Fig. 3.

Disease-introgression dynamics between two species with symmetric initial conditions. The dynamics are described by the two-time-scales model (Fig. 2), following Eqs. (1)–(15). The initial conditions are assumed to be symmetric for the two species (${\beta }_{ii}={\beta }_{jj}$ and ${\beta }_{ij}={\beta }_{ji}$), and therefore, the dynamics for the two species are identical, indicated by red curves. a Between-species contact rates (${\beta }_{ij}$, $i\ne j$) appear in solid curves, and within-species contact rates (${\beta }_{ii}$) appear in dashed curves (Eqs. (10)–(13)). b Pathogen package size ($P_i$), measured as number or diversity of novel pathogens to which the species are vulnerable (Eqs. (14) and (15)). c Disease burden ($D_i$), proportional to pathogen package size $P_i$ and to the impact of diseases on each of the species, $F_i$ (Eqs. (1) and (2)). Three phases are observed in the dynamics: (1) Initial response to heavy disease burden, with decreased contact rates (orange); (2) Long-lasting stable phase with low but steady levels of disease burden (green); (3) Destabilization following the release from disease burden and recovery to initial conditions (blue). The parameters for the scenario modeled are ${\beta }_{11}\left(0\right)={\beta }_{22}\left(0\right)=0.05$; ${\beta }_{12}\left(0\right)={\beta }_{21}\left(0\right)=0.01$; $\gamma =0.045$; $P_1\left(0\right)=P_2\left(0\right)=100$, with scaling parameters $a=5\times 10^{-5}$, $b=0.02$, and $c=100$