Stochastic SIR-V model.

<p>(a) Schematic diagram of the baseline SIR host-parasite model with direct and environmental transmission. The symbol represents the susceptibles, and represent the infected and recovered individuals, respectively, and is the virus concentration in the environment. For host, there is equal birth rate and death rate . (b) A realization of a stochastic SIR-V model and its deterministic counterpart. The parameters used in the simulations are , , , , , , , and . Disease parameters correspond to avian influenza epidemics derived for typical water-borne transmission from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0028873#pone.0028873-Roche1" target="_blank">[33]</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0028873#pone.0028873-Rohani1" target="_blank">[2]</a>. Detailed descriptions of model parameters and sources for their numerical values are presented in tab:2. The deterministic curve was generated by integrating the mean field equations (5), and stochastic simulation was implemented with Gillespie algorithm <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0028873#pone.0028873-Gillespie1" target="_blank">[22]</a> with rates listed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0028873#pone-0028873-t001" target="_blank">Table 1</a>.</p

Temporal periodicity analysis of avian influenza in North America using the wavelet method.

<p>(a) Yearly prevalence of influenza A virus for wild ducks from 1976 to 2001 and for shorebirds from 1985 to 2000, where the data with green square and red circle symbols represent wild duck and shorebird, respectively. Annual prevalence was calculated as a percentage of the total number of samples tested for a given year that contained influenza A virus. We have redrawn this figure here with data kindly provided by Dr. Webster <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0028873#pone.0028873-Krauss1" target="_blank">[13]</a>. Panel (b) shows the time series with yearly prevalence of influenza A virus in wild ducks from 1976 to 2001. (c) The wavelet spectrum analysis corresponds to time series of panel (b), where time runs along the -axis and the contours limit areas of power at the periods indicated in the -axis. High power values are colored in dark red; yellow and green denote intermediate power; cyan and blue, low. Note the bold continuous black line is known as the cone of influence and delimits the region not influenced by edge effects. Only patterns within these lines are therefore considered reliable. Finally, the right panel (d) corresponds to the average wavelet spectrum (black line; see section: wavelet power spectrum) with its significant threshold value of 5% (dotted line). Wavelet software provided by C. Torrence and G. Compo, is available at <a href="http://www.paos.colorado.edu/research/wavelets/" target="_blank">http://www.paos.colorado.edu/research/wavelets/</a>.</p

List of events associated with transition rates.

a<p>Note that here we consider it as a frequency dependent.</p>b<p>There is no empty site, and the population size is constant, thus a new susceptible individual will be born once an infective individual dies.</p

The definitions of the parameters in this model and their values for the special case (AIV).

a<p>Parameter values are based on empirical studies in literature. Since no data are available for and , we let them vary within a reasonable range. We have studied how their values influence the patterns of interest (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0028873#pone-0028873-g003" target="_blank">Fig. 3</a>).</p>b<p>See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0028873#pone.0028873.s001" target="_blank">Methods S1</a>, section A3 for its biological significance.</p

Additional file 1: of SGEF is a potential prognostic and therapeutic target for lung adenocarcinoma

Figure S1. The schematic of the SGEF protein structure. Full length of SGEF protein contains an amino-terminal proline-rich region (Pro), a Dbl homology (DH) domain, and pleckstrin homology (PH) domain, as well as Src homology 3 domain (SH3). (TIFF 58 kb