Szegő's problem on curves

<p>(a) Map of Kenya showing HIV prevalence distributions. The color bar from blue to red is in the order of increasing HIV prevalence. For clarity, the names of counties included are the only ones included in this study (Source of data:ArcGIS.com: shapefile-The 47 counties of Kenya (shapefile by dmuthami <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0142805#pone.0142805.s005" target="_blank">S5 Table</a>) and HIV data from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0142805#pone.0142805.ref039" target="_blank">39</a>]. (b) Human travel networks (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0142805#pone.0142805.s006" target="_blank">S6 Table</a>) as estimated by [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0142805#pone.0142805.ref038" target="_blank">38</a>]. Monthly average number of trips per 1000 individuals between all pairs of regions over the course of the year. For clarity, only trips made per 1000 individuals that are more than 60 trips per year are shown, with arrows indicating the direction of movements from home region to a visited region. The thickness of the arrow represents the number of trips made.</p

The Use of Non-Standard Finite Difference Schemes to Solve the DAMP and SIT Models

Abstract Sterile insect technique (SIT) is a method of biological control that uses sterile male insects to reduce the reproductive rate of a species of target insect. The method relies on the release of sterile or treated males in order to reduce the native population of insects. We propose the model that governs the dynamics of the anopheles mosquito population, and then modify to incorporate the sterile insect technique as an intervention to curtail the reproduction of mosquitoes. The nonstandard finite difference numerical schemes and simulations for these models are provided. The results indicate that sterile technique with frequent and high rate of release can be an alternative to chemical control tools in the fight against malaria

Stability analysis and dynamics preserving nonstandard finite difference schemes for a malaria model

When both human and mosquito populations vary, forward bifurcation occurs if the basic reproduction number R0 is less than one in the absence of disease-induced death. When the disease-induced death rate is large enough R0 = 1 is a subcritical backward bifurcation point. The domain for the study of the dynamics is reduced to a compact and feasible region, where the system admits a speci c algebraic decomposition into infective and non-infected humans and mosquitoes. Stability results are extended and the possibility of backward bifurcation is clari ed. A dynamically consistent nonstandard nite di erence scheme is designed.Yves Dumont was supported jointly by the French Ministry of Health and the 2007–2013 Convergence program of the European Regional Development Fund (ERDF). Roumen Anguelov, Jean Lubuma, and Eunice Mureithi thank the South African National Research Foundation for its support.http://www.tandfonline.com/loi/gmps20hb201

An investigation on the Monkeypox virus dynamics in human and rodent populations for a deterministic mathematical model

A mathematical deterministic model for the dynamics of Monkeypox disease is developed. Monkeypox is a viral zoonotic disease that can be transmitted to humans, through contact with infected rodents. The model captures both the human and rodent populations and incorporates control strategies such as vaccines and quarantine for the human population. The model is analysed for local and global stability of the equilibrium solutions. In addition, numerical simulations of the model equations and sensitivity analysis of the parameters are carried out. The solutions obtained show that an increase in vaccination and quarantine measures could reduce the number of reproductions and ultimately eradicate the virus

Local non-similarity solutions for a forced-free boundary layer flow with viscous dissipation

The boundary layer flow over a horizontal plate with power law variations in the freestream velocity and wall temperature of the form Ue ∼ xn and Tw − T∞ ∼ xm and with viscous dissipation, is studied. The boundary layer equations are transformed to a dimensionless system of equations using a non–similarity variable (x) and a pseudo-similarity variable (x; y). The effects of the various parameters of the flow on velocity and temperature distribution in the boundary layer, on the local skin friction and local heat transfer coefficients and on the non–similar terms, are investigated.http://www.mcajournal.org

Weakly nonlinear wave motions in a thermally stratified boundary layer

James P. Denier and Eunice W. Mureith

The effect of buoyancy on upper branch Tollmien-Schlichting waves

We investigate the effect of buoyancy on the upper-branch linear stability characteristics of an accelerating boundary-layer flow. The presence of a large thermal buoyancy force significantly alters the stability structure. As the factor G (which is related to the Grashof number of the flow, and defined in Section 2) becomes large and positive, the flow structure becomes two layered and disturbances are governed by the Taylor-Goldstein equation. The resulting inviscid modes are unstable for a large component of the wavenumber spectrum, with the result that buoyancy is strongly destabilizing. Restabilization is encountered at sufficiently large wavenumbers. For G large and negative the flow structure is again two layered Disturbances to the basic flow are now governed by the steady Taylor—Goldstein equation in the majority of the boundary layer, coupled with a viscous wall layer. The resulting eigenvalue problem is identical to that found for the corresponding case of lower-branch Tollmien—Schlichting waves, thus suggesting that the neutral curve eventually becomes closed in this limit.Eunice W. Mureithi, James P. Denier and Jillian A. K. Stot