Figure 2: Dynamics without loss of individual immunity or seasonal forcing. There is no loss of individual immunity ( 𝑘 r e c = 0 ; (10), Figure 1) nor seasonal forcing ((18); 𝑠 e n v = 0 ). (a) Short-term dynamics. (b) Long-term dynamics. Parameters and initial conditions have the values in Table 1. Successive epidemics are caused by loss of immunity at the population level from the natural birth and death processes (μ, (2), Table 1).