Northwich time-series data.

<p>Dashed lines are the time points in which the forward simulation resets in the epidemics = ‘break’ argument for a threshold for three.</p

Sampling scales for acute RNA viruses and the associated phylodynamic processes that viral genome sequence data and host sampling can elucidate.

<p>Sampling scales for acute RNA viruses and the associated phylodynamic processes that viral genome sequence data and host sampling can elucidate.</p

Output results from the runtsir function for London.

<p>Subplots A) and B) are the cumulative births against cumulative cases regression and estimated reporting rate, the C) and D) are the profiled from <i>Z</i>_<i>t</i> and then reconstructed <i>S</i>, E) is 26-point <i>β</i>_<i>t</i> with the <i>α</i> and mean <i>β</i> (indicated as ) estimate, and F) and G) are the data (blue) against 10 randomly chosen stochastic simulations (red) and the (inverse) data against mean of the simulations with confidence intervals.</p

The forward simulations for the Northwich time-series data under an epidemic-ahead fit using a threshold of three.

<p>The color coding in the panels shown here are the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0185528#pone.0185528.g001" target="_blank">Fig 1</a>.</p

Summary and description of the main functions in the tsiR package.

<p>Summary and description of the main functions in the tsiR package.</p

Fluctuating genetic diversity of influenza A virus.

<p>The figure shows a Bayesian skyline plot of changing levels of genetic diversity through time for the HA gene (165 sequences) of A/H3N2 virus sampled from the state of New York, US, during the period 2001–2003. The <i>y</i>-axes depict relative genetic diversity (<i>N</i>_e<i>t</i>, where <i>N</i>_e is the effective population size, and <i>t</i> the generation time from infected host to infected host), which can be considered a measure of effective population size under strictly neutral evolution. Peaks of genetic diversity, reflecting the seasonal occurrence of influenza, are clearly visible. See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000505#pcbi.1000505-Rambaut1" target="_blank">[30]</a> for a more detailed analysis.</p

Impact of Birth Seasonality on Dynamics of Acute Immunizing Infections in Sub-Saharan Africa

<div><p>We analyze the impact of birth seasonality (seasonal oscillations in the birth rate) on the dynamics of acute, immunizing childhood infectious diseases. Previous research has explored the effect of human birth seasonality on infectious disease dynamics using parameters appropriate for the developed world. We build on this work by including in our analysis an extended range of baseline birth rates and amplitudes, which correspond to developing world settings. Additionally, our analysis accounts for seasonal forcing both in births and contact rates. We focus in particular on the dynamics of measles. In the absence of seasonal transmission rates or stochastic forcing, for typical measles epidemiological parameters, birth seasonality induces either annual or biennial epidemics. Changes in the magnitude of the birth fluctuations (birth amplitude) can induce significant changes in the size of the epidemic peaks, but have little impact on timing of disease epidemics within the year. In contrast, changes to the birth seasonality phase (location of the peak in birth amplitude within the year) significantly influence the timing of the epidemics. In the presence of seasonality in contact rates, at relatively low birth rates (20 per 1000), birth amplitude has little impact on the dynamics but does have an impact on the magnitude and timing of the epidemics. However, as the mean birth rate increases, both birth amplitude and phase play an important role in driving the dynamics of the epidemic. There are stronger effects at higher birth rates.</p></div

Heat map illustrating how incidence of epidemics change with changing birth rate and amplitude.

<p>The contour plot illustrates the transition from annual to biennial epidemics. The timing of the epidemic did not change significantly with changing birth rate () and amplitude (). ( = 0,  = 1000,  = 0).</p

Bifurcation diagrams showing the impact of varying birth amplitude () on the periodicity of the epidemics.

<p>Simulations use extrapolated initial conditions (the numbers of susceptibles, exposed, infectives, and recovered at the end of one simulation are used to start the next simulation <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0075806#pone.0075806-Keeling1" target="_blank">[27]</a>). In Panel A the first simulation is at  = 0 (left hand of the x axis), then is increased in the subsequent simulations; to further sample the bifurcation structure, Panel B reverses this order, starting at  = 1. Black points represent the relative size of the incidence peaks, blue circles represent the period of the attractor, while the background is a heat map of the power spectral densities where the color red signifies higher power. In Panel B, at high levels of , there are both annual and biennial components present but the power is stronger for the biennial component. ( = 35/1000,  = 0,  = 1000,  = 0).</p

One-dimensional bifurcations of the effect of varying values given different baseline values of (0.1, 0.2, 0.3, 0.4) and (in phase, anti-phase).

<p>Black points represent the relative size of the epidemic peaks, blue circles represent the period of the attractor, while the background is a heat map of the the power spectral densities where the color red signifies higher power. In all of the figures, the presence of an annual and biennial component is always present even though, for instance, an attractor may have a period of four years. The bottom panel in each of the figures shows the main Lyapunov exponent, when the system bifurcates the Lyapunov exponent equals zero (touches the horizontal line), when the Lyapunov exponent is greater than zero the dynamics are said to be chaotic. ( = 30/1000,  = 1000 in all panels).</p