Fig. 5

Infectivity–persistence trade-offs in a biphasic pathogen decay model. a Heatmap of the basic reproduction number \(\mathcal {R}_{0}\) of the biphasic decay disease model (Eq. (1)) as a function of the ratio of the persistences (τ₁/τ₂) and infectivities (π₂/π₁). The line is the contour along which \(\mathcal {R}_{0}=2\). The colored dots correspond to the colored lines in (b) and (c). b Fraction of the population infected over time for the values of pathogen persistence and infectivity ratios given by the dots in (a). Although all points have \(\mathcal {R}_{0}=2\), the epidemic dynamics vary significantly over the parameter ratios. Here, N= 1000, γ= 0.1, κ= 8, ρ= 0.15, α= 0.001, η= 0.99, ϕ₁= 0.1, ϕ₂= 0.01, π₁=0.0195, τ₁=2. c Pathogen decay curves in the absence of a pathogen input illustrate the degree of biphasic behavrior corresponding to the persistence ratios (τ₁/τ₂)