In this paper, we analyze a nonlinear mathematical model of the HIV/AIDS and screening of unaware infectives on the transmission dynamics of the disease in a homogeneous population with constant immigration of susceptibles incorporating use of condom, screening of unaware infectives and treatment of the infected. We consider constant controls and thereafter by incorporating the theory of Volterra–Lyapunov stable matrices into the classical method of Lyapunov functions, we present an approach for global stability analysis of HIV/AIDS. The analysis and results presented in this paper make building blocks toward a comprehensive study and deeper understanding of the fundamental mechanism in HIV/AIDS. A numerical study of the model is also carried out to investigate the analytical results.

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Recent work on virtual reality navigation in humans has suggested that navigational success is inversely correlated with the fractal dimension (FD) of artificial scenes. Here we investigate the generality of this claim by analysing the relationship between the fractal dimension of natural insect navigation environments and a quantitative measure of the navigational information content of natural scenes. We show that the fractal dimension of natural scenes is in general inversely proportional to the information they provide to navigating agents on heading direction as measured by the rotational image difference function (rotIDF). The rotIDF determines the precision and accuracy with which the orientation of a reference image can be recovered or maintained and the range over which a gradient descent in image differences will find the minimum of the rotIDF, that is the reference orientation. However, scenes with similar fractal dimension can differ significantly in the depth of the rotIDF, because FD does not discriminate between the orientations of edges, while the rotIDF is mainly affected by edge orientation parallel to the axis of rotation. We present a new equation for the rotIDF relating navigational information to quantifiable image properties such as contrast to show (1) that for any given scene the maximum value of the rotIDF (its depth) is proportional to pixel variance and (2) that FD is inversely proportional to pixel variance. This contrast dependence, together with scene differences in orientation statistics, explains why there is no strict relationship between FD and navigational information. Our experimental data and their numerical analysis corroborate these results.

We tested a mechanical model of wing,which was constructed using the measurements of wingspan and wing area taken from three species of gliding birds.In this model,we estimated the taper factors of the wings for jackdaw (Corrus monedula), Harris' hawk (Parabuteo unicinctas) and Lagger falcon (Falco jugger) as 1.8, 1.5 and 1.8,respectively. Likewise, by using the data linear regression and curve estimation method,as well as estimating the taper factors and the angle between the humerus and the body, we calculated the relationship between wingspan,wing area and the speed necessary to meet the aerodynamic requirements of sustained flight.In addition,we calculated the relationship between the speed,wing area and wingspan for a specific angle between the humerus and the body over the range of stall speed to maximum speed of gliding flight.We then compared the results for these three species of gliding birds. These comparisons suggest that the aerodynamic characteristics of Harris' hawk wings are similar to those of the falcon but different from those of the jackdaw.This paper also presents two simple equations to estimate the minimum angle between the humerus and the body as well as the minimum span ratio of a bird in gliding flight.