Fig 1.

Ecological stability depends on the host’s intrinsic rate of increase, r, and on ξ⁻¹, the expected persistence time of the free-living pathogen particle. Near the origin, the disease-free equilibrium (DF) is stable. In the region identified by S* stable, the endemic equilibrium is locally stable. In the region identified as S* unstable, endemic equilibrium is no longer an attractor. For most values of r where the host is free of disease, sufficient increase in FLP persistence leads to pathogen invasion. Any endemic equilibrium can be destabilized by sufficient increase in r. Parameter values: α = 0.03, β = 15, γ = 15, θ = 0.35, and c = 1.