Fig. 3.

The basic reproductive number, $R_0$, of B. burgdorferi is greatest when larval activity is concentrated around peak mouse infection prevalence. The left panel depicts $R_0$ as a function of the duration of larval emergence ($l_l$) and time between nymphal and larval emergence ($t_{l0}$). Panels on the right depict within-season dynamics for representative timing parameter values indicated by their respective letters on the left panel. (A) Concentrated larval emergence (small $l_l$) that begins slightly after nymphal emergence ($20<t_{l0}<35$) increases the probability that questing larvae feed on mice recently infected by nymphs ($t_{l0}=25,l_l=18$). (B) Transmission decreases as larvae emerge later ($t_{l0}>35$) because the larval cohort feeds after peak mouse infection prevalence ($t_{l0}=50,l_l=18$). (C) When larval and nymphal emergence is more synchronous (small $t_{l0}$), transmission to larvae increases as larval emergence duration increases (large $l_l$) because more larvae feed after infectious nymphs ($t_{l0}=5,l_l=40$). B. burgdorferi is not maintained in systems where $R_0<1$. $R_0$ is calculated assuming tick emergence is uniformly distributed ($U(l_l)$ where $l_l$ is the larval emergence duration, see Appendix C). $\widehat{L}={\widehat{L}}^{\ast },{\widehat{N}}_i=1,{\widehat{N}}_u={\widehat{N}}^{\ast }-1$ (see Appendix A.) $l_n=25$ days; all other parameter values are shown in Table 1