n this paper, we propose and analyze a detailed mathematical model describing the dynamics of a preypredator model under the influence of an SIS infectious disease by using nonlinear differential
equations. We use the functional response of ratio-dependent Michaelis-Menten type to describe the
predation strategy. In the presence of the disease, prey and predator population are divided into two
disjointed classes, namely infected and susceptible. The first one is governed through due predation
interaction, and the second one is governed through the propagation of disease in the prey and
predator population via predation. Our aim is to analyze the effect of predation on the dynamic of
the disease transmission. Important mathematical results resulting from the transmission of the disease
under influence of predation are offered. First, results concerning boundedness, uniform persistence,
existence and uniqueness of solutions have been developed. In addition, many thresholds have been
computed and used to investigate local and global stability analysis by using Routh-Hurwitz criterion
and Lyapunov principle. We also establish the Hopf bifurcation to highlight periodic fluctuation with
persistence of the disease or without disease in the prey and predator population. Finally, numerical
simulations are carried out to illustrate the feasibility of the theoretical results.