Appendix 1: Failure-rate function \(\lambda _{i,j}(t)\) and repair rate \(\mu _{j,i}\) of the reduced ten states
$$\begin{aligned} \lambda _{10,9}(t)&= \lambda _{2,1}^{1}(t)+\lambda _{3,1}^{1}(t)+\lambda _{4,1}^{1}(t) +\lambda _{5,1}^{1}(t)\\&\quad +\,\lambda _{4,3}^{1}(t)+\lambda _{5,3}^{1}(t)+\lambda _{3,2}^{2}(t)\\&\quad +\,\lambda _{4,2}^{2}(t)+\lambda _{5,2}^{2}(t);\\ \lambda _{10,8}(t)&= 15\lambda _{5,4}^{3}(t);\\ \lambda _{10,7}(t)&= \lambda _{2,1}^{1}(t)+\lambda _{3,1}^{1}(t)+\lambda _{5,1}^{1}(t)\\&\quad +\,\lambda _{5,4}^{1}(t)+\lambda _{2,1}^{2}(t) +\lambda _{3,1}^{2}(t)\!+\!\lambda _{4,1}^{2}(t)\!+\!\lambda _{5,1}^{2}(t);\\ \lambda _{10,6}(t)&= \lambda _{2,1}^{1}(t)+\lambda _{3,1}^{1}(t)+\lambda _{4,1}^{1}(t)\\&\quad +\,\lambda _{5,1}^{1}(t)+\lambda _{4,2}^{1}(t)+\lambda _{5,2}^{1}(t)+\lambda _{3,2}^{2}(t)\\&\quad +\,\lambda _{4,2}^{2}(t)+\lambda _{5,2}^{2}(t);\\ \lambda _{10,5}(t)&= \lambda _{5,3}^{1}(t)+\lambda _{3,1}^{2}(t)+\lambda _{4,1}^{2}(t)\\&\quad +\,\lambda _{5,1}^{2}(t)+15\lambda _{5,3}^{3}(t);\\ \lambda _{10,4}(t)&= \lambda _{5,2}^{1}(t)+\lambda _{3,1}^{2}(t) +\lambda _{4,1}^{2}(t)+\lambda _{5,1}^{2}(t);\\ \lambda _{10,3}(t)&= \lambda _{4,1}^{1}(t)+\lambda _{5,1}^{1}(t);\\ \lambda _{10,2} (t)&= 15\lambda _{5,2}^{3} (t);\\ \lambda _{10,1}(t)&= \lambda _{5,1}^{1}(t)+15\lambda _{5,1}^{3}(t);\\ \lambda _{9,8}(t)&= 2\lambda _{{5},{4}}^{3} (t);\lambda _{9,7}(t)=\lambda _{5,4}^{2}(t);\\ \lambda _{9,6}(t)&= \lambda _{3,2}^{1}(t)+\lambda _{5,3}^{2}(t);\\ \lambda _{9,5}(t)&= \lambda _{2,1}^{2}(t)+\lambda _{5,3}^{3}(t);\\ \lambda _{9,3}(t)&= \lambda _{3,1}^{1}(t)+\lambda _{5,2}^{2}(t);\\ \lambda _{9,2}(t)&= 2\lambda _{5,2}^{3}(t);\\ \lambda _{9,1}(t)&= \lambda _{5,1}^{2}(t)+2\lambda _{5,1}^{3}(t);\\ \lambda _{8,7}(t)&= \lambda _{2,1}^{1}(t)+\lambda _{3,1}^{1}(t)+\lambda _{5,1}^{1}(t)+\lambda _{5,4}^{1}(t)\\&\quad +\,\lambda _{2,1}^{2}(t)+\lambda _{3,1}^{2}(t)+\lambda _{4,1}^{2}(t)\!+\!\lambda _{5,1}^{2}(t)\!+\!\lambda _{5,4}^{2}(t);\\ \lambda _{8,6}(t)&= \lambda _{2,1}^1 (t)+\lambda _{3,1}^1 (t)+\lambda _{4,1}^1 (t)+\lambda _{5,1}^1 (t)+\lambda _{3,2}^1(t)\\&\quad +\,\lambda _{4,2}^1 (t)+\lambda _{5,2}^1 (t)+\lambda _{3,2}^2 (t)+\lambda _{4,2}^2 (t)+\lambda _{5,2}^2(t)\\ \lambda _{8,5}(t)&= \lambda _{5,3}^{1}(t)+\lambda _{3,1}^{2}(t)\!+\!\lambda _{4,1}^{2}(t)\!+\!\lambda _{5,1}^{2}(t)+17\lambda _{4,3}^{3}(t);\\ \lambda _{8,4}(t)&= \lambda _{5,2}^{1}(t)+\lambda _{3,1}^{2}(t)+\lambda _{4,1}^{2}(t)+\lambda _{5,1}^{2}(t);\\ \lambda _{8,3}(t)&= \lambda _{3,1}^{1}(t)+\lambda _{4,1}^{1}(t)+\lambda _{5,1}^{1}(t)+\lambda _{5,2}^{2}(t);\\ \lambda _{8,2}(t)&= 17\lambda _{4,2}^{3} (t);\\ \lambda _{8,1}(t)&= \lambda _{5,1}^{1}(t)+\lambda _{5,1}^{2}(t)+17\lambda _{4,1}^{3}(t);\\ \lambda _{7,6}(t)&= 2\lambda _{4,3}^{2}(t);\\ \lambda _{7,5}(t)&= 2\lambda _{4,3}^{1}(t)+2\lambda _{4,3}^{3}(t)+2\lambda _{5,3}^{3}(t);\\ \lambda _{7,4}(t)&= 2\lambda _{4,2}^1 (t);\lambda _{7,3}(t)=2*\lambda _{4,2}^{2}(t);\\ \lambda _{7,2}(t)&= 2\lambda _{4,2}^{3}(t)+2\lambda _{5,2}^{3}(t);\\ \lambda _{7,1}(t)&= 2\lambda _{4,1}^{1}(t)+2\lambda _{4,1}^{2}(t)+2\lambda _{4,1}^{3}(t)+2\lambda _{5,1}^{3}(t);\\ \lambda _{6,5}(t)&= 2\lambda _{4,3}^{3}(t)+2\lambda _{5,3}^{3}(t);\\ \lambda _{6,4}(t)&= 2\lambda _{2,1}^{2}(t); \end{aligned}$$
