Optimal control and bifurcation analysis of a predator–prey model with self-limiting growth and predator disease

We propose and analyze an eco-epidemiological predator–prey model that incorporates self-limitation and disease transmission within the predator population. The model is formulated as a system of ordinary differential equations describing logistic prey growth under the interspecific interaction with the predator. On the other hand, the predator population is divided into susceptible and infected classes, whose growth is constrained by prey availability. Three biologically relevant equilibria are identified: predator extinction, disease-free coexistence, and coexistence with endemic disease. The existence and stability of these equilibria are determined by key ecological and epidemiological thresholds, including the basic reproduction number. Using numerical continuation methods, we demonstrate the occurrence of backward bifurcation, indicating that predator disease may persist even when the basic reproduction number is below one. This phenomenon arises from reduced predation efficiency in infected predators. Global sensitivity analysis reveals the dominant role of predation efficiency and infection rate in shaping the long-term dynamics of the ecosystem. An optimal control framework with time-dependent selective removal of infected predators demonstrates that disease suppression can be achieved while preserving predator–prey coexistence and minimizing control costs.