Biomathematics SeminarFall 2008Title: Evaluating Treatment of Hepatitis C for Hemolytic Anemia Management Abstract: The combination therapy of antiviral peg-interferon and ribavirin(RBV) has evolved as one of the better treatments for Hepatitis-C (HCV). In spite of its success in controlling HCV infection, it has also been associated with treatment related adverse side-e?ects. The most common among them is hemolytic anemia. More than 67 percent of treated chronic HCV patients show signs of acute anemia leading to dose reduction or even therapy cessation. A drug that contains ery- thropoietin (EPO) is often administered to stimulate the production of RBC in the bone marrow. This paper extends the basic mathe- matical model of Dahari et al. and studies the effect of combination therapy in light of anemia. In order to achieve this we introduce RBC concentration and drug amount in the model. Analysis of this model provides a quantification of the drug amount that is tolerable by the body without succumbing to hemolytic anemia. This will provide an estimate of the increment in RBC production necessary to keep from hemolytic anemia and settle on a balanced HCV treatment. Title: Multi-strain virus dynamics with mutations Abstract: We consider within-host virus models with $n\geq 2$ strains and allow mutations between the strains. If there are no mutations, a Lyapunov function establishes global stability of the steady state corresponding to the fittest strain. For small perturbations this steady state persists, perhaps with small concentrations of some or all other strains, depending on the connectivity of the graph describing all possible mutations. Finally, using a perturbation result due to Smith and Waltman, we show that this steady state also preserves global stability. Title: Spatial patterns in a PDE-based infectious disease model Abstract: A reaction-diffusion model for the spatial spread of some infectious diseases will be presented. Properties of the equilibrium states (existence, uniqueness, and stability) will be discussed. Title: Optimal control of vector-borne diseases Abstract: In this paper, we study the dynamics of a vector-transmitted disease under two assumptions. We first look at time dependent prevention and treatment efforts where optimal control theory is applied. Then we considered the autonomous counter part of the model and calculated an epidemiological parameter. Based on this parameter, we established conditions for the global stability of the disease-free equilibrium point of the model. |
