A Mathematical Model of Immune-System-Melanoma Competition

Figure 1

Conceptual model of the biological scenario. The model is composed by two compartments: the first compartment (bottom) where the treatment is administered, and the skin compartment (top) where the immune-system-melanoma competition occurs. Arrows are used to indicate the interaction between entities (i.e., the interaction between the antibodies and activated CTLs in the skin compartment), the change of a particular condition of an entity (i.e., the activation of naïve CTLs or the migration of antibodies from a compartment to another), the introduction and disappearing of entities (i.e., the production of newborn naïve CTLs by thymus or the disappearing of antigens that are presented to naïve CTLs). White boxes are used to better explain the meaning of the arrows. Both antibodies (𝐴𝑏) and activated OT1 CTLs (𝐸) migrate to the skin compartment. In the skin compartment, antibodies (𝐴_𝑠) stimulate duplication and infiltration into tumor mass of activated OT1 CTLs (𝐸_𝑠), which kill melanoma cells (𝐶). Killed melanoma cells release antigens (𝐴) that are captured by antigen presenting cells and presented to antigen-specific naïve OT1 CTLs (𝑁). Naïve OT1 CTLs are then stimulated to become active CTLs (𝐸_𝑠).