Estimating the Optimal Control of Zoonotic Visceral Leishmaniasis by the Use of a Mathematical Model

Table 1

Model’s parameters. Values from Burattini et al. [14]. The indexes ℎ, 𝑑, and 𝑠 stand for humans, dogs, and sandflies, respectively.

Parameter	Biological meaning	Values
𝜇ℎ	Natural mortality rate	4.11 × 10^−5 days^−1
𝛼ℎ	Disease-induced lethality	5.48 × 10^−3 days^−1
𝑎ℎ	Average daily biting rate	1.25 × 10^−1 days^−1
𝑚ℎ	Vector density per host	1.00 × 10^2
𝑟ℎ	Spontaneous recovery rate	5.48 × 10^−4 days^−1
𝛾ℎ	Loss of immunity rate	5.48 × 10^−4 days^−1
𝛿ℎ	Latent recovery rate	1.10 × 10^−2 days^−1
𝜑ℎ	Inverse of incubation period	4.00 × 10^−4 days^−1
𝜎ℎ	Recovery rate of immunes	1.81 × 10^−3 days^−1
𝑏ℎ	Proportion of infective bites	1.00 × 10^−2
𝜇𝑑	Natural mortality rate	1.81 × 10^−4 days^−1
𝛼𝑑	Disease-induced lethality	1.81 × 10^−3 days^−1
𝑎𝑑	Average daily biting rate	1.25 × 10^−1 days^−1
𝑚𝑑	Vector density per host	5.00 × 10^2
𝑟𝑑	Spontaneous recovery rate	2.74 × 10^−4 days^−1
𝛾𝑑	Loss of immunity rate	2.74 × 10^−3 days^−1
𝜔𝑑	Treatment rate	Variable
𝜈	Vaccination	Variable
𝜉	Culling rate	Variable
𝜃	Insecticide collar	Variable
𝛿𝑑	Latent recovery rate	8.22 × 10^−3 days^−1
𝜑𝑑	Inverse of incubation period	1.10 × 10^−3 days^−1
𝜎𝑑	Recovery rate of immunes	9.04 × 10^−4 days^−1
𝑏𝑑	Proportion of infective bites	2.00 × 10^−2
𝜇𝑠	Natural mortality rate	6.00 × 10^−2 days^−1
𝜏	Extrinsic incubation period	7.00 days
𝑐	Proportion of infective bites	5.00 × 10^−2