Table 1. Symbols and biological meanings of the parameters included in the model with the corresponding values and references.

SYMBOLS AND BIOLOGICAL MEANING		VALUES	REFERENCES
HUMANS
μh	Natural mortality rate	3.69x10-5 day-1	[62]
αh	VL lethality	1.38x10-2 year-1	[2]
ah	Average daily human bites by vector	1.4x10-1day-1	Assumed (based on Ovallos, [63])
mh	Vector density per human	1.07x10-1	Assumed (based on Ovallos, 2013—oral communication)
βh	Latency period (L→A)	3.3x10-2day-1	Estimated (based on Maia et al. [64])
δh	Recovery rate of asymptomatic individuals (A→R)	9.1x10-4 day-1	Estimated (based on Badaro et al. [5]; Carvalho et al. [65]; Silva et al.[66])
fm	Proportion of asymptomatic individuals who recover	83x10-2	[67]
φh	Rate of symptom development (A→D)	4.8x10-3 day-1	Estimated (based on Brazilian Ministery, [10])
fd	Proportion of individuals who become symptomatic	17x10-2	[67]
tth	Treatment rate (T→R)	2.0x10-2 day-1	[68]
σh	Recovery rate of treated individuals (D→R)	1.4x10-3 day-1	Estimated (based on Carvalho et al. [65]; Silva et al.[66]; Alvar [69])
γh	Loss of cell-mediated immunity (R→S)	5.47x10-4 day-1	Estimated (based on Badaro et al. [5]; Carvalho et al. [65]; Silva et al.[66]; Alvar [69])
Ωh	Birth rate	αh + μh
DOGS
μc	Natural mortality rate	9.23x10-4 day-1	[70]
αc	VL lethality	2.12 year-1	[71]
ac	Average daily dog bites by vector	1.4x10-1 day-1	Assumed (based on Galvis [63])
mc	Vector density per dog	1.94	Galvis, 2013 (oral communication)
βc	Latency period (L→A)	3.3x10-2 day-1	[64]
fL	Proportion of individuals that remain asymptomatic	22x10-2	[72]
δc	Recovery rate of asymptomatic individuals (A→R)	5.5x10-3 day-1	Estimated (based on Fisa et al. [73]; Silva et al. [74])
fR	Proportion of asymptomatic individuals that recover	45x10-2	[72]
φc	Rate of development of symptoms (A→D)	1.1x10-2 day-1	Estimated
fe	Proportion of individuals that become symptomatic	32x10-2	[72]
σc	Recovery rate of diseased individuals (D→R)	2.73x10-3 day-1	Estimated (based on Garcia et al. [72]; Pozio et al. [71])
γc	Loss of cell-mediated immunity (R→S)	2.73x10-3 day-1	Assumed
Ωc	Birth rate	αc + μc
VECTOR
μv	Life expectancy of non-infected vectors	9.09x10-2 day-1	[75]
μf	Life expectancy of infected, non-infective vectors	1.67x10-1 day-1	[75]
μm	Life expectancy of infected and infective vectors	2.5x10-1 day-1	Estimated (based on Kamhawi [76])
τ	Extrinsic incubation period	2.0x10-1 day-1	[76]
b	Fraction of infective bites	1.5x10-1	Assumed (based on Burattini et al. [29])
chl	Proportion of insects that acquire infection after biting latent humans	zero	[77]
che	Proportion of insects that acquire infection after biting diseased humans	1.2 x10-2	[77]
ccl	Proportion of insects that acquire infection after biting latent dogs	38.5x10-2	[78]
cce	Proportion of insects that acquire infection after biting diseased dogs	24.7x10-2	[78]
Ωf	Birth rate	μv + μf + μm + μR
SYMBOLS OF INTERVENTIONS
μe	Rate of latent dog culling X test sensitivity	Coverage X Ss
μs	Rate of diseased dog culling X test sensitivity	Coverage X Sa
ρ	Rate of dogs protected by vaccination X vaccine efficacy	Coverage X VE
VE	Vaccine efficacy	75%	Approximated value of vaccine efficacies of Leish-Tec® [26]
ε	Loss of vaccine-induced immunity	2.7x10-3 day-1	[79]
ω	Rate of collar use	Coverage
ψ	Loss of collar effect	2.8x10-3 day-1	[23]
acc	Average daily collar-wearing dog bites by vector ad X (1 –collar repellent effect)	ad X 10x10-2	[23]
CE	Average rate of collar repellent effect	90x10-2	[23]
μR	Mortality of insects that bite collar-wearing dogs	acc X k
k	Average collar-induced vector mortality rate	55x10-2	[23]
Sa	Test sensitivity in asymptomatic dogs	98x10-2	[50]
Ss	Test sensitivity in symptomatic dogs	47x10-2	[50]