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Background: Visceral leishmaniasis belongs to the list of neglected tropical diseases and is considered a public health problem worldwide. Spatial correlation between the occurrence of the disease in humans and high rates of canine infection suggests that in the presence of the vector, canine visceral leishmaniasis is the key factor for triggering transmission to humans. Despite the control strategies implemented, such as the sacrifice of infected dogs being put down, the incidence of American visceral leishmaniasis remains high in many Latin American countries. Methodology/Principal Findings: Mathematical models were developed to describe the transmission dynamics of canine leishmaniasis and its control by culling. Using these models, imperfect control scenarios were implemented to verify the possible factors which alter the effectiveness of controlling this disease in practice. Conclusions/Significance: A long-term continuous program targeting both asymptomatic and symptomatic dogs should be effective in controlling canine leishmaniasis in areas of low to moderate transmission (R0 up to 1.4). However, the indiscriminate sacrifice of asymptomatic dogs with positive diagnosis may jeopardize the effectiveness of the control program, if tests with low specificity are used, increasing the chance of generating outrage in the population, and leading to lower adherence to the program. Therefore, culling must be planned accurately and implemented responsibly and never as a mechanical measure in large scale. In areas with higher transmission, culling alone is not an effective control strategy. Author Summary: Visceral leishmaniasis is listed as a neglected tropical disease and is considered a public health problem worldwide. The disease has been documented since 1885, the first case being reported in India. After over 120 years, the incidence of the disease remains high despite control strategies implemented. In areas where the disease is zoonotic, such as in Brazil, identification as well as removal of infected dogs is recommended in highly endemic areas for they are considered to be the reservoir of the Leishmania chagasi parasite. The theoretical basis that supports the culling of infected dogs is the assumption that the incidence of human infection is directly related to the number of infectious dogs. However, there is no consensus among researchers on the effectiveness of this strategy for controlling either human or canine visceral leishmaniasis. In this context, mathematical models can provide a basis for determining the strategies with the greatest potential for success. This paper aims to contribute to this discussion by introducing further complexities into the problem, in particular, the imperfect diagnosis of this infection and the time gap between laboratory diagnosis and culling and the presence of asymptomatic infections. [ABSTRACT FROM AUTHOR]