Visceral leishmaniasis (VL) is a zoonosis found worldwide. Its incidence has increased in Brazil in recent years, representing a serious public and animal health problem. The strategies applied in Brazil are questionable and are not sufficient to control the disease. Thus, we have compared the efficacy of some of the currently available strategies focused on dogs to prevent and control zoonotic VL in endemic areas by optimizing a mathematical model. The simulations showed that the elimination of seropositive dogs, the use of insecticide-impregnated dog collars, and the vaccination of dogs significantly contribute to reducing the prevalence of infection in both canines and humans. The use of insecticide-impregnated collars presented the highest level of efficacy mainly because it directly affected the force of infection and vector-dog contact. In addition, when used at a coverage rate of 90%, insecticide-impregnated collar was able to decrease the prevalence of seropositive dogs and humans to zero; moreover, because of the easy application and acceptance by the targeted population, these collars may be considered the most feasible for inclusion in public policies among the three simulated measures. Vaccination and euthanasia were efficacious, but the latter method is strongly criticized on ethical grounds, and both methods present difficulties for inclusion in public policies. When we compared the use of euthanasia and vaccination at coverages of 70 and 90%, respectively, the proportion of infected populations were similar. However, on evaluating the implications of both of these methods, particularly the negative aspects of culling dogs and the proportion of animals protected by vaccination, the latter measure appears to be the better option if the total cost is not significantly higher. The comparison of complications and advantages of different control strategies allows us to analyze the optimal measure and offer strategies to veterinary and public health authorities for making decisions to prevent and control zoonotic VL. Hence, improvements in both public and animal health can be achieved in regions with scenarios similar to that considered in the present study; such scenarios are characteristically found in some areas of Brazil and other countries.