Table 1.
Default parameters used in model.
| Parameter | Meaning | Value | Source |
|---|---|---|---|
| w | Increase in mean annual temperature relative to historical | 0- to 5-degree Celsius | Arbitrary |
| b | Per capita egg production per day | 300 | [5, 6] |
| d e | Daily death rate for eggs | 0.015 | [43] |
| d 1 | Daily death rate of young hardening larvae | 0.01 | [44] |
| d n1, dA1 | Daily death rate of engorged larvae and engorged nymphs | 0.001 | [45] |
| d 2, dn2, dA2 | Daily death rate of questing larvae, nymphs, and adults | 0.094 | [44] |
| d 3a = dfna = dA3a | Daily death rate of feeding larva, nymphs, and adults on host type a (IM) | 0.51 | [39] |
| d 3b = dfnb = dA3b | Daily death rate of feeding larva, nymphs, and adults on host type b (IS) | 0.89 | [39] |
| d 3c = dfnc = dA3c = d3e = dfne = dA3e | Daily death rate of feeding larva, nymphs, and adults on host types c and e (CUM, CIM) | 0.73 | [39] |
| d 3d = dfnd = dA3d = d3f = dfnf = dA3f | Daily death rate of feeding larva, nymphs, and adults on host types c and e (CUS, CIS) | 0.72 | [39] |
| d A4 | Daily death rate of engorged adults | 0.5 | [5, 6] |
| m e(T) | Egg to larvae maturation rate | m e(T)= 0.0552 ∗ exp(−((T − 25.83)/4.946)2) ∗ HS(T − 15) | [6] |
| m 1 | Young hardening larvae to questing larvae maturation rate | 0.033 | [43] |
| m 2, mn2, mA2 | Questing tick to feeding tick maturation (all stages) | 0.5 | Estimated questing period of 5–6 days |
| m 3, mfn, mA3 | Feeding tick maturation rate, all stages, all hosts | 0.5 | [46] |
| m n1(T) | Engorged larvae maturation rate | m n1(T)= 0.04001∗ exp(−((T − 26.68)/9.533)2) ∗ HS(T − 15) | [6] |
| m A1(T) | Engorged nymph maturation rate | m A1(T)= 0.03173 ∗ exp(−((T − 23.85)/9.042)2) ∗ HS(T − 15) | [6] |
| r | A numerical feature to ensure you never divide by 0 | 0.001 | |
| p L | Probability of larvae infection | 0.1 | Estimated |
| p N | Probability of nymph infection | 0.1 | Estimated |
| C a | Per host tick carrying capacity of host type a, incompetent mobile | 239 | [39] |
| C b | Per host tick carrying capacity of incompetent stationary hosts | 176.75 | [39] |
| C c = Ce | Per host tick carrying capacity of CUM and CIM hosts | 11.4 | [39] |
| C d = Cf | Per host tick carrying capacity of CUS and CIS hosts | 46.84 | [39] |
| b IM | Birth rate of incompetent mobile hosts | 0.00261 | [39, 40, 47] |
| b IS | Birth rate of incompetent stationary hosts | 0.0102 | [39, 40, 47] |
| b CUM | Birth rate of competent uninfected mobile hosts | 0.00753 | [39, 40, 48] |
| b CUS | Birth rate of competent uninfected stationary host | 0.0176 | [39, 40, 47] |
| d IM | Death rate of IM hosts | 0.000609 | [39, 40, 47] |
| d IS | Death rate of IS hosts | 0.00129 | [39, 40, 47] |
| d CUM = dCIM | Death rate of competent uninfected mobile hosts | 0.00157 | [39, 40, 48] |
| d CUS = dCIS | Death rate of competent uninfected stationary hosts | 0.00345 | [39, 40, 47] |
| K IM | Cell carrying capacity of IM host | 25 | [39] |
| K IS | Cell carrying capacity of IS hosts | 45 | [39] |
| K CM | Cell carrying capacity of CUM + CIS hosts | 3100 | [39] |
| K CS | Cell carrying capacity of CUS + CIS hosts | 9,335 | [39] |
| p CUM | Probability of CUM host infection (per infective tick per day × number of hosts of that type) | 0.117 | [39] |
| p CUS | Probability of competent uninfected stationary host infection (per infective tick per day × number of hosts of that type) | 0.6635 | [39] |
| E(0) | Initial number of eggs | 10,000,000 | |
| NU1(0) | Initial uninfected engorged larvae | 5,000,000 | |
| AU1(0) | Initial uninfected engorged nymphs | 300,000 | |
| IM(0) | Initial incompetent mobile hosts | 25 | |
| IS(0) | Initial incompetent stationary hosts | 45 | |
| CUM(0) | Initial competent mobile hosts | 3,100 | |
| CUS(0) | Initial competent stationary hosts | 9,335 | |
| All other initial conditions | 0 |