Effects of deterministic and random refuge in a prey–predator model with parasite infection

• Published in: Mathematical biosciences 2012-09, Vol.239 (1), p.124-130
• Main Authors: Mukhopadhyay, B., Bhattacharyya, R.
• Format: Article
• Language: English
• Subjects: Animals; Eco-epidemiology; Exponential mean square stability; Extinction, Biological; Gaussian white noise; Global stability; Host-Parasite Interactions; Humans; Models, Biological; Models, Statistical; Numerical Analysis, Computer-Assisted; Parasitic Diseases - epidemiology; Population Dynamics; Predatory Behavior; Prey refuge; Random refuge
• ISSN: 0025-5564; 1879-3134
• DOI: 10.1016/j.mbs.2012.04.007

► We study the role of prey refuge on the predator–prey-pathogen interaction. ► Both the susceptible and the infected prey are assumed to undergo constant size refuges. ► The refuge sizes are shown to control predator extinction as well as species co-existence. ► The model with random refuge is analyzed for exponential mean square stability. ► Numerical study revealed stabilizing effect of larger refuge on stochastic dynamics. Most natural ecosystem populations suffer from various infectious diseases and the resulting host-pathogen dynamics is dependent on host’s characteristics. On the other hand, empirical evidences show that for most host pathogen systems, a part of the host population always forms a refuge. To study the role of refuge on the host-pathogen interaction, we study a predator–prey-pathogen model where the susceptible and the infected prey can undergo refugia of constant size to evade predator attack. The stability aspects of the model system is investigated from a local and global perspective. The study reveals that the refuge sizes for the susceptible and the infected prey are the key parameters that control possible predator extinction as well as species co-existence. Next we perform a global study of the model system using Lyapunov functions and show the existence of a global attractor. Finally we perform a stochastic extension of the basic model to study the phenomenon of random refuge arising from various intrinsic, habitat-related and environmental factors. The stochastic model is analyzed for exponential mean square stability. Numerical study of the stochastic model shows that increasing the refuge rates has a stabilizing effect on the stochastic dynamics.