The geographic spread of "El mal de las caderas" in Capybaras (Hydrochaeris hydrochaeris)

The aim of this work is to describe an epidemiological model for a capybara (Hydrochaeris hydrochaeris) population. The model considers a tabanid ("mutuca") population (Diptera: tabanidae), as a vector for the disease called "mal de las caderas" in Estero del Ibera, Corrientes, Argentina. The study of this problem has ecological and economical importance since the meat and the hide of the capybara can be an exploitation resource. At first, a threshold value is determined as a function of the model parameters, obtaining a critical carrying capacity which determines the disease propagation or eradication. Then as the carrying capacity condition for the disease existence is satisfied, the existence of traveling wave solution is studied. Independent speeds are considered for the susceptible capybaras, the noninfected insect, and the disease. The speed of propagation for this model is obtained as function of model parameters followed by a discussion of strategies for controlling the spread of the disease.