Risk factors for oesophageal, lung, oral and laryngeal cancers in black South Africans

The authors used data collected from 1995 to 1999, from an on-going cancer case–control study in greater Johannesburg, to estimate the importance of tobacco and alcohol consumption and other suspected risk factors with respect to cancer of the oesophagus (267 men and 138 women), lung (105 men and 41 women), oral cavity (87 men and 37 women), and larynx (51 men). Cancers not associated with tobacco or alcohol consumption were used as controls (804 men and 1370 women). Tobacco smoking was found to be the major risk factor for all of these cancers with odds ratios ranging from 2.6 (95% CI 1.5–4.5) for oesophageal cancer in female ex-smokers to 50.9 (95% CI 12.6–204.6) for lung cancer in women, and 23.9 (95% CI 9.5–60.3) for lung cancer and 23.6 (95% CI 4.6–121.2) for laryngeal cancer in men who smoked 15 or more grams of tobacco a day. This is the first time an association between smoking and oral and laryngeal cancers has been shown in sub-Saharan Africa. Long-term residence in the Transkei region in the southeast of the country continues to be a risk factor for oesophageal cancer, especially in women (odds ratio=14.7, 95% CI 4.7–46.0), possibly due to nutritional factors. There was a slight increase in lung cancer (odds ratio=2.9, 95% CI 1.1–7.5) in men working in ‘potentially noxious’ industries. ‘Frequent’ alcohol consumption, on its own, caused a marginally elevated risk for oesophageal cancer (odds ratio=1.7, 95% CI 1.0–2.9, for women and odds ratio=1.8, 95% CI 1.2–2.8, for men). The risks for oesophageal cancer in relation to alcohol consumption increased significantly in male and female smokers (odds ratio=4.7, 95% CI=2.8–7.9 in males and odds ratio=4.8, 95% CI 3.2–6.1 in females). The above results are broadly in line with international findings.

Antibodies against human herpesvirus 8 in black South African patients with cancer

Background Infection with human herpesvirus 8 (HHV-8) has been consistently linked to Kaposi's sarcoma, but its mode of transmission, association with other cancers, and interaction with the human immunodeficiency virus type 1 (HIV-1) are largely unknown. Methods Between January 1992 and December 1997, we interviewed 3591 black patients with cancer in Johannesburg and Soweto, South Africa. Blood was tested for antibodies against HIV-1 and HHV-8 in 3344 of the patients. Antibodies against HHV-8 were detected with an indirect immunofluorescence assay. The intensity of the fluorescent signal correlated well with the titers of antibodies (P<0.001). The relations among the presence of anti–HHV-8 antibodies, sociodemographic and behavioral factors, type of cancer, and the presence or absence of coexistent HIV-1 infection were examined with the use of unconditional logistic-regression models. Results Among the 3293 subjects with cancers other than Kaposi's sarcoma, the standardized seroprevalence of antibodies against HHV-8 was 32 percent, which did not differ significantly from the standardized seroprevalence among black blood donors. Among these 3293 patients, the prevalence of antibodies against HHV-8 increased with increasing age (P<0.001) and an increasing number of sexual partners (P=0.05) and decreased with increasing years of education (P=0.007); it was not strongly associated with HIV-1 infection. Anti–HHV-8 antibodies were more frequent among black than white blood donors (P<0.001). Among the 51 patients with Kaposi's sarcoma, the standardized seroprevalence of antibodies against HHV-8 was 83 percent, significantly higher than the prevalence among those without Kaposi's sarcoma (P<0.001). For 16 other specific types of cancer, including multiple myeloma (108 cases) and prostate cancer (202 cases), the variation in the standardized seroprevalence of antibodies against HHV-8 was not remarkable. At a given intensity of fluorescence of anti–HHV-8 antibodies, Kaposi's sarcoma was more frequent among HIV-1–positive patients than among those who were HIV-1–negative (P<0.001). Conclusions Among black patients with cancer in South Africa, the seroprevalence of anti–HHV-8 antibodies is high and is specifically associated with Kaposi's sarcoma, particularly at high titers.

