Fig. 12.

The basic reproductive number, $R_0$, of B. burgdorferi is greatest when larval emergence begins shortly after nymphal emergence such that larvae are active during the peak in mouse infection prevalence. The left-hand panel depicts $R_0$ as a function of the time between the start of nymphal and larval emergence ($t_{l0}$), and the nymphal emergence width parameter (${\lambda }_n$), and the letters indicate the parameters for the within-season dynamics on the right-hand panels. (A) Concentrated nymphal emergence (large ${\lambda }_n$) coupled with a slight difference between when nymphs and larvae begin emerging ($t_{l0}<25$) increases the probability that questing larvae feed on mice recently infected by nymphs ($t_{l0}=10,{\lambda }_n=0.55$). (B) Greater differences between when nymphs and larvae begin emerging ($t_{l0}>25$) result in lower mouse-to-larvae transmission rates as many mice infected by nymphs die and are replaced by mice born uninfected such that larvae are likely to feed on uninfected mice ($t_{l0}=50,{\lambda }_n=0.55$). (C) Synchronous emergence ($t_{l0}=0$) can also reduce B. burgdorferi fitness when nymphal emergence duration is long (small ${\lambda }_n$) as many larvae feed before nymphs infect mice ($t_{l0}=5,{\lambda }_n=0.2$). $R_0$ is calculated assuming tick emergence is Gamma distributed. ${\lambda }_l=0.5,{\varphi }_l={\varphi }_n=10,\widehat{L}={\widehat{L}}^{\ast },{\widehat{N}}_i=1,{\widehat{N}}_u={\widehat{N}}^{\ast }-1$ (see Appendix A). All other parameter values are shown in Table 1