Comparison of gradient and simplex methods of the numerical solution of the inverse problem for the simplest model of infectious disease

The organism releases antibodies after antigens are recognized. This anti- bodies help to cope with disease. Individual characteristics of immunity and disease are different. Therefore the reaction of different people to the disease is not similar. In spite of this doctors often make a standard treatment plan for patients. Therefore it is important to be able to identify individual parameters of immunity and disease for each patient by blood, urine tests and so on. In this paper the problem for determining of the immune and disease parameters by measurements of the antigen and antibody concentrations in fixed times is numerically investigated. We use the misfit functional that describes the deviation between experimental and model data. The explicit expre- ssion of the gradient of the misfit functional based on the adjoint problem solution is obtained. The results of numerical calculations of inverse problem is discussed. The results obtained using the methods of Landveber's iterations and Nelder-Mead. Comparative analysis of these methods is discussed. It was demonstrated that Nelder- Mead method is more sensitive to the choice of the initial guess than the method of Landweber iteration. If the initial guess has been chosen “good enough” than it needs less steps than Landweber iteration method. But there are some set of possible initial guesses when Landweber iteration method converges but the Nelder-Mead method gives no results.