Black comedy : the ABC makes bold foray into race relations

ABC’s new Indigenous sketch show Black Comedy, which premiered last night, is touted as a “show by blackfellas … for everyone”. As a blackfella, I’m not sure I agree that it is for “everyone” but that’s precisely why I love it. It’s been over 40 years since Basically Black, the first Indigenous sketch show aired on our screens, and it’s been too long a wait to see our mob doing humour our way in our living rooms once again. The characters we met last night were, as promised, bigger and blacker than ever. When it comes to Australian television … well it’s about time.

A meshless method based on Point Interpolation Method (PIM) for the space fractional diffusion equation

This paper aims to develop a meshless approach based on the Point Interpolation Method (PIM) for numerical simulation of a space fractional diffusion equation. Two fully-discrete schemes for the one-dimensional space fractional diffusion equation are obtained by using the PIM and the strong-forms of the space diffusion equation. Numerical examples with different nodal distributions are studied to validate and investigate the accuracy and efficiency of the newly developed meshless approach.

Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy

This article aims to fill in the gap of the second-order accurate schemes for the time-fractional subdiffusion equation with unconditional stability. Two fully discrete schemes are first proposed for the time-fractional subdiffusion equation with space discretized by finite element and time discretized by the fractional linear multistep methods. These two methods are unconditionally stable with maximum global convergence order of $O(\tau+h^{r+1})$ in the $L^2$ norm, where $\tau$ and $h$ are the step sizes in time and space, respectively, and $r$ is the degree of the piecewise polynomial space. The average convergence rates for the two methods in time are also investigated, which shows that the average convergence rates of the two methods are $O(\tau^{1.5}+h^{r+1})$. Furthermore, two improved algorithms are constrcted, they are also unconditionally stable and convergent of order $O(\tau^2+h^{r+1})$. Numerical examples are provided to verify the theoretical analysis. The comparisons between the present algorithms and the existing ones are included, which show that our numerical algorithms exhibit better performances than the known ones.

High order unconditionally stable difference schemes for the Riesz space-fractional telegraph equation

In this paper, a class of unconditionally stable difference schemes based on the Pad´e approximation is presented for the Riesz space-fractional telegraph equation. Firstly, we introduce a new variable to transform the original dfferential equation to an equivalent differential equation system. Then, we apply a second order fractional central difference scheme to discretise the Riesz space-fractional operator. Finally, we use (1, 1), (2, 2) and (3, 3) Pad´e approximations to give a fully discrete difference scheme for the resulting linear system of ordinary differential equations. Matrix analysis is used to show the unconditional stability of the proposed algorithms. Two examples with known exact solutions are chosen to assess the proposed difference schemes. Numerical results demonstrate that these schemes provide accurate and efficient methods for solving a space-fractional hyperbolic equation.

A fast semi-implicit difference method for a nonlinear two-sided space-fractional diffusion equation with variable diffusivity coefficients

In this paper, we derive a new nonlinear two-sided space-fractional diffusion equation with variable coefficients from the fractional Fick’s law. A semi-implicit difference method (SIDM) for this equation is proposed. The stability and convergence of the SIDM are discussed. For the implementation, we develop a fast accurate iterative method for the SIDM by decomposing the dense coefficient matrix into a combination of Toeplitz-like matrices. This fast iterative method significantly reduces the storage requirement of O(n2)O(n2) and computational cost of O(n3)O(n3) down to n and O(nlogn)O(nlogn), where n is the number of grid points. The method retains the same accuracy as the underlying SIDM solved with Gaussian elimination. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.

A Crank--Nicolson ADI spectral method for a two-dimensional riesz space fractional nonlinear reaction-diffusion equation

In this paper, a new alternating direction implicit Galerkin--Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank--Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly proven, which shows that the derived method is stable and convergent of order $2$ in time. An optimal error estimate in space is also obtained by introducing a new orthogonal projector. The present method is extended to solve the fractional FitzHugh--Nagumo model. Numerical results are provided to verify the theoretical analysis.