On the Interaction of the Human Immune System with Foreign Body: Mathematical Modeling Approach

Abstract

In this study, we present a simple but novel mathematical model to show the interaction of the five immunological cells in the lymphocyte family – the cytotoxic-Lymphocytes (T), B-cell antibody, killer T – cell (K), the helper T – cell (H) and the Regulatory T – cell (R) –with foreign bodies with or without treatment. The feasibility of the model and important parameters of invasion in mathematical epidemiology: the reproductive number, free and infection persistence equilibrium, local and global stability among others were established. Results confirm the effectiveness of booster (vaccination or drugs) of these cells (of the immune system as recovery of infected cells is quicker and sustainable with vaccinations that boost these body cells. By this study drug producers are better informed about the effectiveness of the boosting components of vaccination and drugs they produce and health workers have good insight and handful understanding of the efficacy of drugs and vaccines administered in the treatment of virus infection.