A weighted networked eco-epidemiological model with nonlinear $p$-Laplacian

This paper investigates a eco-epidemiological model with a graph $p$-Laplacian $(p\ge 2)$. We first overcome the difficulties caused by the nonlinearity of the $p$-Laplacian and show the existence and uniqueness of the global solution to the system. By the approach of Lyapunov functions and the comparison principle, we show that the trivial equilibrium, the disease-free equilibrium without predators, the coexisting disease-free equilibrium, the prey's endemic equilibrium, and the coexisting endemic equilibrium are asymptotically stable under the given conditions. With numerical simulations, we apply our generalized weighed graph to the Watts-Strogatz network, which illustrates the effect of population mobility.