the Hayflick checkpoint on a single chromosome cells cease to proliferate. The main conclusion is that the end-replication hypothesis provides an explanation for the cell aging process which is quantitatively consistent with the data. As a secondary outcome, estimates were obtained of the rate of shortening of telomeres and several interesting mathematical results for branching processes with infinite type spaces arise.
Animals↗
A nonlinear structured population model of tumor growth with quiescence.
A nonlinear structured cell population model of tumor growth is considered. The model distinguishes between two types of cells within the tumor: proliferating and quiescent. Within each class the behavior of individual cells depends on cell size, whereas the probabilities of becoming quiescent and returning to the proliferative cycle are in addition controlled by total tumor size. The asymptotic behavior of solutions of the full nonlinear model, as well as some linear special cases, is investigated using spectral theory of positive simigroup of operators.
Animals↗
Dispersion population models discrete in time and continuous in space.
We analyze a discrete-time model of populations that grow and disperse in separate phases. The growth phase is a nonlinear process that allows for the effects of local crowding. The dispersion phase is a linear process that distributes the population throughout its spatial habitat. Our study quantifies the issues of survival and extinction, the existence and stability of nontrivial steady states, and the comparison of various dispersion strategies. Our results show that all of these issues are tied to the global nature of various model parameters. The extreme strategies of staying-in-place and going-everywhere-uniformly are compared numerically to diffusion strategies in various contexts. We approach the mathematical analysis of our model from a functional analysis and an operator theory point of view. We use recent results from the theory of positive operators in Banach lattices.
Environment↗
A model of proliferating cell populations with inherited cycle length.
A mathematical model of cell population growth introduced by J.L. Lebowitz and S.I. Rubinow is analyzed. Individual cells are distinguished by age and cell cycle length. The cell cycle length is viewed as an inherited property determined at birth. The density of the population satisfies a first order linear partial differential equation with initial and boundary conditions. The boundary condition models the process of cell division of mother cells and the inheritance of cycle length by daughter cells. The mathematical analysis of the model employs the theory of operator semigroups and the spectral theory of linear operators. It is proved that the solutions exhibit the property of asynchronous exponential growth.
Cell Cycle↗
A recovery-relapse epidemic model with spatial diffusion.
Explore the source record for details and available documents.
Age Factors↗
Diffusion epidemic models with incubation and crisscross dynamics.
A diffusion age-structured epidemic model is analyzed. The model describes an epidemic in a host-vector two-population system. Each population is diffusing in a spatial region. Each population is divided into susceptible, incubating, and infectious subclasses. The incubating and infectious subclasses in each population are determined by a structure variable corresponding to age since infection. The model consists of a system of nonlinear partial differential equations with crisscross dynamics. The existence, uniqueness, and asymptotic behavior of solutions are analyzed.
Chagas Disease↗
Asynchronous exponential growth in an age structured population of proliferating and quiescent cells.
A model of a proliferating cell population is analyzed. The model distinguishes individual cells by cell age, which corresponds to phase of the cell cycle. The model also distinguishes individual cells by proliferating or quiescent status. The model allows cells to transit between these two states at any age, that is, any phase of the cell cycle. The model also allows newly divided cells to enter quiescence at cell birth, that is, cell age 0. Sufficient conditions are established to assure that the cell population has asynchronous exponential growth. As a consequence of this asynchronous exponential growth the population stabilizes in the sense that the proportion of the population in any age range, or the fraction in proliferating or quiescent state, converges to a limiting value as time evolves, independently of the age distribution and proliferating or quiescent fractions of the initial cell population. The asynchronous exponential growth is proved by demonstrating that the strongly continuous linear semi-group associated with the partial differential equations of the model is positive, irreducible, and eventually compact.
Cell Cycle↗
Resistance, remission, and qualitative differences in HIV chemotherapy.
To understand the role of qualitative differences in multidrug chemotherapy for human immunodeficiency virus (HIV) infection in virus remission and drug resistance, we designed a mathematical system that models HIV multidrug chemotherapy including uninfected CD4+ T cells, infected CD4+ T cells, and virus populations. The model, which includes the latent and progressive stages of the disease and introduces chemotherapy, is a system of differential equations describing the interaction of two distinct classes of HIV (drug-sensitive [wild type] and drug-resistant [mutant]) with lymphocytes in the peripheral blood; the external lymphoid system contributes to the viral load. The simulations indicate that to preclude resistance, antiviral drugs must be strong enough and act fast enough to drive the viral population below a threshold level. The threshold depends upon the capacity of the virus to mutate to strains resistant to the drugs. Above the threshold, mutant strains rapidly replace wild-type strains. Below the threshold, resistant strains do not become established, and remission occurs. An important distinction between resistance and remission is the reduction of viral production in the external lymphoid system. Also the virus population rapidly rebounds when treatment is stopped even after extended periods of remission.
Anti-HIV Agents↗
Quiescence as an explanation of Gompertzian tumor growth.
In this paper we propose a mathematical model for the growth of solid tumors which employs quiescence as a mechanism to explain characteristic Gompertz-type growth curves. The model distinguishes between two types of cells within the tumor, proliferating and quiescent. Empirical data strongly suggest that the larger the tumor, the more likely it is that a proliferating cell becomes quiescent and the more unlikely it is that a quiescent cell reenters the proliferating cycle. These facts are taken as the basic assumptions of the model. It is shown that these assumptions imply diminishing of the growth fraction (i.e. proportion of proliferating cells), a phenomenon found in most tumors. Three qualitatively different cases are analyzed in detail and illustrated by examples. In the case of a tumor forming a necrotic center the model predicts that the tumor grows monotonically to its ultimate size according to a typical S-shaped Gompertz curve, and that the growth fraction tends to zero. In the case of true quiescence, where the dormant cells retain their capability of becoming proliferating, we distinguish between two types of tumors: one in which only proliferating cells can die and one in which there is mortality among quiescent cells, too. In the first case the predicted tumor growth occurs in the early stages in a way that is very similar to that of tumors forming a necrotic center; the growth fraction still tends to zero, but ultimately the tumor grows without bound. In the second case the tumor grows to a finite limit depending only on the vital rates, while the growth fraction decreases to a strictly positive value.
Cell Division↗