As shown in Fig 1, the cytokines are secreted from their associated immune cells. In particular, TD also contributes to the I4 and I6 productions, respectively, as discussed previously. The cytokine secretion processes are often down-regulated by I10. Accordingly, the population dynamics of the cytokines can be described by dIidt=∑j=1Nki,jCjfj(I10)+kIi,TDTDfjD(I10)−diIi(7) where Cj is the density of the j-th cell, which produces Ii with a maxima rate ki,j, kIi,TD is the rate constant of the Ii production by TD, fj(I10) is the regulation function, i.e., the Hill function fj(I10)=11+(I10KCj,I10)2(8)