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

Abstract

We argue that the strategy of culling infected dogs is not the most efficient way to control zoonotic visceral leishmaniasis (ZVL) and that, in the presence of alternative control strategies with better potential results, official programs of compulsory culling adopted by some countries are inefficient and unethical. We base our arguments on a mathematical model for the study of control strategies against ZVL, which allows the comparison of the efficacies of 5, alternative strategies. We demonstrate that the culling program, previously questioned on both theoretical and practical grounds is the less effective control strategy. In addition, we show that vector control and the use of insecticide-impregnated dog collars are, by far, more efficient at reducing the prevalence of ZVL in humans.

Progress in the Mathematical Modelling of Visceral Leishmaniasis

“…Some models take a standard SI (Mejhed et al, 2009), SEI (Salah et al, 1994;Reithinger et al, 2004) or SEIR (Ribas et al, 2013) compartmental progression for dogs, however the first model of VL in dogs (Dye, 1988) takes the approach where some dogs have an innate resistance which is fixed at birth. These dogs, which will be referred to here as "never-infectious" (to use terminology coined later by Courtenay et al (2002b)), play no role in the transmission cycle (see Figure 8).…”

“…All red boxes correspond to infective dogs, although asymptomatic dogs are around 3-fold less infective to sandflies than those which are symptomatic. Ribas et al (2013) total recruitment rate…”

“…In the case of endemic L. infantum infection in dogs in Brazil, dog infection prevalence is around 19%, with a sandfly biting rate of approximately once every 3 days (Reithinger et al, 2004), sandfly life expectancy of 14 days (this is an upper estimate from the huge range of 2.4 (Dye, 1996) to 16.7 days (Ribas et al, 2013)) and infectivity towards sandflies of 10.7% (Courtenay et al, 2002b). Under this parameterisation µ V ≈ 0.0714 and λ V ≈ 0.0068 and so µ V is an order of magnitude larger.…”

“…Whilst this model does not include asymptomatics, it is interesting to note that this logic extends to them as well and it should be expected that bed nets work well at reducing the contribution of infection from all humans, regardless of whether their disease status is known/treated. Dye (1996) and Ribas et al (2013) used another similar approach to model control for humans. Both incorporated (direct) insecticidal vector control such as IRS by increasing vector mortality in their models.…”

“…Even though Dye found that prevalence in the dog population was lower under treatment than under quite modest insecticide interventions, the reduction in the total bites taken caused by increasing vector mortality was sufficient that insecticide was still the best option for reducing transmission to humans where they are a spill-over host. Ribas et al (2013) examine the use of DMC in their model by altering the ROIs to and from dogs:…”