Estimation of immune response model parameters based on maximum likelihood method

Abstract

As a rule mathematical models used for investigations of disease mechanisms represent a system of ordinary differential equations. From the immunological point of view a disease is a process of an interaction between an antigen and cell populations of the immune system. Therefore concentrations of an antigen and immune system cells are state variables of the model.

The interaction between cell populations in the model is described by nonlinear terms, which are the product of state variables. These terms of the right part of the model with some coefficients make the model linear with respect to coefficients and nonlinear with respect to state variables. Bylinear systems [1] serve as an example of such models. Within the framework of the mathematical model the coefficients characterize the immune status of an organism. Therefore the problem of their estimation on the base of experimental and clinical data is of great importance for clinical practice and theoretical investigations. The paper deals with the approach mentioned in [2].