Mathematical Medicine and Biology - current issueMathematical Medicine and Biology - RSS feed of current issuePredator-prey model with disease infection in both populations- August 29, 2008 A predator–prey model with disease infection in both populations is proposed to account for the possibility of a contagious disease crossing species barrier from prey to predator. We obtain several threshold parameters from local analysis of various equilibria of the proposed system as well as coupled conditions on these threshold parameters which determine the stability of these equilibria. One of the coupled conditions, in the form of an ecological threshold number for the...http://imammb.oxfordjournals.org/cgi/content/short/25/3/247?rss=1 Identification of a chemotactic sensitivity in a coupled system- August 29, 2008 Chemotaxis is the process by which cells behave in a way that follows the chemical gradient. Applications to bacteria growth, tissue inflammation and vascular tumours provide a focus on optimization strategies. Experiments can characterize the form of possible chemotactic sensitivities. This paper addresses the recovery of the chemotactic sensitivity from these experiments while allowing for non-linear dependence of the parameter on the state variables. The existence of solutions to the forward.http://imammb.oxfordjournals.org/cgi/content/short/25/3/215?rss=1 An overset grid method for the study of reflex tearing- August 29, 2008 We present an overset grid method to simulate the evolution of human tear film thickness subject to reflex tearing. The free-surface evolution is governed by a single fourth-order non-linear equation derived from lubrication theory with specified film thickness and volume flux at each end. The model arises from considering the limiting case where the surfactant is strongly affecting the surface tension. In numerical simulations, the overset grid is composed of fine boundary grids near the upper.http://imammb.oxfordjournals.org/cgi/content/short/25/3/187?rss=1 An enzyme kinetic model of blood island formation- August 29, 2008 Blood islands are conglomerations of prevascular stem cells that form during vasculogenesis, a function critical to early vascular and hematopoietic development. In this paper, a model of blood island formation is proposed employing the approach of classical enzyme kinetics. Deterministic simulations of the model show the formation of blood island-like structures. These are compared to murine blood islands.http://imammb.oxfordjournals.org/cgi/content/short/25/3/233?rss=1 Inducing catastrophe in malignant growth- August 29, 2008 Mathematical catastrophe theory is used to describe cancer growth during any time-dependent program a(t) of therapeutic activity. The program may be actively imposed, e.g. as chemotherapy, or occur passively as an immune response. With constant therapy a(t), the theory predicts that cancer mass p(t) grows in time t as a cosine-modulated power law, with power = 1.618···, the Fibonacci constant. The cosine modulation predicts the familiar relapses and remissions of cancer...http://imammb.oxfordjournals.org/cgi/content/short/25/3/267?rss=1 |