Figure 1.

Phase-plane of dynamical system (4). (a) Phase-plane views of 3 regions of system (4) in terms of relative growth rate α : y-domination (equilibrium y₂, left); coexistence (equilibrium I, middle) and x-domination (equilibrium x₁, right). Stable equilibria are marked in black. In all 3 cases, adding sources (inoculations) produces a stable coexistence equilibrium (intersection of asymptotic hyperbolae). The two solid lines are x-nullclines F(x, y) = 0, the two dashed lines are y-nullclines G(x, y) = 0. (b) Equilibria (4) for stationary sources S_X,Y (x(ε) – solid, y(ε) – dashed), with the parameters of Table 1, in 3 different ranges of α, as functions of EIR, 0 <ε < 100. Two sets of curves on each plot correspond to different partitions of EIR among strains: (i) p_X = p_Y = .5 (outer curves), (ii) p_X = .9; p_Y = .1 (inner 'x-biased' curves). The two solid lines are x-strains, and the dashed lines are y-strains.