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

Incidence rate versus prevalence rate.

<p>A dot represents the dynamics of HIV infections without human mobility between the regions and a star represents the dynamics of HIV infections when there is human mobility between the regions for <i>R</i>_<i>B</i> > 1.</p

Time evolution of the metapopulation model for (a) Nairobi, (b) Kisumu, (c) Homa Bay and (d) Siaya for <i>R</i>_<i>B</i> < 1.

<p>The dotted blue lines represent infectious individuals when there is human mobility and the solid green lines represent infectious individuals when there is no human mobility between the regions.</p

Time evolution of the metapopulation model for (a) Wajir, (b) Laikipia, (c) Kirinyaga, (d) Marsabit for <i>R</i>_<i>B</i> > 1.

<p>The dotted blue lines represent infectious individuals when there is human mobility and the solid green lines represent Infectious individuals when there is no human mobility between the regions.</p

Incidence rate versus prevalence rate.

<p>A dot represents the dynamics of HIV infections without human mobility between the regions and a star represents the dynamics of HIV infections when there is human mobility between the regions for <i>R</i>_<i>B</i> < 1.</p

Bifurcation diagram of the of the system in Eq (8).

<p>The solid and dotted lines show the values at which the disease-free equilibrium point is stable and unstable respectively. The solid curves show the values at which the endemic equilibrium point is stable.</p

Flow diagram between regions for the SIR model with n-patches.

<p>For clarity, we consider individuals travelling to another region after returning home first.</p