Hamiltonian Analysis of Subcritical Stochastic Epidemic Dynamics

Figure 2

Phase plane of Hamiltonian dynamical system for subcritical SIS system . Flow is represented by arrows and the three invariant curves of the dynamics (solution curves of ) are shown in gray, as in Figure 1. In this case, the nontrivial curve is shifted to a different position, and its intersections with the axes are located above and to the left of the origin, where in the supercritical case (Figure 1) they are below and to the right of the origin. This leads to qualitatively different dynamics, requiring a different analysis to explain the quasistationary behavior of the model.