$$\begin{aligned} \lambda _{6,3}(t)&= 2\lambda _{2,1}^{1}(t)+2\lambda _{3,2}^{2}(t);\\ \lambda _{6,2}(t)&= 2\lambda _{4,2}^{3}(t)+2\lambda _{5,2}^{3}(t);\\ \lambda _{6,1}(t)&= 3\lambda _{3,1}^{2}(t)\!+\!\lambda _{4,1}^{2}(t)\!+\!\lambda _{5,1}^{2}(t)+2\lambda _{4,1}^{3}(t)+2\lambda _{5,1}^{3}(t);\\ \lambda _{5,4}(t)&= 3\lambda _{3,2}^{1}(t)+\lambda _{4,2}^{1}(t)+\lambda _{5,2}^{1}(t)+\lambda _{2,1}^{2}(t)+\lambda _{3,1}^{2}(t)\\&\quad +\,\lambda _{4,1}^{2}(t)+\lambda _{5,1}^{2}(t);\\ \lambda _{5,3}(t)&= \lambda _{2,1}^{1}(t)+\lambda _{3,1}^{1}(t)+\lambda _{4,1}^{1}(t)+\lambda _{5,1}^{1}(t)\\&\quad +\,\lambda _{3,2}^{2}(t)+\lambda _{4,2}^{2}(t)+\lambda _{5,2}^{2}(t);\\ \lambda _{5,2} (t)&= 22\lambda _{3,2}^{3} (t)+\lambda _{4,2}^{3} (t)+\lambda _{5,2}^{3} (t);\\ \lambda _{5,1}(t)&= 3\lambda _{3,1}^{1}(t)+\lambda _{4,1}^{1}(t)+\lambda _{5,1}^{1}(t)\\&\quad +\,17\lambda _{3,1}^{3}(t)+\lambda _{4,1}^{3}(t)+\lambda _{5,1}^{3}(t);\\ \lambda _{4,2}(t)&= \lambda _{3,2}^{2}(t)+\lambda _{4,2}^{2}(t)+\lambda _{5,2}^{2}(t);\\ \lambda _{4,1}(t)&= 2\lambda _{{2},{1}}^{1} (t)+\lambda _{{3},{1}}^{3} (t)\\&\quad +\,\lambda _{{4},{1}}^{3} (t)+\lambda _{{5},{1}}^{3} (t);\\ \lambda _{3,2}(t)&= \lambda _{3,2}^{3}(t)+\lambda _{4,2}^{3}(t)+\lambda _{5,2}^{3}(t);\\ \lambda _{3,1}(t)&= 3\lambda _{2,1}^{2}(t)+\lambda _{3,1}^{3}(t)+\lambda _{4,1}^{3}(t)+\lambda _{5,1}^{3}(t);\\ \lambda _{2,1}(t)&= 2\lambda _{2,1}^{1}(t)+\lambda _{3,1}^{1}(t)+\lambda _{4,1}^{1}(t)+\lambda _{5,1}^{1}(t)+\lambda _{2,1}^{2}(t)\\&\quad +\,\lambda _{3,1}^{2}(t)+\lambda _{4,1}^{2}(t)+\lambda _{5,1}^{2}(t)+24\lambda _{2,1}^{3}(t);\\ \mu _{9,10}&= \mu _{1,2}^{1}+\mu _{1,3}^{1}+\mu _{1,4}^{1}+\mu _{1,5}^{1}+\mu _{3,4}^{1}+\mu _{3,5}^{1}\\&\quad +\,\mu _{2,4}^{2}+\mu _{2,5}^{2};\\ \mu _{8,10}&= 15\mu _{4,5}^{3};\\ \mu _{7,10}&= \mu _{1,2}^{1}+\mu _{1,3}^{1}+\mu _{1,4}^{1}+\mu _{1,5}^{1}+\mu _{4,5}^{1}\\&\quad +\,\mu _{3,4}^{1}+\mu _{3,5}^{1}+\mu _{2,4}^{2}+\mu _{2,5}^{2};\\ \mu _{6,10}&= \mu _{1,2}^{1}+\mu _{1,3}^{1}+\mu _{1,4}^{1}+\mu _{1,5}^{1}+\mu _{2,4}^{1}+\mu _{2,5}^{1}\\&\quad +\,\mu _{2,4}^{2}+\mu _{2,5}^{2};\\ \mu _{5,10}&= \mu _{3,5}^{1}+\mu _{1,3}^{2}+\mu _{1,4}^{2}+\mu _{1,5}^{2}+15\mu _{3,5}^{3};\\ \mu _{4,10}&= \mu _{2,5}^{1}+\mu _{1,3}^{2}+\mu _{1,4}^{2}+\mu _{1,5}^{2};\\ \mu _{3,10}&= \mu _{1,4}^1 +\mu _{1,5}^1 ;\mu _{2,10}=15\mu _{2,5}^{3};\\ \mu _{1,10}&= 15\mu _{1,5}^{3};\\ \mu _{8,9}&= 2\mu _{4,5}^3 ;\mu _{7,9}=\mu _{4,5}^{2};\\ \mu _{6,9}&= \mu _{2,3}^{1}+\mu _{3,5}^{2};\\ \mu _{5,9}&= 2\mu _{3,5}^{3};\\ \mu _{3,9}&= \mu _{1,3}^{1}+\mu _{2,5}^{2};\\ \mu _{2,9}&= 2\mu _{2,5}^{3};\\ \mu _{1,9}&= \mu _{1,5}^{2}+2\mu _{1,5}^{3};\\ \mu _{7,8}&= \mu _{1,2}^{1}+\mu _{1,3}^{1}+\mu _{1,4}^{1}+\mu _{1,5}^{1}+\mu _{4,5}^{1}\\&\quad +\,\mu _{1,2}^{2}+\mu _{1,3}^{2}+\mu _{1,4}^{2}+\mu _{1,5}^{2}+\mu _{4,5}^{2};\\ \mu _{6,8}&= \mu _{1,2}^{1}+\mu _{1,3}^{1}+\mu _{1,4}^{1}+\mu _{1,5}^{1}+\mu _{2,3}^{1}\\&\quad +\,\mu _{2,4}^{1}+\mu _{2,5}^{1}+\mu _{2,4}^{2}+\mu _{2,5}^{2}+\mu _{3,5}^{2};\\ \mu _{5,8}&= \mu _{3,5}^{1}+\mu _{1,3}^{2}+\mu _{1,4}^{2}+\mu _{1,5}^{2}+17\mu _{3,4}^{3};\\ \mu _{4,8}&= \mu _{2,5}^{1}+\mu _{1,3}^{2}+\mu _{1,4}^{2}+\mu _{1,5}^{2}; \end{aligned}$$
$$\begin{aligned} \mu _{3,8}&= \mu _{1,3}^{1}+\mu _{1,4}^{1}+\mu _{1,5}^{1}+\mu _{2,5}^{2};\\ \mu _{2,8}&= 17\mu _{2,4}^{3};\\ \mu _{1,8}&= \mu _{1,5}^{2}+17\mu _{1,4}^{3};\\ \mu _{7,8}&= \mu _{1,2}^{1}+\mu _{1,3}^{1}+\mu _{1,4}^{1}+\mu _{1,5}^{1}+\mu _{4,5}^{1}\\&\quad +\,\mu _{1,2}^{2}+\mu _{1,3}^{2}+\mu _{1,4}^{2}+\mu _{1,5}^{2}+\mu _{4,5}^{2};\\ \mu _{6,8}&= \mu _{1,2}^{1}+\mu _{1,3}^{1}+\mu _{1,4}^{1}+\mu _{1,5}^{1}+\mu _{2,3}^{1}+\mu _{2,4}^{1}\\&\quad +\,\mu _{2,5}^{1}+\mu _{2,4}^{2}+\mu _{2,5}^{2}+\mu _{3,5}^{2};\\ \mu _{5,8}&= \mu _{3,5}^{1}+\mu _{1,3}^{2}+\mu _{1,4}^{2}+\mu _{1,5}^{2}+17\mu _{3,4}^{3};\\ \mu _{4,8}&= \mu _{2,5}^{1}+\mu _{1,3}^{2}+\mu _{1,4}^{2}+\mu _{1,5}^{2};\\ \mu _{3,8}&= \mu _{1,3}^{1}+\mu _{1,4}^{1}+\mu _{1,5}^{1}+\mu _{2,5}^{2};\\ \mu _{2,8}&= 17\mu _{2,4}^{3};\\ \mu _{1,8}&= \mu _{1,5}^{2}+17\mu _{1,4}^{3};\\ \mu _{7,8}&= \mu _{1,2}^{1}+\mu _{1,3}^{1}+\mu _{1,4}^{1}+\mu _{1,5}^{1}+\mu _{4,5}^{1}+\mu _{1,2}^{2}\\&\quad +\,\mu _{1,3}^{2}+\mu _{1,4}^{2}+\mu _{1,5}^{2}+\mu _{4,5}^{2};\\ \mu _{6,8}&= \mu _{1,2}^{1}+\mu _{1,3}^{1}+\mu _{1,4}^{1}+\mu _{1,5}^{1}+\mu _{2,3}^{1}+\mu _{2,4}^{1}\\&\quad +\,\mu _{2,5}^{1}+\mu _{2,4}^{2}+\mu _{2,5}^{2}+\mu _{3,5}^{2};\\ \mu _{5,8}&= \mu _{3,5}^{1}+\mu _{1,3}^{2}+\mu _{1,4}^{2}+\mu _{1,5}^{2}+17\mu _{3,4}^{3};\\ \mu _{4,8}&= \mu _{2,5}^{1}+\mu _{1,3}^{2}+\mu _{1,4}^{2}+\mu _{1,5}^{2};\\ \mu _{3,8}&= \mu _{1,3}^{1}+\mu _{1,4}^{1}+\mu _{1,5}^{1}+\mu _{2,5}^{2};\\ \mu _{2,8}&= 17\mu _{2,4}^{3};\\ \mu _{1,8}&= \mu _{1,5}^{2}+17\mu _{1,4}^{3};\\ \mu _{6,7}&= 2\mu _{3,4}^{2};\\ \mu _{5,7}&= 2\mu _{3,4}^{1}+2\mu _{3,4}^{3}+2\mu _{3,5}^{3};\\ \mu _{4,7}&= 2\mu _{2,4}^{1};\\ \mu _{3,7}&= 2\mu _{2,4}^{2};\\ \mu _{2,7}&= 2\mu _{2,4}^{3}+2\mu _{2,5}^{3};\\ \mu _{1,7}&= \mu _{1,4}^{1}+2\mu _{1,4}^{2}+2\mu _{1,4}^{3}+2\mu _{1,5}^{3};\\ \mu _{5,6}&= 2\mu _{3,4}^{3}+2\mu _{3,5}^{3};\\ \mu _{4,6}&= 2\mu _{1,2}^{2};\\ \mu _{3,6}&= 2\mu _{1,2}^{1}+2\mu _{2,3}^{2};\\ \mu _{2,6}&= 2\mu _{2,4}^{3}+2\mu _{2,5}^{3};\\ \mu _{1,6}&= 2\mu _{1,3}^{2}+2\mu _{1,4}^{3}+2\mu _{1,5}^{3};\\ \mu _{4,5}&= 3\mu _{2,3}^{1}+\mu _{2,4}^{1}+\mu _{2,5}^{1}+\mu _{1,2}^{2}\\&\quad +\,\mu _{1,3}^{2}+\mu _{1,4}^{2}+\mu _{1,5}^{2};\\ \mu _{3,5}&= \mu _{1,2}^{1}+\mu _{1,3}^{1}+\mu _{1,4}^{1}+\mu _{1,5}^{1}\\&\quad +\,\mu _{2,3}^{2}+\mu _{2,4}^{2}+\mu _{2,5}^{2};\\ \mu _{2,5}&= 22\mu _{2,3}^{3}+\mu _{2,4}^{3}+\mu _{2,5}^{3}; \end{aligned}$$
$$\begin{aligned} \mu _{1,5}&= \mu _{1,3}^{2}+\mu _{1,4}^{2}+\mu _{1,5}^{2}+22\mu _{1,3}^{3}+\mu _{1,4}^{3}+\mu _{1,5}^{3};\\ \mu _{2,4}&= \mu _{2,3}^{3}+\mu _{2,4}^{3}+\mu _{2,5}^{3};\\ \mu _{1,4}&= 3\mu _{1,2}^{1}+\mu _{1,3}^{3}+\mu _{1,4}^{3}+\mu _{1,5}^{3};\\ \mu _{2,3}&= \mu _{2,3}^{3}+\mu _{2,4}^{3}+\mu _{2,5}^{3};\\ \mu _{1,3}&= 3\mu _{1,2}^{2}+\mu _{1,3}^{3}+\mu _{1,4}^{3}+\mu _{1,5}^{3};\\ \mu _{1,2}&= \mu _{1,2}^{1}+2\mu _{1,2}^{2}+2\mu _{1,3}^{2}+\mu _{1,5}^{2}+24\mu _{1,2}^{3}+\mu _{1,4}^{2}; \end{aligned}$$
Appendix 2: NHCTMM Chapman–Kolmogorov equations of the reduced ten states
$$\begin{aligned} dP_{10} (t)/dt&= -\alpha _{10}(t)P_{10} (t)+\mu _{9,10} P_9 (t)+\mu _{8,10} P_8 (t)\\&\quad +\,\mu _{7,10} P_7 (t)+\mu _{6,10} P_6 (t)+\mu _{5,10} P_5 (t)\\&\quad +\,\mu _{4,10} P_4 (t) +\,\mu _{3,10} P_3 (t)+\mu _{2,10} P_2 (t)\\&\quad +\,\mu _{1,10} P_1 (t)\\ dP_9 (t)/dt&= \lambda _{10,9}(t)P_{10} (t)-\alpha _9(t)P_9 (t)\\&\quad +\,\mu _{8,9} P_8 (t)+\,\mu _{7,9} P_7 (t)+\mu _{6,9} P_6 (t)\\&\quad +\,\mu _{5,9} P_5 (t) +\mu _{4,9} P_4 (t)+\,\mu _{3,9} P_3 (t)\\&\quad +\,\mu _{2,9} P_2 (t)+\mu _{1,9} P_1 (t) \\ dP_8 (t)/dt&= \lambda _{10,8}(t)P_{10} (t)+\lambda _{9,8}(t)P_9 (t)-\alpha _8(t)P_8 (t)\\&\quad +\,\mu _{7,8} P_7 (t)+\mu _{6,8} P_6 (t)+\mu _{5,8} P_5 (t) \\&\quad +\,\mu _{4,8} P_4 (t)+\,\mu _{3,8} P_3 (t)+\mu _{2,8} P_2 (t)\\&\quad +\,\mu _{1,8} P_1 (t) \\ dP_7 (t)/dt&= \lambda _{10,7}(t)P_{10} (t)+\lambda _{9,7}(t)P_9 (t)+\lambda _{8,7}(t)P_8 (t)\\&\quad -\,\alpha _7(t)P_7 (t)+\mu _{6,7} P_6 (t)\\&\quad +\,\mu _{5,7} P_5 (t)+\mu _{4,7} P_4 (t) \\&\quad +\,\mu _{3,7} P_3 (t)+\mu _{2,7} P_2 (t)+\mu _{1,7} P_1 (t) \\ dP_6 (t)/dt&= \lambda _{10,6}(t)P_{10} (t)+\lambda _{9,6}(t)P_9 (t)+\lambda _{8,6}(t)P_8 (t)\\&\quad +\,\lambda _{7,6}(t)P_7 (t)-\alpha _6(t)P_6 (t)+\mu _{5,6} P_5 (t) \\&\quad +\,\mu _{4,6} P_4 (t)+\mu _{3,6} P_3 (t)+\mu _{2,6} P_2 (t)\\&\quad +\,\mu _{1,6} P_1 (t) \\ dP_5 (t)/dt&= \lambda _{10,5}(t)P_{10} (t)+\lambda _{9,5}(t)P_9 (t)+\lambda _{8,5}(t)P_8 (t)\\&\quad +\,\lambda _{7,5}(t)P_7 (t)+\lambda _{6,5}(t)P_6 (t)-\alpha _5(t)P_5 (t) \\&\quad +\,\mu _{4,5} P_4 (t)+\mu _{3,5} P_3 (t)+\mu _{2,5} P_2 (t)\\&\quad +\,\mu _{1,5} P_1 (t) \\ dP_4 (t)/dt&= \lambda _{10,4}(t)P_{10} (t)+\lambda _{9,4}(t)P_9 (t)+\lambda _{8,4}(t)P_8 (t)\\&\quad +\,\lambda _{7,4}(t)P_7 (t)+\lambda _{6,4}(t)P_6 (t)+\lambda _{5,4}(t)P_5 (t) \\&\quad -\,\alpha _4(t)P_4 (t)+\mu _{3,4} P_3 (t)+\mu _{2,4} P_2 (t)\\&\quad +\,\mu _{1,4} P_1 (t) \\ dP_3 (t)/dt&= \lambda _{10,3}(t)P_{10} (t)+\lambda _{9,3}(t)P_9 (t)+\lambda _{8,3}(t)P_8 (t)\\&\quad +\,\lambda _{7,3}(t)P_7 (t)+\lambda _{6,3}(t)P_6 (t)+\lambda _{5,3}(t)P_5 (t) \\&\quad +\,\lambda _{4,3}(t)P_4 (t)-\alpha _3(t)P_3 (t)+\mu _{2,3} P_2 (t)\\&\quad +\,\mu _{1,3} P_1 (t) \\ dP_2 (t)/dt&= \lambda _{10,2}(t)P_{10} (t)+\lambda _{9,2}(t)P_9 (t)+\lambda _{8,2}(t)P_8 (t)\\&\quad +\,\lambda _{7,2}(t)P_7 (t)+\lambda _{6,2}(t)P_6 (t)+\lambda _{5,2}(t)P_5 (t) \\&\quad +\,\lambda _{4,2}(t)P_4 (t)+\lambda _{3,2}(t)P_3 (t)-\alpha _2(t)P_2 (t)\\&\quad +\,\mu _{1,2} P_1 (t) \\ dP_1 (t)/dt&= \lambda _{10,1}(t)P_{10} (t)+\lambda _{9,1}(t)P_9 (t)+\lambda _{8,1}(t)P_8 (t)\\&\quad +\,\lambda _{7,1}(t)P_7 (t)+\lambda _{6,1}(t)P_6 (t)+\lambda _{5,1}(t)P_5 (t) \\&\quad +\,\lambda _{4,1}(t)P_4 (t)+\lambda _{3,1}(t)P_3 (t)+\lambda _{2,1}(t)P_2 (t)\\&\quad -\,\alpha _1(t)P_1 (t) \end{aligned}$$
where:
$$\begin{aligned} \alpha _{10}(t)&= \lambda _{{2},{1}}^{1} (t)+\lambda _{{4},{3}}^{1} (t)+\lambda _{{3},{2}}^{2} (t)+\,15\lambda _{{5},{4}}^{3} (t)+\lambda _{{2},{1}}^{1} (t)\\&\quad +\,\lambda _{{5},{4}}^{1} (t)\!+\!\lambda _{{2},{1}}^{2} (t)\!+\!\lambda _{{2},{1}}^{1} (t)+\lambda {{3},{2}}^{2} (t)+\lambda _{{3},{1}}^{1} (t) \\&\quad +\,\lambda _{{4},{1}}^{1} (t)+\,\lambda _{{5},{1}}^{1} (t)+\lambda _{{5},{3}}^{1}(t)+\lambda _{{4},{2}}^{2} (t)+\lambda _{{5},{2}}^{2} (t)\\&\quad +\,\lambda _{{3},{1}}^{1} (t)+\lambda _{{5},{1}}^{1}(t)+\lambda _{{3},{1}}^{2} (t)+\lambda _{{4},{1}}^{2} (t)+\,\lambda _{{5},{1}}^{2} (t) \\&\quad +\,\lambda _{{3},{1}}^{1}(t)+\lambda _{{4},{1}}^{1} (t)+\,\lambda _{{5},{1}}^{1} (t)+\lambda _{{4},{2}}^{1} (t)+\lambda _{{5},{2}}^{1} (t)\\&\quad +\,\lambda _{{4},{2}}^{2} (t)+\lambda _{{5},{2}}^{2} (t)\lambda _{{5},{3}}^{1} (t)+\,\lambda _{{3},{1}}^{2} (t)\\&\quad +\,\lambda _{{4},1}^2 (t)+\lambda _{5,1}^{2} (t)+15\lambda _{5,{3}}^3 (t)\!+\!\lambda _{5,{2}}^1 (t)\!+\!\lambda _{3,1}^2 (t)\\&\quad +\,\lambda _{4,1}^{2} (t)+\lambda _{5,1}^2 (t)+\lambda _{4,1}^1 (t)+\,\lambda _{5,1}^{1} (t)\\&\quad +\,15\lambda _{5,{2}}^3 (t)+\lambda _{5,1}^{1} (t)+15\lambda _{5,1}^3 (t) \\ \alpha _9(t)&= \mu _{1,2}^{1} +\mu _{1,3}^{1} +\mu _{1,4}^{1} +\mu _{1,5}^{1} +\mu _{3,4}^{1} +\mu _{{2},5}^2 \\&\quad +\,2\lambda _{5,4}^3 (t)+\lambda _{5,4}^2 (t)+\,\mu _{3,5}^{1} +\mu _{{2},4}^2 \\&\quad +\,\lambda _{3,2}^{1} (t)+\lambda _{{5},3}^2 (t)+\lambda _{2,1}^2 (t)+2\lambda _{5,3}^3 (t) \\&\quad +\,\lambda _{3,1}^1 (t)+\lambda _{5,2}^2 (t)+{2}\lambda _{{5},2}^3 (t)+2\lambda _{5,{1}}^3 (t)\!+\!\lambda _{5,{1}}^{2} (t) \\ \alpha _8(t)&= 15\mu _{4,5}^3 +2\mu _{4,5}^3 +\lambda _{2,1}^1 (t)+\lambda _{{5},{4}}^1 (t)+\lambda _{{2},{1}}^2 (t)\\&\quad +\,\lambda _{3,1}^{1} (t)+\lambda _{5,{1}}^1 (t)+\lambda _{3,{1}}^2 (t)+\lambda _{4,1}^{2} (t)+\lambda _{5,{1}}^2 (t)\\&\quad +\,\lambda _{5,4}^2 (t)+\,\lambda _{3,{1}}^{1} (t)+\lambda _{4,1}^{1} (t)+\lambda _{5,1}^1 (t)+\lambda _{4,{2}}^1 (t)\\&\quad +\,\lambda _{5,2}^{1} (t)+\lambda _{4,2}^2 (t)+\lambda _{5,2}^{2} (t)+17\lambda _{{4},3}^3 (t)\!