Structure-preserving discretizations of the SIR model are presented by focusing on the hodograph transformation and the conditions for integrability for their discrete SIR models are given. For those integrable discrete SIR models, we derive their exact solutions as well as conserved quantities. If we choose the parameter appropriately for one of our proposed discrete SIR models, it conserves the conserved quantities of the SIR model. We also investigate an ultradiscretizable discrete SIR model.

翻译：通过关注射线变换，提出了SIR模型的结构保持离散化方法，并给出了其离散SIR模型的可积性条件。针对这些可积的离散SIR模型，我们推导了它们的精确解及守恒量。若对本文提出的某个离散SIR模型适当选取参数，该模型可保持SIR模型的守恒量。此外，我们还研究了一个超离散化的离散SIR模型。