Figure 1

Blue curve: Evolution of normal cells. Red curve: Evolution of tumor cells. In this figure the blue curve illustrates the evolution of the normal cell population and the red curve illustrates the evolution of tumor cell population. The horizontal dashed line represents the magnitude of the critical population of tumor cells T^*; a) In this figure, the normal and the tumor cells grow, uncoupled following a Gompertzian law. K _T  = K _N  = 1.1*10⁶; r _T  = 0.4; r _n  = 0.4;T^* _C  = 3*10⁵; b) In this figure, the normal and the tumor cells grow conjointly using the following parameter values β = 1;ρ ₀  = 1;ρ1 = 1000; κ =0.028. In this case, the tumor cells can now suppress the growth behavior of normal cells. The population of the normal cells declines as the population magnitude of the tumor cells passes the critical value of T^* _C  = 3*10⁵ (the horizontal dashed line). The inhibition time in which the normal cells begin to decrease is approximately t = 30 (unit of time); c)β = 50. In this simulation the role of normal cells on the growth of tumor cells is significantly increased. As can be seen, the growth of tumor cells starts with a delay. As compared with the Figure 1b, the shrinkage starts at almost t = 40. Therefore, the normal cells maintain a higher population for a longer time. Figure 1d, expresses the evolution of normal and tumor cells when κ =0.039, β = 1. This time, the interaction effect of tumor cells on normal cells is increased. Under this set of simulation conditions, the population of normal cells goes to minimum value and they die out of system.