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Abstract: This paper deals with the analysis of simple model of an avascular solid tumour growth dynamics with a necrotic core. The analysis is focused to the conditions which guarantee existence and stability of a stationary solution to the model. The second part of the paper deals with the analysis of effects of an external source of nutrient on the process of necrotic core formation. This influence is visualised by numerical simulations. [Copyright &y& Elsevier]

In the paper, a model of multicellular spheroids dynamics is studied. It can be also interpreted as avascular tumour growth. The model is based on the diffusion of nutrient and mass conservation for two processes cell proliferation and apoptosis. Two types of apoptosis is taken into account-underlying and regulatory apoptosis. It is assumed that the process of regulatory apoptosis is delayed compared to proliferation and underlying apoptosis.Nonnegativity of solutions, steady state stability, and existence of periodic solutions are studied in the paper. Computer simulations of solutions are presented. Some conclusions for special values of the model parameters are stated. [Copyright &y& Elsevier]

In the paper, a simple model of solid avascular tumour growth is studied. The model is based on the reaction-diffusion dynamics and mass conservation law and is considered with delay in cell proliferation process. In the case considered in this paper, the model reduces to one ordinary differential equation with time delay which describes the evolution of tumour radius.Basic properties of the model are studied in the paper. Steady-state analysis is presented with respect to the magnitude of delay. Existence of periodic solutions is proved for some parameter values. Global stability is proved for other ones. Results are illustrated by computer simulations. [Copyright &y& Elsevier]

Abstract: The capability of the HIV to persist latent inside CD4+ T-cells is currently regarded as a barrier to recovery from infection. On the other hand, immune activation, which is a normal immune reaction to pathogens, is now recognized as a key ingredient to sustaining the HIV caused infection. Further, it has been shown that activation of infected memory T-cells indirectly promotes apoptosis (programmed cell death) of bystander CD4+ and CD8+ T-cells. In this paper we use standard modeling techniques to develop a model compliant with the above mentioned mechanisms. Our farthest goal is to study how the long-term depletion of T-cells that characterizes HIV pathogenesis depends on these mechanisms. Consequently, we conduct parameter estimation, and apply standard results of sensitivity analysis and principal component analysis of the state variables with respect to the parameters. [ABSTRACT FROM AUTHOR]

Abstract: We investigate a very simple model of growth of the dead zone in ischemic stroke, and in particular, the influence of the way cells die: necrosis or apoptosis. In necrosis the cells “explose” and release their interiors in extracellular space, which may lead to large variations in the extracellular concentrations of various ions and toxins. These ions may destabilize the cells which border the dead zone, leading in some cases to propagation phenomena (spreading depressions). In apoptosis on the contrary, the cells shrink by expulsing water in the extracellular space, and do not release their various toxins. As a consequence, it is assumed that they do not disturb their neighboring cells. This phenomenological model is aimed at weighting the various major mechanisms known to be involved in brain injury following an ischemic stroke. In this paper, we model the growth of the dead zone during ischemic stroke and discuss the influence of the way cells die on the final size of the ischemic core. We show that the model exhibits threshold phenomena, which is quite surprising, since this model spatially couples ordinary differential equations, therefore more complex behavior is awaited. [Copyright &y& Elsevier]