The role of transmissible diseases in the Holling-Tanner predator-prey model

Transmissible diseases are known to induce remarkable major behavioral changes in predator-prey systems. However, little attention has been paid to model such situations. The latter would allow to predict useful applications in both dynamics and control. Here the Holling-Tanner model is revisited to account for the influence of a transmissible disease, under the assumption that it spreads among the prey species only. We have found the equilibria and analyzed the behavior of the system around each one of them. A threshold result determining when the disease dies out has been identified. We also investigated the parametric space under which the system enters into Hopf and transcritical bifurcations, around the disease free equilibrium. The system is shown to experience neither saddle-node nor pitch-fork bifurcation. Global stability results are obtained by constructing suitable Lyapunov functions.