Fall 1998 Mathematical Biology Seminar

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• 21 October at UH, special time 1:30
  Lajos Pusztai , Medical Oncology Fellow, MD Anderson Cancer Center
  "Contribution of non-linear dynamics to the biological behavior of cancer"
  
  ABSTRACT: Variation in biological behavior, from patient to patient and cell to cell within the same tumor, is fundamental to cancer. This variation is usually ascribed as the cumulative effect of a multitude of external or/and internal events that interact in a linear and predictable manner or are stochastic by nature. However, the origin of chance-like variations such as survival time of patients, or fluctuations of gene expression among individual cells, could also be traced to deterministic, non-linear (i.e. chaotic) systems. During the seminar examples will be presented when non-linear models adequately describe cancer-related biological phenomena. Such examples include chaotic oscillations and fractal patterns in cultured cancer cells, and order-disorder transitions in DNA structure during malignant transformation. One of the aims of the presentation is to further explore experimental designs that could evaluate the relevance of non-linear models to cancer biology.
• 4 November at Rice
  Michel Langlais , Mathematiques Appliquees de Bordeaux, Universite Victor Segalen, Bordeaux 2
  "Diffusive ecological and epidemiological models"
  
  ABSTRACT: For a variety of reasons stemming from both ecological and public health concerns it is important to understand the spatial spread of disease among animal populations. Elementary models use systems of ordinary differential equations to portray the circulation of epidemics and many epidemiological features may be incorporated into the modeling process. For example, one may wish to incorporate population dynamics, competition for resources, both horizontal and vertical transmission of disease, the effect of periods of latency, vaccination and temporary immunity the process. The most common method of accounting for the spatial spread of organisms is the use of diffusion approximations of Brownian dispersion. This typically produces weakly coupled systems of partial differential equations of reaction diffusion type. In this regard the speaker will survey recent and ongoing work concerning the use of differential equations in the modeling of ecological systems and the spread the of different infections.