Populations of infected livestock and mosquitoes.

<p>(a), (b) and (c) represent the populations of infectious livestock (solid line) and vectors (dashed line) in patches 1, 2 and 3, respectively. Same values of parameters are adopted in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003388#pntd-0003388-g003" target="_blank">Fig. 3</a>. Populations of both infected livestock and mosquitoes alter their patterns during the festival time. Due to the effect of increased movement rates during the festival, the peak of infected livestock population is not necessary to be the same as that of the infected mosquito population, i.e. patch 2.</p

Basic reproduction number.

<p>(a), (b) and (c) represent the populations of infectious livestock (solid line), the instantaneously local basic reproduction number (dashed line) and the instantaneously global basic reproduction number (dotted line) in patches 1, 2 and 3, respectively. Values of other parameters are identical with those in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003388#pntd-0003388-g003" target="_blank">Fig. 3</a>. The instantaneously global basic reproduction number is computed by considering the three patches as an entirety, while the instantaneously local basic reproduction number is measured only within the local patch based on the current disease dynamics.</p

How the starting time of festival preparation impacts patterns of disease outbreaks: infectious classes.

<p>(a)-(c) and (d)-(f), simulations of the populations of infectious livestock and vectors in patches 1–3, respectively. The starting time of festival preparation varies from 2, 3, to 4 weeks ago (n =  days), represented by solid, dashed and dotted lines, respectively. Values of other parameters are identical with those used in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003388#pntd-0003388-g003" target="_blank">Fig. 3</a> and . Unit: daily. When the preparation starts early, we are expecting a larger scale of disease outbreaks due to the higher concentration of livestock, larger scale infectious population appear in patches 1 and 3. However, less number of infectious individuals exist due to the exposed period in patch 2.</p

Interaction between the daily increment in movement speeds and the daily imported number on the size of cumulative infected livestock population.

<p>(a)-(i), simulations of the cumulative numbers of infected livestock at year 4, 29, and 62 (by row) in patches 1, 2, and 3 (by column). Same values of parameters used in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003388#pntd-0003388-g003" target="_blank">Fig. 3</a>.</p

How daily increment in the daily imported number of livestock impacts patterns of disease outbreaks.

<p>(a)-(c) and (d)-(f) show the populations of infectious livestock and vectors in patches 1–3, respectively. The increment on the daily imported number in patch 1 are 20, 100 and180 per day, represented by solid, dashed and dotted lines, respectively. Values of other parameters are identical with those used in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003388#pntd-0003388-g003" target="_blank">Fig. 3</a> and (km per day).</p

How daily increment in movement speed impacts basic reproduction numbers.

<p>(a) Instantaneously global reproduction number; (b)-(d) Instantaneously local reproduction numbers in patches 1, 2 and 3. In (b)-(d), km per day, described by solid, dashed and dotted lines, respectively. (e) Local reproduction number in patches 1, 2 and 3 are simulated by solid, dashed and dotted lines when km per day. Values of other parameters are identical with those used in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003388#pntd-0003388-g003" target="_blank">Fig. 3</a>.</p

Model comparison.

<p>(a), (b) and (c) show the populations of infectious livestock in patches 1, 2 and 3, respectively. The dashed, dotted, and solid lines represent three scenarios with 1) no periodic factors; 2) only the capacity of mosquitoes is periodic; and 3) parameters incorporating both seasonal and festival impacts. Values of parameters: Initial conditions: Units: daily.</p

Map of Rift valley fever in Egypt and flow chart.

<p>(a) Map of Egypt; (b)The flow chart of RVFV transmission and spatial dispersal. The sub-script represents the related compartment in patch , and the other parameters are listed in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003388#pntd-0003388-t002" target="_blank">Table 2</a>. Only the first patch has import of livestock, and then livestock, regardless of infection status, move from patch 1 to patch 3, via patch 2 with human demand. Within each of the patches, the disease pathogens are transmitted between livestock and mosquitoes causing infections. Directions in dash represent the seasonally or socioeconomically driven flows.</p

How the starting time of festival preparation impacts patterns of disease outbreaks: exposed classes.

<p>(a)-(c) and (d)-(f), simulations of the populations of exposed livestock and vectors in patches 1–3, respectively. The starting time of festival preparation varies from 2, 4, to 6 weeks ago (n =  days), represented by solid, dashed and dotted lines, respectively. Values of other parameters are identical with those used in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003388#pntd-0003388-g003" target="_blank">Fig. 3</a> and . Unit: daily. When the preparation starts early, we are expecting a larger scale of disease outbreaks due to the higher concentration of livestock. Therefore, more individuals in exposed period we can observe when the starting time varies from 2 to 6 weeks ago.</p

How daily increment in movement speeds impacts patterns of disease outbreaks.

<p>(a)-(c) show the populations of infectious livestock and (d)-(f) simulate the populations of infectious vectors in patches 1, 2 and 3, respectively. The daily increment of movement speeds are 10, 54 and 98 km/per day, represented by solid, dashed and dotted lines, respectively. Values of other parameters are identical with those used in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003388#pntd-0003388-g003" target="_blank">Fig. 3</a>. During the festival season, infectious livestock are transported from patch 1 to patch 3, via patch 2, therefore we can observe that the population of infectious livestock has a sudden drop in patches 1 and 2 while an increase in patch 3 in the case that movement speed is relative fast (the increment ).</p