Effect of Rising Temperature on Lyme Disease: Ixodes scapularis Population Dynamics and Borrelia burgdorferi Transmission and Prevalence

Table 1

Default parameters used in model.

Parameter	Meaning	Value	Source
	Increase in mean annual temperature relative to historical	0- to 5-degree Celsius	Arbitrary
b	Per capita egg production per day	300	[5, 6]
de	Daily death rate for eggs	0.015	[43]
d1	Daily death rate of young hardening larvae	0.01	[44]
dn1, dA1	Daily death rate of engorged larvae and engorged nymphs	0.001	[45]
d2, dn2, dA2	Daily death rate of questing larvae, nymphs, and adults	0.094	[44]
d3a = dfna = dA3a	Daily death rate of feeding larva, nymphs, and adults on host type a (IM)	0.51	[39]
d3b = dfnb = dA3b	Daily death rate of feeding larva, nymphs, and adults on host type b (IS)	0.89	[39]
d3c = 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]
d3d = 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]
dA4	Daily death rate of engorged adults	0.5	[5, 6]
me(T)	Egg to larvae maturation rate		[6]
m1	Young hardening larvae to questing larvae maturation rate	0.033	[43]
m2, mn2, mA2	Questing tick to feeding tick maturation (all stages)	0.5	Estimated questing period of 5–6 days
m3, mfn, mA3	Feeding tick maturation rate, all stages, all hosts	0.5	[46]
mn1(T)	Engorged larvae maturation rate		[6]
mA1(T)	Engorged nymph maturation rate		[6]
r	A numerical feature to ensure you never divide by 0	0.001
	Probability of larvae infection	0.1	Estimated
	Probability of nymph infection	0.1	Estimated
Ca	Per host tick carrying capacity of host type a, incompetent mobile	239	[39]
Cb	Per host tick carrying capacity of incompetent stationary hosts	176.75	[39]
Cc = Ce	Per host tick carrying capacity of CUM and CIM hosts	11.4	[39]
Cd = Cf	Per host tick carrying capacity of CUS and CIS hosts	46.84	[39]
bIM	Birth rate of incompetent mobile hosts	0.00261	[39, 40, 47]
bIS	Birth rate of incompetent stationary hosts	0.0102	[39, 40, 47]
bCUM	Birth rate of competent uninfected mobile hosts	0.00753	[39, 40, 48]
bCUS	Birth rate of competent uninfected stationary host	0.0176	[39, 40, 47]
dIM	Death rate of IM hosts	0.000609	[39, 40, 47]
dIS	Death rate of IS hosts	0.00129	[39, 40, 47]
dCUM = dCIM	Death rate of competent uninfected mobile hosts	0.00157	[39, 40, 48]
dCUS = dCIS	Death rate of competent uninfected stationary hosts	0.00345	[39, 40, 47]
KIM	Cell carrying capacity of IM host	25	[39]
KIS	Cell carrying capacity of IS hosts	45	[39]
KCM	Cell carrying capacity of CUM + CIS hosts	3100	[39]
KCS	Cell carrying capacity of CUS + CIS hosts	9,335	[39]
	Probability of CUM host infection (per infective tick per day × number of hosts of that type)	0.117	[39]
	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