+\!\lambda _{{5},3}^1 (t)\\&\quad +\,\lambda _{3,1}^2 (t)+\lambda _{{3},{1}}^2 (t) +\lambda _{{4},{1}}^2 (t)+\,\lambda _{{5},{1}}^2 (t)+\lambda _{5,{2}}^{1} (t)\\&\quad +\,\lambda _{{4},1}^{2} (t)+\lambda _{{5},1}^{2} (t)+\lambda _{{5},2}^2 (t)+\,\lambda _{{3}{1}}^1 (t)+\lambda _{{4},1}^1 (t)\\&\quad +\,\lambda _{5,1}^1 (t)\!+\!17\lambda _{4,2}^3 (t) \!+\!\lambda _{5,1}^1 (t) \!+\!17\lambda _{{4},1}^{3} (t)\!+\!\lambda _{{5},1}^{2} (t) \\ \alpha _7(t)&= \mu _{{1},{2}}^{1} +\mu _{{1},{3}}^{1} +\mu _{{1},{4}}^1 +\mu _{{1},{5}}^1 +\mu _{{4},{5}}^{1} \\&\quad +\,\mu _{{1},{2}}^{2} +\mu _{{1},{3}}^{2} +\mu _{{1},{4}}^2 +\mu _{{1},{5}}^{2} +\mu _{{4},{5}}^2 +\mu _{{1},{2}}^{1} \\&\quad +\,\mu _{{1},{3}}^{1} +\mu _{{1},{4}}^{1} +\mu _{{1},{5}}^1 +\mu _{4,{5}}^1 +\mu _{{1},2}^{2} \\&\quad +\,\mu _{{1},{3}}^2 +\mu _{{1},{4}}^{2} +\mu _{{1},{5}}^{2} +\mu _{{4},{5}}^{2} +{2}\lambda _{{4},{3}}^2 (t)\\&\quad +\,2\lambda _{{4},{3}}^{1} (t)+{2}\lambda _{{4},{3}}^{3} (t)+{2}\lambda _{5,{3}}^{3} (t)\\&\quad +\,{2}\lambda _{{4},{2}}^{1} (t)+2\lambda _{{4},{2}}^{3} (t)\\&\quad +\,2\lambda _{{5},{2}}^{3} (t)+{2}\lambda _{{4},2}^2 (t)+{2}\lambda _{{4},{1}}^1 (t)\\&\quad +\,2\lambda _{{4},1}^{3} (t)+{2}\lambda _{5,1}^{3} (t)+{2}\lambda _{4,{1}}^{1} (t) \\ \alpha _6(t)&= \mu _{{1},{2}}^{1} +\mu _{{1},{3}}^{1} +\mu _{{1},{4}}^1 +\mu _{{1},{5}}^1 \\&\quad +\,\mu _{{2},{4}}^{1} +\mu _{{2},{5}}^{1} +\mu _{{2},{4}}^{2} +\mu _{{2},{5}}^2 +\mu _{{2},{3}}^{1} \\&\quad +\,\mu _{{3},{5}}^2 +\mu _{{1},{2}}^{1} +\mu _{{1},{3}}^{1} +\mu _{{1},{4}}^{1} +\mu _{{1},{5}}^1 +\,\mu _{{2},{3}}^1 \\&\quad +\,\mu _{{2},{4}}^{1}+\,\mu _{{2},{5}}^{1} +\mu _{{2},{4}}^{2} +\mu _{{2},{5}}^{2} +\mu _{{3},{5}}^{2} +{2}\mu _{{3},{4}}^2\\&\quad +\,2\lambda _{{4},{3}}^{3} (t)+{2}\lambda _{{5},{3}}^{3} (t)+{2}\lambda _{{2},{1}}^{2} (t)+{2}\lambda _{{2},{1}}^{1} (t)\\&\quad +\,2\lambda _{{3},{2}}^{2} (t)+{2}\lambda _{{4},{2}}^{3} (t) \\&\quad +\,{2}\lambda _{{5},2}^{3} (t)+{2}\lambda _{{3},{1}}^{2} (t)+2\lambda _{{4},1}^{3} (t)+{2}\lambda _{5,1}^{3} (t) \end{aligned}$$
$$\begin{aligned} \alpha _5(t)&= \mu _{3,5}^{1} +\mu _{{1},{3}}^2 +\mu _{{1},{4}}^2 +\mu _{{1},{5}}^2 +15\mu _{3,5}^3 \\&\quad +\,2\mu _{3,{5}}^3 +\mu _{3,5}^1 +\mu _{1,3}^2 +\mu _{1,4}^2 +\mu _{1,{5}}^2 +17\mu _{3,4}^3 \\&\quad +\,2\mu _{3,4}^{1} +2\mu _{3,{4}}^3 \\&\quad +\,2\mu _{3,{5}}^3 +2\mu _{3,4}^3 +2\mu _{3,5}^3 +3\lambda _{3,2}^1 (t)+\lambda _{{2},{1}}^{2} (t)\\&\quad +\,\lambda _{3,{1}}^2 (t)+\lambda _{4,1}^{2} (t)+\lambda _{5,1}^2 (t)+\lambda _{4,2}^1 (t)\\&\quad +\,\lambda _{5,2}^1 (t)+\lambda _{2,1}^1 (t)\\&\quad +\,\lambda _{3,2}^2 (t)+\lambda _{3,1}^1 (t)+\lambda _{4,1}^1 (t)+\lambda _{5,{1}}^1 (t)+\lambda _{4,2}^2 (t)\\&\quad +\,\lambda _{5,{2}}^{2} (t)+22\lambda _{3,{2}}^{3} (t)+\lambda _{4,2}^{3} (t)+\lambda _{5,2}^3 (t)\\&\quad +\,\lambda _{{4},2}^1 (t)+\lambda _{5,{2}}^{1} (t)\\&\quad +\,3\lambda _{{3},1}^{1} (t)+\lambda _{{4},{1}}^{1} (t)+\lambda _{{5},{1}}^{1} (t)\\&\quad +\,22\lambda _{{3},{1}}^{3} (t)+\lambda _{{4,1}}^{3} (t)+\lambda _{{5},1}^{3} (t)+\lambda _{{3},{1}}^{2} (t)\\&\quad +\,\lambda _{{4},{1}}^{2} (t)+\lambda _{{5},{1}}^{2} (t) \end{aligned}$$
