Testing non-autonomous models of antibody dynamics by parametric fitting of data on HAV vaccination: Exploratory study

Abstract

We explore the antibody dynamical system in our body, against Hepatitis A virus post vaccination. In this study, we explore this dynamical system comprising of antibodies, and plasma cells (short lived, and long lived memory cells), as analogous to the population dynamic system in demography. The common part of both systems is that, we are interested in the parameters of production and decay, since we observe that in humans, immunity decreases with age. We also explore the different existing statistical methods that help us in making inference about the dynamical system parameters, with the help of empirically observed data, antibody count in our case. One particular method of likelihood based estimation, Stochastic Approximation of the EM algorithm has been stressed in this project, but it comes with its share of problems too. We also present problems and difficulties that were faced in implementing other statistical tools, through standard statistical software.