Figure 1.
The typical life cycle of the black-legged or deer tick (Ixodes scapularis).
The light grey arrows represent the first year, and the dark grey arrows indicate the second year. The dotted areas on the arrows indicate the time period where two cohorts can overlap. Larvae emerge in mid to late summer and quest for 3–4 months and then moult followed by diapause in fall until next spring. The nymphs emerge in late spring and quest for 3–4 months before they moult into adults in fall. The adults emerge in fall and quest until late spring except during the coldest months when they undergo diapause. The larvae and nymphs usually feed on small mammals, mainly rodents, for blood meals, while the adults feed on larger mammals such as deer. The figure is based on Fig. 1 in [34]. Temporal dynamics of the tick and host populations from a typical run of the model is presented in Fig. S1.
Table 1.
Parameter definitions and the values used in the simulations.
Figure 2.
Pathogen prevalence in adult ticks in October with one route turned off at a time.
The figures in the top row show the cases when the two cohorts (larvae and nymphs) overlap, and the bottom row show the cases when they do not overlap: without vertical transmission ( = 0; A, D), without cofeeding transmission (all
's = 0; B, E), and without systemic transmission (
and
= 0; C, F). The blank colour means prevalence = 0. Cofeeding transmission is expressed as the multiples of the baseline rates (0.24 and 0.72). Neither vertical nor systemic transmission along can maintain the pathogen, while cofeeding transmission is necessary and can be sufficient by itself to sustain the pathogen in the tick population. The corresponding figures for R0 values are presented in Fig. S2.
Figure 3.
Relative importance of the three transmission routes.
Elasticity values when two cohorts overlap for vertical (A, D), cofeeding (B, E), and systemic transmission (C,F) with the vertical transmission rate() = 0.001, with inter-cohort overlap (A, B, C) and without (D, E, F). In both cases, relative importance of the three routes varies over the parameter space, notably cofeeding and systemic transmission exchanging relative importance as the baseline cofeeding transmission rate increases (Fig. 3B, C, E, F). Cohort overlap did not qualitatively change the results, but vertical transmission increased its relative importance by 10–15% (Fig. 3A,D).
Figure 4.
Relative importance of the input parameters.
Elasticity values of the input parameters with inter-cohort overlap (A, B) and without overlap (C, D). Case 1 – lower vertical and higher cofeeding transmission – the parameters related to nymphs have much higher elasticities, indicating that nymphs play the critical role in determining R0. The cofeeing transmission parameter () has high elasticity, and it is dominated by the pathway from nymphs to larvae (
). Case 2 – higher vertical and lower cofeeding transmission – the parameters for larvae increase elasticities.
Figure 5.
Prevalence of the pathogen with and without inter-cohort overlap for adults (A, B) and nymphs (C).
5A and 5B show the prevalence in adult ticks in October with inter-cohort overlap and without overlap, respectively. 5C shows the prevalence in nymphs in July with overlap. Systemic transmission is set at 0.9. These figures suggest that low, steady prevalence (>0–5%) in tick-borne flaviviruses could be maintained by low vertical, intermediate cofeeing, and high systemic transmission rates.
Figure 6.
The proposed major transmission paths based on the elasticity analysis.
The relative thickness of arrows qualitatively reflects the magnitudes of elasticity. When cohorts with the vertical transmission rate at 0.1% overlap (A), inter-cohort cofeeding transmission serves as the major route. With higher vertical transmission (1%), in addition to the above route, the importance of the two intra-cohort cofeeding transmission routes increases (B). When inter-cohort overlap is removed, the larva-nymph cofeeding route disappears, and the intra-cohort routes will maintain the pathogen with increased importance of the survival of the pathogen within ticks (C).
Figure 7.
Relative importance of the three transmission routes with varied host recovery rates (γ).
Relative importance of the three transmission routes with varied host recovery rates (γ); A) vertical, B) cofeeding, and C) systemic transmission. Cofeeding transmission rate was varied on the y-axis as described in the main text and specified in Table 1 and Table S1. Vertical transmission rate = 0.001 and systemic transmission rate = 0.9. Note that the scale of the x-axes is not linear. These figures suggest that the contributions from cofeeding transmission to pathogen persistence can be substantial even for pathogens with long infectious periods.
Figure 8.
The effects of recovery rates on pathogen prevalence in adult ticks in October.
Pathogen prevalence under longer infectious periods; A) about 4 months (γ = 0.03), B) chronic infection (γ = 0.001). Cofeeding and vertical transmission rates were varied, and systemic transmission was set at 0.9. Even when infection is chronic in hosts, cofeeding transmission can elevate prevalence. Recovery rates have larger effects when the cofeeding transmission rate is low. 8C shows prevalence of a pathogen that causes chronic infections in its host and has a relatively high vertical transmission rate, such as the agent of Lyme disease (the x-axis goes from 0 to 0.2 for this panel).