Mathematical modelling of growth of tumour cells with chemotherapeutic cells by using Yang–Abdel–Cattani fractional derivative operator

Figures & data

Table

S.N.	Parameters	Notation	Values taken
1	Fractional kill rate	$a_1$, $a_2$, $a_3$	0.2, 0.3, 0.1
2	Carrying capacity	$b_1$, $b_2$	1, 0.81
3	Competition terms	$c_1$, $c_2$, $c_3$, $c_4$	1, 0.55, 0.9, 1
4	Immune source rate	ε	0.33
5	Death rate	$d_1$, $d_2$	0.2, 1
6	Resistance response rate	ρ	0.2
7	Resistance threshold rate	μ	0.3
8	Per capita growth rate	$r_1$, $r_2$	1.1, 1
9	Diffusion rate	$D_N$, $D_T$, $D_I$, $D_U$	0.001, 0.001, 0.001, 0.001

Table

t	N	T	I	U
0.1	$5.4\times {10}^{-3}$	$1.2\times {10}^{-3}$	$5.1\times {10}^{-4}$	$2.2\times {10}^{-3}$
0.3	$4.4\times {10}^{-3}$	$1.18\times {10}^{-3}$	$4.6\times {10}^{-4}$	$2\times {10}^{-3}$
0.5	$3.9\times {10}^{-3}$	$1.12\times {10}^{-3}$	$2.1\times {10}^{-4}$	$1.7\times {10}^{-3}$
0.7	$2.9\times {10}^{-3}$	$0.98\times {10}^{-3}$	$6.9\times {10}^{-4}$	$1.2\times {10}^{-3}$

Figure 1. Growth rate of different cells – 3D representation. (a) Change rate of normal cells, (b) change rate of cancerous cells,(c) change rate of immune cells and (d) effect of chemotherapeutic drug.

Figure 2. Growth rate of different cells- 2D representation for t = 1. (a) Growth rate of normal cells for $\alpha =0.5,0.7$ and 0.9, (b) growth rate of cancerous cells for $\alpha =0.5,0.7$ and 0.9, (c) growth rate of resistant cells for $\alpha =0.5,0.7$ and 0.9 and (d) effect of chemotherapeutic drug for $\alpha =0.5,0.7$ and 0.9.

Data availability statement

The availability of statistics is already cited in the article.