$$\begin{aligned} \alpha _4(t)&= \mu _{{2},5}^{1} +\mu _{{1},{3}}^2 +\mu _{{1},{4}}^2 +\mu _{{1},{5}}^2\\&\quad +\,\mu _{{2},5}^{1} +\mu _{{1},{3}}^{2} +\mu _{1,4}^2 +\mu _{1,{5}}^2 +{2}\mu _{{2},4}^{1}\\&\quad +\,2\mu _{{1},{2}}^{2} +{3}\mu _{{2},{3}}^{1} +\mu _{{2},{4}}^{1} +\mu _{{2},{5}}^{1}\\&\quad +\,\mu _{{1},{2}}^{2}+\mu _{{1},{3}}^{2} \\&\quad +\,\mu _{{1},{4}}^{2} +\mu _{1,{5}}^2 +\lambda _{3,2}^{3} (t)+\lambda _{{4},{2}}^{3} (t)\\&\quad +\,\lambda _{{5},{2}}^{3} (t)+2\lambda _{{2},1}^{1} (t)+\lambda _{{3},1}^{3} (t)+\lambda _{4,{1}}^{3} (t)\\&\quad +\,\lambda _{5,{1}}^{3} (t) \\ \alpha _3(t)&= \mu _{{1},{4}}^{1} +\mu _{{1},{5}}^{1} +\mu _{{1},{3}}^{1} +\mu _{{2},{5}}^2 +\mu _{{1},{3}}^{1}\\&\quad +\,\mu _{{1},{4}}^{1} +\mu _{1,{5}}^{1} +\mu _{{2},{5}}^2 +{2}\mu _{{2},4}^{2} +2\mu _{{1},{2}}^{1}\\&\quad +\,{2}\mu _{{2},{3}}^{2} +\mu _{{1},{2}}^{1} +\mu _{{1},{3}}^{1} +\mu _{{1},{4}}^{1} +\mu _{{1},{5}}^{1} \\&\quad +\,\mu _{{2},{3}}^{2} +\mu _{{2},{4}}^2 +\mu _{{2},{5}}^2 +\lambda _{3,2}^{3} (t)+\lambda _{{4},{2}}^{3} (t)\\&\quad +\,\lambda _{{5},{2}}^{3} (t){+3}\lambda _{{2},1}^{2} (t)+\lambda _{{3},1}^{3} (t)+\lambda _{4,{1}}^{3} (t)+\lambda _{5,{1}}^{3} (t) \\ \alpha _2(t)&= 15\mu _{{2},{5}}^{3} +2\mu _{{2},{5}}^{3} +17\mu _{{2},{4}}^{3} +{2}\mu _{{2},{4}}^{3} +{2}\mu _{{2},{5}}^{3} \!+\!2\mu _{{2},{4}}^{3}\\&\quad +\,{2}\mu _{{2},{5}}^{3} {+22}\mu _{{2},{3}}^{3} +\mu _{{2},4}^{3} +\mu _{{2},{5}}^{3} +\mu _{{2},{3}}^{3} +\mu _{{2},{4}}^{3} \\&\quad +\,\mu _{{2},{5}}^{3} +\mu _{{2},{3}}^{3} +\mu _{{2},{4}}^{3} +\mu _{{2},{5}}^{3} +2\lambda _{{2},{1}}^{1} (t)+\lambda _{{2},{1}}^{2} (t)\\&\quad +\,{24}\lambda _{{2},{1}}^{3} (t)+\lambda _{{3},1}^{1} (t)+\lambda _{{4},1}^{1} (t)+\lambda _{{5},{1}}^{1} (t)+\lambda _{{3},{1}}^{2} (t)\\&\quad +\,\lambda _{{4},1}^{2} (t)+\,\lambda _{{5},{1}}^{2} (t) \\ \alpha _1(t)&= 15\mu _{{1},{5}}^{3} +\mu _{{1},{5}}^{2} +{2}\mu _{{1},{5}}^{3} +\mu _{{1},{5}}^{2} \\&\quad +\,17\mu _{{1},{4}}^{3} +\mu _{{1},{4}}^{1} +{2}\mu _{{1},{4}}^{2} +2\mu _{{1},{4}}^{3} +{2}\mu _{{1},{5}}^{3} +{2}\mu _{{1},{3}}^{2}\\&\quad +\,{2}\mu _{{1},{4}}^{3} +2\mu _{{1},{5}}^{3} +\mu _{{1},{3}}^{2} \\&\quad +\,\mu _{{1},{4}}^{2} +\mu _{{1},{5}}^{2} +22\mu _{{1},{3}}^{3} +\mu _{{1},{4}}^{3} \\&\quad +\,\mu _{{1},{5}}^{3} +{3}\mu _{{1},{2}}^{1} +\mu _{{1},{3}}^{3} +\mu _{{1},{4}}^{3} +\mu _{{1},{5}}^{3} +{3}\mu _{{1},{2}}^{2} \\&\quad +\,\mu _{{1},{3}}^{3}+\mu _{{1},4}^{3} +\mu _{{1},{5}}^{3} +\mu _{{1},{2}}^{1} \\&\quad +\,\mu _{{1},{2}}^{2} +\,\mu _{{1},{3}}^{2} +\mu _{{1},{5}}^{2} {+24}\mu _{{1},{2}}^{3} +\mu _{{1},{4}}^{2} \\ \end{aligned}$$
Appendix 3: NHCTMM Chapman–Kolmogorov equations of each component
$$\begin{aligned}&Component 1\\&\quad \times \left\{ {\begin{array}{lll} dP_5 (t)/dt&{}=&{}-(\lambda _{5,4}^1 (t)+\lambda _{5,3}^1 (t)+\lambda _{5,2}^1 (t)+\lambda _{5,1}^1 (t))P_5 (t)+\mu _{4,5}^1 P_4 (t)+\,\mu _{3,5}^1 P_3 (t) +\mu _{2,5}^1 P_2 (t)+\mu _{1,5}^1 P_1 (t) \\ dP_4 (t)/dt&{}=&{}\lambda _{5,4}^{1} (t)P_5 (t)-(\mu _{{4},{5}}^1 +\lambda _{{4},3}^1 (t) +\lambda _{{4},2}^1 (t)+\lambda _{{4},1}^1 (t))P_4 (t)+\,\mu _{{3},{4}}^{1} P_3 (t)+\mu _{2,4}^{1} P_2 (t)+\mu _{1,4}^{1}P_1 (t) \\ dP_3 (t)/dt&{}=&{}\lambda _{5,3}^{1} (t)P_5 (t)+\lambda _{4,3}^{1} (t)P_4 (t)-\,(\mu _{{3},{5}}^1+\mu _{{3},{4}}^1+\lambda _{{3},2}^1(t) +\lambda _{{3},1}^1 (t))P_3 (t)+\mu _{2,3}^{1} P_2 (t)+\mu _{1,3}^{1} P_1 (t) \\ dP_2 (t)/dt&{}=&{}\lambda _{5,2}^{1} (t)P_5 (t)+\lambda _{4,2}^{1} (t)P_4 (t) +\lambda _{3,2}^{1} (t)P_3 (t)-\,(\mu _{{2},{5}}^1+\mu _{{2},{4}}^1 +\mu _{{2},{3}}^1 +\lambda _{{2},1}^1 (t))P_2 (t) +\mu _{1,2}^{1} P_1 (t) \\ dP_1 (t)/dt&{}=&{}\lambda _{5,1}^{1} (t)P_5 (t)+\lambda _{4,1}^{1} (t)P_4 (t) +\lambda _{3,1}^{1} (t)P_3 (t)+\lambda _{2,1}^{1} (t)P_2 (t) -\,(\mu _{{1},{5}}^1+\mu _{{1},{4}}^1 +\mu _{{1},{3}}^1 +\mu _{{1},{2}}^1)P_1 (t) \\ \end{array}} \right. \end{aligned}$$
