In this chapter, we consider how seasonally varying parameters act as a forcing mechanism and examine their dynamical consequences. For the most part, we will use measles as a prototypical directly transmitted infectious disease. We demonstrate how such temporally forced models allow us to better capture the observed pattern of recurrent epidemics in contrast to unforced models, which predict oscillations that are damped toward equilibrium (see Chapter 2).
The programs 5.1-5.3 can either model the epidemic for a fixed set of parameters (in which case the output is the level of susceptible and infected against time) or can generate the type of bifurcation diagrams seen in this chapter by sweeping though a range of parameter values (in which case the output is the parameter and the level of susceptible and infected individuals at one point each year).