This paper introduces a mathematical model of control for an animal epidemic outbreak in an ideal farm. What has been considered for this is poultry, aquaculture or livestock affected by an infectious disease (without immunity), which moderately threatens its economic performance and the local biosecurity. In this context, a control strategy is proposed, which is described by a sequence of rotative partial quarantines, where a fraction of the infected livestock is isolated to receive special care (hospitalization). A parametric threshold is obtained, ensuring a future healthy livestock. Furthermore, some economic and epidemiologic consequences have been studied.