<p>In the current study, the authors develop an eco-epidemic model that incorporates fear effects, prey refuge, and nonlinear harvesting terms, and considers the predator biomass to be affected by disease. This study analyses the positivity, boundedness, and stability properties of the system and, by deriving the basic reproduction number, also known as the disease invasion number and the predator invasion number, quantifies the critical thresholds governing disease transmission and predator persistence. This research also investigates the occurrence of transcritical and Hopf bifurcations at different equilibria and determines the direction and stability of the Hopf bifurcation. To identify the effect of the movement of prey-predator species, a diffusion term is incorporated to establish the conditions for Turing instability, leading to the emergence of pattern formation. Turing patterns like labyrinthine stripes, stripe-spot mixtures, and isolated spots are observed as the diffusion parameter of the infected species varies. Also, this study observes that augmenting the levels of fear and refuge reduces the infected population and contributes to the destabilisation of the system. Furthermore, our investigation reveals that an increasing refuge level leads the system to exhibit stable, periodic, period-doubling, and chaotic behaviours. To verify and validate the analytical findings, numerical simulations have been performed.</p>

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Invasion Number in Fear and Refuge Driven Spatial Predator-Prey Model with Nonlinear Harvesting

  • Sharada Nandan Raw,
  • Reena Choudhary

摘要

In the current study, the authors develop an eco-epidemic model that incorporates fear effects, prey refuge, and nonlinear harvesting terms, and considers the predator biomass to be affected by disease. This study analyses the positivity, boundedness, and stability properties of the system and, by deriving the basic reproduction number, also known as the disease invasion number and the predator invasion number, quantifies the critical thresholds governing disease transmission and predator persistence. This research also investigates the occurrence of transcritical and Hopf bifurcations at different equilibria and determines the direction and stability of the Hopf bifurcation. To identify the effect of the movement of prey-predator species, a diffusion term is incorporated to establish the conditions for Turing instability, leading to the emergence of pattern formation. Turing patterns like labyrinthine stripes, stripe-spot mixtures, and isolated spots are observed as the diffusion parameter of the infected species varies. Also, this study observes that augmenting the levels of fear and refuge reduces the infected population and contributes to the destabilisation of the system. Furthermore, our investigation reveals that an increasing refuge level leads the system to exhibit stable, periodic, period-doubling, and chaotic behaviours. To verify and validate the analytical findings, numerical simulations have been performed.