Stability, Bifurcation, and a Pair of Conserved Quantities in a Simple Epidemic System with Reinfection for the Spread of Diseases Caused by Coronaviruses

Figure 8

Phase plane of system (9), for the case where ; the other rates are , , and . The vector field and some trajectories are indicated by lines and arrows in gray. In this case, the first vertical nullcline (15) is a line of zero slope whose intersection with the vertical axis coincides with the first horizontal nullcline (16), that is, (see black line); the horizontal and vertical remaining pair coincides with the -axis. The disease-free equilibrium point is unstable, and the endemic is a singly degenerate equilibrium; both points are indicated by a black circle.