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. 2015 May 6;12(106):20150024. doi: 10.1098/rsif.2015.0024

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© 2015 The Author(s) Published by the Royal Society. All rights reserved.

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Figure 6. — Attractor analysis diagram for measles parametrized for NYC, constructed using XPPAUT [42]. This figure is similar to Krylova [6, fig. 9], but the seasonal amplitude here is α = 0.12 rather than α = 0.08. (a) For each value of on the x-axis, yearly values of the infected SIR compartment are shown (on a log-scale) from long-term solutions of the system (ignoring transient dynamics). The light grey lines show repellers, which can have important influences on dynamics [43]. Parameter values used are μ = ν = 0.02 yr⁻¹, α = 0.12, . Longer period attractors exist for this parametrization of the SIR model, but their basins of attraction are small and they have not been observed in real-world systems. Our analysis is focused on the main branch, which shows, from left to right, a stable period doubling and an unstable period doubling bifurcation. (b) Transient periods associated with each of the attractors displayed in (a), computed as in [4,27]. (Online version in colour.)

Inline graphic — Attractor analysis diagram for measles parametrized for NYC, constructed using XPPAUT [42]. This figure is similar to Krylova [6, fig. 9], but the seasonal amplitude here is α = 0.12 rather than α = 0.08. (a) For each value of on the x-axis, yearly values of the infected SIR compartment are shown (on a log-scale) from long-term solutions of the system (ignoring transient dynamics). The light grey lines show repellers, which can have important influences on dynamics [43]. Parameter values used are μ = ν = 0.02 yr⁻¹, α = 0.12, . Longer period attractors exist for this parametrization of the SIR model, but their basins of attraction are small and they have not been observed in real-world systems. Our analysis is focused on the main branch, which shows, from left to right, a stable period doubling and an unstable period doubling bifurcation. (b) Transient periods associated with each of the attractors displayed in (a), computed as in [4,27]. (Online version in colour.)