Analysis of a Heroin Epidemic Model with Saturated Treatment Function

Figure 3

(a) and (b) represent bifurcations where drug users, , not in treatment equilibrium are plotted as a function of The blue solid line represents the stable equilibrium while the red solid line represents the unstable equilibrium. (a) represents forward bifurcation and the parameters used include , , , , , , , , , and while (b) represents backward bifurcation and parameters used are the same as in (a) except (c) depicts the critical value as a function of saturation parameter The black dotted line represents the threshold which if exceeded gives rise to backward bifurcation. (d) depicts the critical value as a function of treatment rate .

(a)

(b)

(c)

(d)