Table 1.
Model parameters and values used in simulations.
Fig 1.
The effect of periodic variation.
The effect of the variance of periodic environmental variation on the severity of outbreaks and healthy host density. Left panels (A) and (B): variations affect pathogen growth rate rp. Right panels (C) and (D): variations affect 50% infective dose ID50. Top panels (A) and (C) show the peak areas (outbreak severities). Bottom panels (B) and (D) show healthy host (S + R) density minima. Colours red, black, and blue show results on rapid, intermediate, and slow immunity loss rates, respectively. Under short immunity, interaction with a small cyclic range of pathogen growth rates (see Methods) causes three different peak areas per value, corresponding to three differently shaped infection cycles. See Table 1 for model parameters.
Fig 2.
The effect of stochastic variation strength.
The effect of pink stochastic variation on outbreak dynamics at different environmental variances. Left panels (A)–(C): variations affect pathogen growth rate rp. Right panels (D)–(F): variation affects 50% infective dose ID50. Top panels (A) and (D): cumulative incidences. Each dot represents a single outbreak, the number of which varies between simulations. The lines show a marginal kernel density estimate of peak areas. Panels (B), (C), (E) and (F): number of peaks and minimum values of healthy host density. Each dot represents a single simulation run. The lines show a smoothing spline fit to the points. In all simulations the spectral exponent γ = 1, i.e. pink noise. Colours red, black, and blue show results on rapid, intermediate, and slow immunity loss rates, respectively. See Table 1 for model parameters.
Fig 3.
The effect of stochastic variation colour.
The effect of the colour of stochastic variation (spectral exponent) on epidemiology. Left panels (A)–(C): variations affect pathogen growth rate rp. Right panels (D)–(F): variations affect 50% infective dose ID50. Top panels (A) and (D): Cumulative incidences. Each dot represents a single outbreak, the number of which varies between simulations, and the lines show a marginal kernel density estimate of peak areas. Panels (B), (C), (E) and (F): number of peaks and minimum value of healthy host density. Each dot represents a single simulation run. The lines show smoothing spline fits to the points. In the left panels variance A = 0.0625. In the right panels variance A = 0.01. Colours red, black, and blue show results on rapid, intermediate, and slow immunity loss rates, respectively. See Table 1 for model parameters.
Fig 4.
The effect of correlated variations.
Effects of two stochastic environmental variations directed at pathogen growth rate rp and 50% infective dose (ID50) in negative (A), and positive (B) correlation. X-axis shows relative variances of the two variations. Temporal colour of stochastic environmental variation was set to γ = –1, i.e. pink noise. The environmental variance directed to pathogen growth rate was set to A1 = 0.09. Line and dot colours red, black, and blue show results on rapid, intermediate, and long immunity loss rates, respectively. Each dot is a result of an individual stochastic simulation, while the lines present results from simulations with periodic forcing. See Table 1 for model parameters.