Kirschner and Panetta [33] developed a mathematical model of immunotherapy of a tumor: dtdE=cT1E+g1+ILp1EIL+s1,dtdT=rT(1KT)g2+TaET,dtdIL=g3+Tp2ET2IL+s2, where E(t) are the activated immune-system cells (commonly called effector cells) such as cytotoxic T-cells, macrophages, and natural killer cells that are cytotoxic to the tumor cells, T(t) are the tumor cells, IL(t) is the concentration of IL-2 (a type of cytokine signaling molecule in the im- mune system) in the single tumor-site compartment, and s1 and s2 are treatment terms, in this case the basal rates of effector cell formation and IL-2 formation, which are independent of the model parameters. (a) You may have very little knowledge about this particular system, but one way of understanding the model is to first identify the variables and parameters. We are given that E and T represent numbers of cells, IL is a chemical concentration in pg/L, and t is in days. Determine the missing parameter units in Table 3.1. (b) In Eq. (3.4) the first term on the right side of the equation, cT, represents the production of effector cells where the parameter c represents the antigenicity of the tumor, that is, the ability of the tumor to elicit an immune response. The form cT assumes that the production rate increases without bound as the number of tumor cells increases. Interpret all the other terms on the right-hand sides of Eqs. (3.4)-(3.6). (c) The mathematical representation of each of these terms you interpreted in part (b) comes along with assumptions of that particular biological process. Discuss these assumptions (e.g., what does the rate depend on? Is the rate assumed to saturate at large concentrations of some variable, or is it unbounded?). Table 3.1 Units and meanings of parameters in Eqs. (3.4)-(3.6) [33]