Figure 6.

Introducing a single new case of a disease into the population can affect the long-pause oscillation of the disease frequency differently, depending on when it is introduced. (a) Introduction early in the apparent extinction of the disease. (b) Introduction late in the apparent extinction of the disease. (c) Introduction after the disease has re-established and is oscillating towards an endemic equilibrium. (d–f) Disease-susceptible (S) and anti-vaccine (A) frequencies for the trajectories in (a–c). An arrow indicates the new case. In all panels, for the grey trajectory, provided as a reference, no new case is introduced. The vertical dashed line indicates the point at which disease frequency starts increasing after the initial epidemic, during its apparent extinction. The horizontal dashed line in (d–f) is the 1/R₀ threshold frequency of disease-susceptible individuals necessary for disease spread. Parameters used in this example are the same as in Figure 4c, except w is increased to 0.5 to provide a longer pause for illustration.