It is well understood that there are key differences between a primary immune response and subsequent responses. Specifically, memory T cells that remain after a primary response drive the clearance of antigen in later encounters. While the existence of memory T cells is widely accepted, the specific mechanisms that govern their function are generally debated. In this paper, we develop a mathematical model of the immune response. This model follows the creation, activation, and regulation of memory T cells, which allows us to explore the differences between the primary and secondary immune responses. Through the incorporation of memory T cells, we demonstrate how the immune system can mount a faster and more effective secondary response. This mathematical model provides a quantitative framework for studying chronic infections and auto-immune diseases.
Keywords: Chronic infections; Immune memory; Memory T cells; Secondary immune response.