Table 1 Parameters used in simulations in different therapeutic cases introduced above

Resistance Detected Growth Parameters Specifications of Drug I τ 2 τ M → R τ 1 Specifications of Drug II
Drug-Induced KT = KN = KR = 106 (cells)
rT = rr = rM = 0.25
rn = 0.5 day−1
κ = 0124 day−1
T* = 3*105 cells
Constant Drug
C = 0.2 (mg.m-2)
a T = 0.15 (day−1)
t(start) = 50 days
10−3/day
Mutation starts at t = 0 day
10−4/day
Conversion starts at t = 50 days
0
(No intrinsic
resistance)
0 (No combination therapy)
Drug-Induced Same as above Constant Drug
C = 0.2 (mg.m-2)
aT = 0.15 (day−1)
t(start) = 50 days
10−3/day
Mutation starts at t = 0 day
10−4/day
Conversion starts at t = 150 days
0
(No intrinsic
resistance)
0 (No combination therapy)
Drug-Induced Same as above Decaying Drug
C = 0.2exp(-0.001 t) (mg.m-2)
aT = 0.15 (day−1)
t(start) = 50 days
10−3/day
Mutation starts at t = 0 day
10−4/day
Conversion starts at t = 50 days
0
(No intrinsic
resistance)
0 (No combination therapy)
Drug-Induced and Intrinsic Same as above Decaying Drug
C = 0.2exp(-0.001 t) (mg.m-2)
aT = 0.15 (day−1)
t(start) = 50 days
10−3/day
Mutation starts at t = 0 day
10−4/day
Conversion starts at t = 50 days
10−4/day C2 = 0.6 (mg.m-2)
aTR = 0.15(day-1)
t(start) = 50 days
1. The description of parameters are: τ 2: Mutation rate of wild tumor cells to tumor cells with the gene that can potentially go through second mutation to drug-resistant cells as they interact with the drug. τ M → R : Mutation/ conversion rate of mutated tumor cells with targeted gene to drug-resistant tumor cells. τ 1: Mutation rate of wild tumor cells to drug-resistant tumor cells. Specifications of Drug I (Effective on wild and mutated tumor cells). Specifications of Drug II (Effective on drug resistant tumor cells). Also, the common parameters related to the tumor growth are: KN, KT, K R: the carrying capacity of normal cells and two types of tumor cells. The per capita growth rate for the drug-responsive tumor cells, two groups of drug-resistant tumor cells, and normal cells are expressed by rT, rR, rM, rN. The T* is the critical size of the collection of tumor cells. κ is the parameter expresses interaction between tumor and normal cells