Dental plaster casts of 97 6-8-year-old and 173 12-year-old Maasai, Kikuyu, and Kalenjin children were studied. The Kikuyu are Bantu, while Maasai and Kalenjin are Nilo-Hamitic subjects. The variables measured were palatal depth (PD) and length (PL); maxillary and mandibular anterior arc circumferences (AC1) and (AC2), respectively; posterior arc circumferences (PC1) and (PC2), inter-canine (CC1), and (CC2); inter-molar (MM1) and (MM2) distances, and mandibular length (ML). The data were analysed using SPSS package. The mean values of all the variables were generally higher in the males compared with the females and significant sex differences in the means (P < 0.01) were found in AC1, PC1, PC2, CC1, CC2, MM1, and MM2 in the 12-year-old subjects. The means of all variables, except PL, ML, PC2, and CC2, increased from 6 to 12 years of age and significant differences in the means for age were found in ML, AC1, PC2, PD, MM1, MM2, and CC1. Mean maxillary inter-molar distance increased with age by 0.17-0.34 mm in the three groups. Mean values of mandibular variables were highest in the Kikuyu, while maxillary variables were highest in the Maasai. The Maasai casts showed a marked decrease in CC2, PC2, AC2, and ML compared with the Kikuyu and Kalenjin. Ethnic and sex differences in the dental arches may be masked by anterior tooth positions that are influenced by the dento-alveolar complex and soft tissues. Corresponding mandibular and maxillary variables were strongly correlated and anterior and posterior arc circumferences were correlated with inter-canine and intermolar distances. Details of the norms for dental arch dimensions and changes with age may allow for appropriate assessment of dental occlusion and treatment planning for Kenyan children.

Mean ages of eruption of the permanent teeth (except 3rd molars) in African and Asian children were derived from a cross-sectional study of 2847 children aged 4-14 years, in selected nursery and primary schools in Nairobi, Kenya. Except for the premolars, the mandibular teeth erupted earlier than the maxillary ones in both races. The mandibular incisors and canines erupted earlier by 0.9-1.1 yr in Africans and 0.6-0.8 yr in Asians, and the molar by 0.2-0.4 yr in both races. The maxillary premolars were ahead of mandibular premolars by 0.1-0.2 yr in both races. The females were ahead of males in both races. Compared with the Asians, the African permanent teeth erupted earlier by 0.2-0.7 yr. The most frequent order of eruption in Africans is Mand I1, Mand M1, Max M1, Mand I2, and Max I1 between 5-7 years, while in the Asians the most frequent order is Mand M1, Mand I1, or Max M1, Max I1 and Mand I2 between 6-8 years. The incidence of Cusp of Carabelli in Africans and Asians is about 19-25%.

Malaria is one of the three most dangerous infectious diseases worldwide (along with HIV/AIDS and tuberculosis). In this paper we compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in malaria transmission dynamics. Relationships between the basic reproduction number for malaria transmission dynamics between humans and mosquitoes and the extinction thresholds of corresponding continuous-time Markov chain models are derived under certain assumptions. The stochastic model is formulated using the continuous-time discrete state Galton-Watson branching process (CTDSGWbp). The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction from stochastic models contribute crucial knowledge on disease control and elimination and mitigation of infectious diseases. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that malaria outbreak is more likely if the disease is introduced by infected mosquitoes as opposed to infected humans. These insights demonstrate the importance of a policy or intervention focusing on controlling the infected mosquito population if the control of malaria is to be realized.

Kernel density estimators due to boundary effects are often not consistent when estimating a density near a finite endpoint of the support of the density to be estimated. To address this, researchers have proposed the application of an optimal bandwidth to balance the bias-variance trade-off in estimation of a finite population mean. This, however, does not eliminate the boundary bias. In this paper weighting method of compensating for nonresponse is proposed. Asymptotic properties of the proposed estimator of the population mean are derived. Under mild assumptions, the estimator is shown to be asymptotically consistent.

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