Table 4 Rules for actions and interactions between agents (\({\mathcal {N}}\): Normal distribution)

Cancer growth through (1) with \(a=10\,\beta -1, \,k=4, \,t_0 = 0.5,\, \beta \sim {\mathcal {N}}(\mu _2,\sigma _2)\)

Generate Innate IS cells: \(\{\text{K}, \text{M}_1, \text{N}_1\}= 100\times \{\eta _4:\eta _6\}\)

Recruiting of IS cells through (4) with \(\{p_2,p_6,p_{1,3}\}=\{\eta _7,\eta _8,\eta _9\}\)

Success of attack by IS cells through (4) with \(\{p_{A_8}, p_{A_6}, p_{A_3} \} = \{\eta _{10}, \eta _{11}, \eta _{12}\}\)

M\(\upvarphi\)s and Ns become pro-tumoral with \(\{p_7, p_{1,4}\} = \{\eta _{13},\eta _{14}\}\sim {\mathcal {N}}( \mu _1 / (\mu _1 + \mu _2), \sigma _1)\)

Generate Adaptive IS cells: \(\{\texttt{CD4+}T, \texttt{CD8+}T, \text{T}_{\mathrm{reg}}\}= 100\times \{\eta _{22}, \eta _{23}, \eta _{24}\}\)

Recruiting of T cells through (4) with \(\{p_7,p_8,p_9\}=\{\eta _{25},\eta _{26},\eta _{27}\}\)

T-cells strengthen each other using (4) with \(\{u_1,u_2,u_4\}=\{\eta _{28},\eta _{29},\eta _{30}\}\)

Success of CD8+T cells attacking CCs (4) with probability \(u_{3} = \eta _{31}\)