In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

The genetic polymorphisms of biotransformation phase I enzymes, cytochrome P450 (CYP1A1 and CYP2D6), and phase II enzymes, glutathione S-transferase (GSTM1 and GSTT1), were analyzed in 204 healthy persons and 348 leukemia patients, who suffered from also acute lymphoblastic leukemia (ALL), acute nonlymphoblastic leukemia (ANLL) chronic myelogenous leukemia (CML), from the Han ethnic group in Changsha City of Hunan Province of China. Our results showed that the frequencies of polymorphisms of CYP1A1, CYP2D6 and GSTT1 among the groups including acute lymphoblastic leukemia, ANLL, chronic myelogenous leukemia and healthy control have no significant differences. The variation of GSTM1-null genotype alone correlated with the development of ANLL. The combined genotypes of GSTM1-null with GSTT1-null, or GSTM1-null with CYP1A1 heterozygous mutant, or GSTM1-null with CYP1A1 heterozygous mutant and CYP2D6 heterozygous mutant, or GSTM1-null with CYP1A1 heterozygous mutant, CYP2D6 heterozygous mutant and GSTT1-null were found in individuals with high risk of ANLL. All these findings suggest that GSTM1-null genotype alone or in coordination with the relevant genotypes of other metabolic enzymes might be susceptibility factors in the etiology of ANLL.

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The risk factors in this study have the ability to identify patients with HMs and BSIs at high risk for mortality. Our model provides an excellent foundation for predicting 30-day morality in HM patients suffering from BSI and helps target high-risk patients for management decision making.

A case-control study was conducted for analyzing the genetic polymorphisms of phase II metabolic enzymes in 97 patients with lung cancer and 197 healthy subjects from Han ethnic group of Hunan Province located in Central South China. The results showed that the frequencies of glutathione S-transferase (GST) M1-null (GSTM1-) or GSTT1-null (GSTT1-) genotype alone, or combined form of both in lung cancer patients were significantly higher than those of the controls. Genotypes of combining GSTP1 mutant/GSTM1(-) or GSTP1 mutant/GSTT1(-) led to high risk of lung cancer. Individuals carrying any two or all three of GSTM1(-), GSTT1(-) and GSTP1 mutant genotypes have a distinctly increased risk of lung cancer when compared to those with GSTM1 present (GSTM1+: GSTM1+/+ or GSTM1+/−), GSTT1 present (GSTT1+: GSTT1+/+ or GSTT1+/−) and GSTP1 wild genotypes. Furthermore, individuals possessing combined genotypes of N-acetyltransferase 2 (NAT2) rapid acetylator, GSTP1 mutant and both GSTT1(-) and GSTM1(-) have a remarkably higher lung cancer risk than those carrying combined NAT2 slow acetylator genotype, GSTP1 wild genotype and both GSTT1(+) and GSTM1(+) genotypes. All these findings suggest that the genetic polymorphisms of phase II metabolic enzymes affect the susceptibility of lung cancer in the Han ethnic group of Central South China.