Infectious diseases affect prey populations, and predators choosing susceptible prey may lead to the extinction of the prey population. We propose a mathematical model of prey–predator interaction with the prey population divided into two classes: susceptible and infected. The susceptible prey subpopulation becomes infected by direct contact with the infected prey subpopulation, and the predator consumes only susceptible prey. An analysis of the model enabled the establishment of thresholds for the spread of disease in the absence and presence of predators. In the absence of predators, we obtain the classic basic reproduction number ℜ0, and in the presence of predators, we obtain a new threshold , which measures the effect of predators in the disease spread. Furthermore, these thresholds establish conditions for the existence and stability of biologically viable equilibrium points. Using numerical simulations, we determined the different biological characteristics of the model and illustrated the analytical results.