The M1 population originates from a constant source of M0  whose differentiation is stimulated by the external stimulus, CS . The M0 differentiation process, which is inhibited by I10, is up-regulated by Iγ and Iα at maximal rate k2 . As shown in Fig 1, TD also increases the M1 population and this process is also down-regulated by I10. Equation for describing the population dynamics of M1 with a decay rate, dM1, is then given by dM1dt=k1S11+(I10K1)2+k2(IγK2)2+(IαK3)21+(IγK2)2+(IαK3)2+(I10K4)2+k3TD11+(I10K5)2−dM1M1,(1) where k1=k1'M0, k2=k2'M0 (k1' and k2' are rate constants), and the regulation of the M0→M1 differentiation process is characterized by the Hill function whose coefficients are often chosen to be 2 to allow sufficient nonlinearity . In Eq 1, S is cigarette smoking intensity, whose values are given below.