Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays

Figure 3

(a and b) Stability of the endemic equilibrium showing Hopf-bifurcation, with initial variables: , , , , and . (c and d) The evolution of the infected, the susceptible and corresponding I-S portrait, and 3D phase trajectories, with , , and parameters: ; . The rest of the parameters remain fixed as in Table 2.

(a)

(b)

(c)

(d)