$$\begin{aligned}&Component 2\\&\quad \times \left\{ {\begin{array}{lll} dP_5 (t)/dt&{}=&{}-(\lambda _{5,4}^{2} (t)+\lambda _{5,3}^{2} (t) +\lambda _{5,2}^{2} (t)+\lambda _{5,1}^{2} (t))P_5 (t) +\,\mu _{4,5}^{2} P_4(t)+\mu _{3,5}^{2} P_3 (t) +\mu _{2,5}^{2} P_2 (t)+\mu _{1,5}^{2} P_1(t) \\ dP_4 (t)/dt&{}=&{}\lambda _{5,4}^{2} (t)P_5 (t)-(\mu _{{4},{5}}^{2} +\lambda _{{4},3}^{2} (t)+\lambda _{{4},2}^{2} (t) +\lambda _{{4},1}^{2} (t))P_4 (t) +\,\mu _{{3},{4}}^{2} P_3 (t) +\mu _{2,4}^{2}P_2 (t)+\mu _{1,4}^{2} P_1 (t) \\ dP_3 (t)/dt&{}=&{}\lambda _{5,3}^{2} (t)P_5 (t)+\lambda _{4,3}^{2} (t)P_4 (t) -\,(\mu _{{3},{5}}^{2}+\mu _{{3},{4}}^{2} +\lambda _{{3},2}^{2}(t)+\lambda _{{3},1}^{2} (t))P_3 (t) +\mu _{2,3}^{2} P_2 (t)+\mu _{1,3}^{2} P_1 (t) \\ dP_2 (t)/dt&{}=&{}\lambda _{5,2}^{2} (t)P_5 (t)+\lambda _{4,2}^2 (t)P_4(t) +\lambda _{3,2}^2 (t)P_3 (t) -\,(\mu _{{2},{5}}^2 +\mu _{{2},{4}}^2+\mu _{{2},{3}}^2 +\lambda _{{2},1}^2 (t))P_2 (t)+\mu _{1,2}^2 P_1(t) \\ dP_1 (t)/dt&{}=&{}\lambda _{5,1}^2 (t)P_5 (t)+\lambda _{4,1}^2 (t)P_4(t) +\lambda _{3,1}^2 (t)P_3 (t)+\lambda _{2,1}^2 (t)P_2 (t) -\,(\mu _{{1},{5}}^2+\mu _{{1},{4}}^2 +\mu _{{1},{3}}^2 +\mu _{{1},{2}}^2)P_1 (t) \end{array}} \right. \end{aligned}$$
$$\begin{aligned}&Component 3\\&\quad \times \left\{ {\begin{array}{lll} dP_5 (t)/dt&{}=&{}-(\lambda _{5,4}^3 (t)+\lambda _{5,3}^3 (t) +\lambda _{5,2}^3 (t)+\lambda _{5,1}^3 (t))P_5 (t) +\,\mu _{4,5}^3 P_4 (t)+\mu _{3,5}^3 P_3 (t) +\mu _{2,5}^3 P_2 (t)+\mu _{1,5}^3 P_1 (t) \\ dP_4 (t)/dt&{}=&{}\lambda _{5,4}^3 (t)P_5 (t)-(\mu _{{4},{5}}^3 +\lambda _{{4},3}^3 (t)+\lambda _{{4},2}^3 (t) +\lambda _{{4},1}^3 (t))P_4(t)+\,\mu _{{3},{4}}^3 P_3 (t) +\mu _{2,4}^3 P_2 (t)+\mu _{1,4}^3 P_1(t)\\ dP_3 (t)/dt&{}=&{}\lambda _{5,3}^3 (t)P_5 (t)+\lambda _{4,3}^3 (t)P_4 (t) -\,(\mu _{{3},{5}}^3+\mu _{{3},{4}}^3 +\lambda _{{3},2}^3(t)+\lambda _{{3},1}^3 (t))P_3 (t) +\mu _{2,3}^3 P_2 (t)+\mu _{1,3}^3P_1 (t) \\ dP_2 (t)/dt&{}=&{}\lambda _{5,2}^3 (t)P_5 (t)+\lambda _{4,2}^3 (t)P_4(t) +\lambda _{3,2}^3 (t)P_3 (t)-\,(\mu _{{2},{5}}^{3} +\mu _{{2},{4}}^{3} +\mu _{{2},{3}}^{3} +\lambda _{{2},1}^{3} (t))P_2(t)+\mu _{1,2}^{3} P_1 (t) \\ dP_1 (t)/dt&{}=&{}\lambda _{5,1}^{3} (t)P_5 (t)+\lambda _{4,1}^{3} (t)P_4(t) +\lambda _{3,1}^{3} (t)P_3 (t)+\lambda _{2,1}^{3} (t)P_2 (t) -\,(\mu _{{1},{5}}^{3}+\mu _{{1},{4}}^{3} +\mu _{{1},{3}}^{3} +\mu _{{1},{2}}^{3} )P_1 (t) \\ \end{array}} \right. \end{aligned}$$
Appendix 4: NHCTMRM Chapman–Kolmogorov equations of each component
$$\begin{aligned}&Component 1\\&\quad \times \left\{ {\begin{array}{lll} dV_5 (t)/dt&{}=&{}-(\lambda _{5,4}^1 (t)+\lambda _{5,3}^1 (t) +\lambda _{5,2}^1 (t)+\lambda _{5,1}^1 (t))V_5 (t) +\lambda _{5,4}^1 (t)V_4(t)+\lambda _{5,3}^1 (t)V_3 (t) +\,\lambda _{5,2}^1 (t)V_2 (t)\\ &{}&{} +\,\,\lambda _{5,1}^1 (t)V_1 (t)\\ dV_4 (t)/dt&{}=&{}54\mu _{4,5}^{1} +\mu _{4,5}^{1} V_5 (t) -(\mu _{{4},{5}}^1 +\lambda _{{4},3}^1 (t) +\lambda _{{4},2}^1 (t)+\lambda _{{4},1}^1 (t))V_4 (t) +\lambda _{4,3}^{1} (t)V_3 (t) +\,\lambda _{4,2}^{1} (t)V_2 (t)\\ &{}&{}+\,\lambda _{4,1}^{1} (t)V_1 (t)\\ dV_3 (t)/dt&{}=&{}72\mu _{3,5}^{1} +54\mu _{3,4}^{1} +\mu _{3,5}^{1} V_5(t)+\mu _{3,4}^{1} V_4 (t) -(\mu _{{3},{5}}^1 +\mu _{{3},{4}}^1 +\lambda _{{3},2}^1 (t)+\lambda _{{3},1}^1 (t))V_3 (t) +\,\lambda _{3,2}^{1} (t)V_2 (t)\\ &{}&{} +\,\,\lambda _{3,1}^{1} (t)V_1 (t)\\ dV_2 (t)/dt&{}=&{}90\mu _{2,5}^{1} +72\mu _{2,4}^{1} +54\mu _{2,3}^{1}+\mu _{2,5}^{1} V_5 (t) +\mu _{2,4}^{1} V_4 (t)+\mu _{2,3}^{1} V_3(t) -\,(\mu _{{2},{5}}^1 +\mu _{{2},{4}}^1 +\mu _{{2},{3}}^1\\ &{}&{} +\,\,\lambda _{{2},1}^1 (t))V_2 (t) +\lambda _{2,1}^{1}(t)V_1 (t)\\ dV_1 (t)/dt&{}=&{}180\mu _{1,5}^{1} +90\mu _{1,4}^{1} +72\mu _{1,3}^{1}+54\mu _{1,2}^{1} +\mu _{1,5}^{1} V_5 (t)+\mu _{1,4}^{1} V_4 (t) +\mu _{1,3}^{1} V_3 (t) +\,\mu _{1,2}^{1} V_2 (t)\\ &{}&{} -\,\,(\mu _{{1},{5}}^1 +\mu _{{1},{4}}^1 +\mu _{{1},{3}}^1 +\mu _{{1},{2}}^1 )V_1 (t) \end{array}} \right. \end{aligned}$$
$$\begin{aligned}&Component 2\\&\quad \times \left\{ {\begin{array}{lll} dV_5 (t)/dt&{}=&{}-(\lambda _{5,4}^{2} (t)+\lambda _{5,3}^{2}(t) +\lambda _{5,2}^{2} (t)+\lambda _{5,1}^{2} (t))V_5 (t) +\lambda _{5,4}^{2} (t)V_4 (t)+\lambda _{5,3}^{2} (t)V_3 (t) +\,\lambda _{5,2}^{2} (t)V_2 (t)\\ &{}&{}+\,\,\lambda _{5,1}^{2} (t)V_1 (t)\\ dV_4 (t)/dt&{}=&{}72\mu _{4,5}^{2} +\mu _{4,5}^{2} V_5 (t) -(\mu _{{4},{5}}^{2} +\lambda _{{4},3}^{2} (t) +\lambda _{{4},2}^{2}(t)+\lambda _{{4},1}^{2} (t))V_4 (t) +\lambda _{4,3}^{2} (t)V_3 (t)+\,\lambda _{4,2}^{2} (t)V_2 (t)\\ &{}&{}+\,\,\lambda _{4,1}^{2} (t)V_1(t)\\ dV_3 (t)/dt&{}=&{}96\mu _{3,5}^{2} +72\mu _{3,4}^{2} +\mu _{3,5}^{2} V_5(t)+\mu _{3,4}^{2} V_4 (t) -(\mu _{{3},{5}}^{2} +\mu _{{3},{4}}^{2} +\lambda _{{3},2}^{2} (t)+\lambda _{{3},1}^{2} (t))V_3 (t) +\,\lambda _{3,2}^{2} (t)V_2 (t)\\ &{}&{}+\,\,\lambda _{3,1}^{2} (t)V_1 (t)\\ dV_2 (t)/dt&{}=&{}120\mu _{2,5}^{2} +96\mu _{2,4}^{2} +72\mu _{2,3}^{2}+\mu _{2,5}^{2} V_5 (t) +\mu _{2,4}^{2} V_4 (t)+\mu _{2,3}^{2} V_3(t) -\,(\mu _{{2},{5}}^{2} +\mu _{{2},{4}}^{2} +\mu _{{2},{3}}^{2}\\ &{}&{} +\,\,\lambda _{{2},1}^{2} (t))V_2 (t) +\lambda _{2,1}^{2} V_1 (t)\\ dV_1 (t)/dt&{}=&{}240\mu _{1,5}^{2} +120\mu _{1,4}^{2} +96\mu _{1,3}^{2}+72\mu _{1,2}^{2} +\mu _{1,5}^{2} V_5 (t)+\mu _{1,4}^{2} V_4 (t) +\mu _{1,3}^{2} V_3 (t) +\,\mu _{1,2}^{2} V_2 (t)\\ &{}&{}-\,\,(\mu _{{1},{5}}^{2} +\mu _{{1},{4}}^{2} +\mu _{{1},{3}}^{2} +\mu _{{1},{2}}^{2} )V_1 (t) \end{array}} \right. \end{aligned}$$
$$\begin{aligned}&Component 3\\&\quad \times \left\{ {\begin{array}{lll} dV_5 (t)/dt&{}=&{}-(\lambda _{5,4}^{3} (t)+\lambda _{5,3}^{3}(t) +\lambda _{5,2}^{3} (t)+\lambda _{5,1}^{3} (t))V_5 (t) +\lambda _{5,4}^{3} (t)V_4 (t)+\lambda _{5,3}^{3} (t)V_3 (t) +\,\lambda _{5,2}^{3} (t)V_2 (t)\\ &{}&{}+\,\,\lambda _{5,1}^{3} (t)V_1 (t)\\ dV_4 (t)/dt&{}=&{}120\mu _{4,5}^{3} +\mu _{4,5}^{3} V_5 (t) -(\mu _{{4},{5}}^{3} +\lambda _{{4},3}^{3} (t) +\lambda _{{4},2}^{3}(t)+\lambda _{{4},1}^{3} (t))V_4 (t) +\lambda _{4,3}^{3} (t)V_3 (t)+\,\lambda _{4,2}^{3} (t)V_2 (t)\\ &{}&{}+\,\,\lambda _{4,1}^{3} (t)V_1(t)\\ dV_3 (t)/dt&{}=&{}160\mu _{3,5}^{3} +120\mu _{3,4}^{3} +\mu _{3,5}^{3}V_5 (t)+\mu _{3,4}^{3} V_4 (t) -(\mu _{{3},{5}}^{3} +\mu _{{3},{4}}^{3} +\lambda _{{3},2}^{3} (t)+\lambda _{{3},1}^{3}(t))V_3 (t) +\,\lambda _{3,2}^{3} V_2 (t)\\ &{}&{}+\,\,\lambda _{3,1}^{3} (t)V_1 (t)\\ dV_2 (t)/dt&{}=&{}200\mu _{2,5}^{3} +160\mu _{2,4}^{3} +120\mu _{2,3}^{3}+\mu _{2,5}^{3} V_5 (t) +\mu _{2,4}^{3} V_4 (t)+\mu _{2,3}^{3} V_3(t) -\,(\mu _{{2},{5}}^{3} +\mu _{{2},{4}}^{3} +\mu _{{2},{3}}^{3}\\ &{}&{} +\,\,\lambda _{{2},1}^{3} (t))V_2 (t) +\lambda _{2,1}^{3} V_1 (t)\\ dV_1 (t)/dt&{}=&{}240\mu _{1,5}^{3} +200\mu _{1,4}^{3} +160\mu _{1,3}^{3} +120\mu _{1,2}^{3} +\mu _{1,5}^{3} V_5 (t)+\mu _{1,4}^{3}V_4 (t) +\mu _{1,3}^{3} V_3 (t) +\,\mu _{1,2}^{3} V_2 (t)\\ &{}&{}-\,\,(\mu _{{1},{5}}^{3} +\mu _{{1},{4}}^{3} +\mu _{{1},{3}}^{3} +\mu _{{1},{2}}^{3} )V_1 (t) \end{array}} \right. \end{aligned}$$
