Statistical Methods for Dynamic Models with Application

Recent outbreak of Human Influenza A H1N1 virus infection commands statistics playing an important role on guidance of prevention and treatment. Viral Dynamic Model, a set of ordinary differential equations (ODE) which describes interaction between virus and the immune system, has been proved useful in understanding the pathogenesis of virus infection and developing treatment strategy for many viral infection diseases, such as HIV, HCV, HBV and so on. In order to estimate biological/clinical meaningful parameters in various dynamic models, many statistical approaches have been developed in the last decade, from simple nonlinear least square (NLS) approach to more general nonlinear Mixed-effect modeling approach. However, for a general nonlinear ODE model, no close form solution is available and it has to be solved numerically. In such a situation, a general approach has to be developed to deal with this complexity. Two iomarkers, viral load and number of immune cells, are critical data source for dynamical models.