Fig. 8.

The difference between $R_0$ that takes into account ${\widehat{L}}^{\ast }$ (black line) and $R_{0nc}$ that assumes constant $\widehat{L}$ regardless of phenology (gray line) is most dramatic for large offset between nymphal and larval activity, low contact rates between ticks and mice (${\gamma }_l=0.002,{\gamma }_n=0.004$) and low mouse density ($M=20$). The difference between $R_0$ and $R_{0nc}$ is negligible for higher contact rates (${\gamma }_l=0.004,{\gamma }_n=0.008$) and higher mouse density ($M=45$). $\widehat{L}$ was calculated using the equation (A.3) for ${\widehat{L}}^{\ast }$ when nymphal and larval phenology is synchronous ($t_{l0}$ = 0). As the offset between nymphal and larval activity increases, ${\widehat{L}}^{\ast }$ and $\widehat{L}$ diverge driving differences in estimates for $R_0$ and $R_{0}nc$