Contribution to the study of periodic chronic myelogenous leukemia

The period (in the order of 40 to 80 days) in periodic chronic myelogenous leukemia (PCML) oscillations is quite long compared with the duration of the cell cycle of the hematopoietic stem cells from which the oscillations are presumed to originate (in the order of one or two days). Our objective is to understand the origin of these long-period oscillations using a G0 model for stem cell dynamics. We determine the local stability conditions and show under what conditions the Hopf bifurcation may occur. We interpret the role of each parameter in the loss of stability, and then examine a simpler model to try to deduce possible changes at the stem-cell level that might be responsible for the characteristics PCML.     

HIV treatment models with time delay

The present paper shows possible effects of antiretroviral treatment on the dynamics of the spread of the disease of human immunodeficiency virus infection in a population of varying size. By introducing time delays, we model the latency period and the delayed onset of positive treatment effects in the patients. The Hopf bifurcation and stability behaviour of the delay differential-equation model are analysed and simulations for different scenarios depending on the size of the treatment-induced delay are presented, and the results are discussed in detail.     

Structured population on two patches: modeling dispersal and delay

We derive from the age-structured model a system of delay differential equations to describe the interaction of spatial dispersal (over two patches) and time delay (arising from the maturation period). Our model analysis shows that varying the immature death rate can alter the behavior of the homogeneous equilibria, leading to transient oscillations around an intermediate equilibrium and complicated dynamics (in the form of the coexistence of possibly stable synchronized periodic oscillations and unstable phase-locked oscillations) near the largest equilibrium.     

A simple SIS epidemic model with a backward bifurcation

It is shown that an SIS epidemic model with a non-constant contact rate may have multiple stable equilibria, a backward bifurcation and hysteresis. The consequences for disease control are discussed. The model is based on a Volterra integral equation and allows for a distributed infective period. The analysis includes both local and global stability of equilibria.     

Society's Metabolism

In this article, we inquire into the intellectual history ofthe application of the biological concept of metabolism to social systems-not as a metaphor; but as a material and energetic process within the economy and society vis-A-vis various natural systems. The paper reviews several scientific traditions that may contribute to such a view, including biology and ecology, social theory, cultural anthropology, and social geography It assembles widely scattered approaches dating from the 1860s onward and shows how they prepare the ground for the pioneers of "industrial metabolism" in the late 1960s. In connection to varying political perspedives, metabolism gradually takes shape as a powerful interdisciplinary concept It will take another 25 years before this approach becomes one of the most important paradigms for the empirical analysis of the society-nature-interaction across various disciplines. This later period will be the subject of part II of this literature review     

Population dynamics of a pathogen: the conundrum of vivax malaria

Building a mathematical model of population dynamics of pathogens within their host involves considerations of factors similar to those in ecology, as pathogens can prey on cells in the host. But within the multicellular host, attacked cell types are integrated with other cellular systems, which in turn intervene in the infection. For example, immune responses attempt to sense and then eliminate or contain pathogens, and homeostatic mechanisms try to compensate for cell loss. This review focuses on modeling applied to malarias, diseases caused by single-cell eukaryote parasites that infect red blood cells, with special concern given to vivax malaria, a disease often thought to be benign (if sometimes incapacitating) because the parasite only attacks a small proportion of red blood cells, the very youngest ones. However, I will use mathematical modeling to argue that depletion of this pool of red blood cells can be disastrous to the host if growth of the parasite is not vigorously check by host immune responses. Also, modeling can elucidate aspects of new field observations that indicate that vivax malaria is more dangerous than previously thought.     

Mean-square stability of a stochastic model for bacteriophage infection with time delays

We consider the stability properties of the positive equilibrium of a stochastic model for bacteriophage infection with discrete time delay. Conditions for mean-square stability of the trivial solution of the linearized system around the equilibrium are given by the construction of suitable Lyapunov functionals. The numerical simulations of the strong solutions of the arising stochastic delay differential system suggest that, even for the original non-linear model, the longer the incubation time the more the phage and bacteria populations can coexist on a stable equilibrium in a noisy environment for very long time.