Inference for Ecological Dynamical Systems: A Case Study of Two Endemic Diseases
Figure 10
Plot of estimated per year rate of infection (labeled gamma on the -axis) versus (labeled on the -axis) in analytically predicted bounds expected for multiscale dynamics leading to coherence resonance. The light green line represents the V-shaped boundary of computed using and . This region is approximately the same size when computed for ranges of between 500000 and 2,000000 [11]. The blue line represents the contour of the bound . Both measles (red) and pertussis (blue) estimates lie well within the bound set by for coherence resonance; however, pertussis lies on the boundary of the bound, which seems to suggest that these epidemics are not as likely to exhibit multiscale dynamics as measles epidemics. This can be seen visually by comparing the reconstruction of the stochastic oscillators for measles (red) and pertussis (blue), respectively, for London shown in Figure 7.
