Modelling HIV infection: model identification and global sensitivity analysis

Mathematical modelling can be very useful in studying complex objects in modern systems immunology. In this work we studied the problem of modelling immune cell population dynamics for HIV infection through the set of models with different levels of complexity, which include several characteristics of HIV infection dynamics (antigen presenting, cell and humoral immune reactions, the effect of regulatory T-lymphocytes). We formulated and solved the parameter estimation problem using maximal likelihood approach, for two variants of modelling error quantifying. The global sensitivity analysis was implemented with LHS-PRCC method. Models were compared by the residual functional values and using the information-theoretical framework. We present the extended Marchuk-Petrov model for HIV infection with delays. For solving the parameter estimation problem for this model we compared a number of numerical optimization methods.