A ratio-dependent predator-prey model with disease in the prey

In this paper, a ratio-dependent predator-prey system with disease in the prey is formulated and analyzed. Mathematical analyses of the model equations with regard to invariance of nonnegativity, boundedness of solutions, nature of equilibria, permanence and global stability are analyzed. Specially, we shall show that ratio-dependent predator-prey models are rich in boundary dynamics, and most importantly, we shall show that a periodic solution can occur whether the system is permanent or not, that is, there are solutions which tend to disease-free equilibrium while bifurcating periodic solution exists.