The Humoral Immune Response toHaemophilus influenzaeType b: a Mathematical Model Based on T-zone and Germinal Center B-cell Dynamics

Abstract

Through careful mapping of the physiology of the T-zone and GC B-blast dynamics to a mathematical representation of the cell processes including proliferation, migration, differentiation, and cell death, a mathematical model is constructed to capture the dominant nominal primary, late follicular, and secondary humoral response toHaemophilus influenzaeType b. This model explicitly incorporates the dynamics of memory B-cells, T-zone and GC B-dynamics, IgM and IgG antibodies, avidity maturation, and IC presentation by FDCs into a coherent framework. This paper describes the relevant immunology, the pertinent physiological assumptions, the developed model, and the parameter identification procedure. The model parameters were found using a parameter identification procedure that capitalizes on the timing and interactions of certain dominant physiological attributes. Simulation results and validation tests indicate that the model reflects not only a nominal primary and secondary humoral immune response but also the tertiary and T-independent responses. The model shows robustness to variations in infection dosage, bacterial growth rate (virulence of the strain), and onset-timing of the secondary response. The utility of this model in studying the humoral immune response is demonstrated through suggested physiological assumptions, mechanisms, and rates to be eventually clinically evaluated as well as insights into vaccination design. The model and parameter identification techniques are easily adapted to other diseases which primarily evoke a humoral immune response.