T cells derive from a constant source of immature T-cells (Th0 or T0), which are recruited and activated by DC in combination with specific cytokines as mentioned previously. For T1, T2, T8, and T17, the associated T-cell differentiation processes are down-regulated by I10. With inclusion of a decay rate, equations describing the dynamics of these T-cell populations can be expressed by dTidt=ki(IiKTi)21+(IiKTi)2+(I10KTi,10)2+kipTi11+(I10KTi,I10p)2−dTiTi(4) where Ti represents T1, T2, or T8, ki = k7, k8, or k9; Ii = I12, I4, or I21, and kpi = kp1, kp2, or kp8, which are the maximum rates for the self-proliferation of T1, T2, and T8, respectively. The T17 dynamics, which is up-regulated by both I6 and Iβ and is down- regulated by I10, can be described by dT17dt=k10(IβI6KT17,I6)21+(IβI6KT17,I6)2+(I10KT17,I10)2+k17pT1711+(I10KT17,I10p)2−dT17T17(5)