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

Ling Zhou; Guoqing Ding; Zuhan Liu; Ling Zhou; Guoqing Ding; Zuhan Liu

doi:10.3934/math.2025423

AIMS Mathematics

2025, Volume 10, Issue 4: 9202-9236. doi: 10.3934/math.2025423

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

School of Mathematical Science, Yangzhou University, Yangzhou 225002, China

Received: 26 January 2025 Revised: 30 March 2025 Accepted: 11 April 2025 Published: 22 April 2025
MSC : 35B40, 35K51, 35R35, 92B05

This paper investigates a eco-epidemiological model with a graph $ p\, $-Laplacian $ (p\geq 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.
- network,
- $ p\, $-Laplacian,
- eco-epidemiological model,
- global stability
Citation: Ling Zhou, Guoqing Ding, Zuhan Liu. A weighted networked eco-epidemiological model with nonlinear $ p\, $-Laplacian[J]. AIMS Mathematics, 2025, 10(4): 9202-9236. doi: 10.3934/math.2025423

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Abstract

This paper investigates a eco-epidemiological model with a graph $ p\, $-Laplacian $ (p\geq 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.

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