Bulletin of Mathematical Biology

, 70:2195

Spatiotemporal Dynamics of the Epidemic Transmission in a Predator-Prey System

Original Article

DOI: 10.1007/s11538-008-9340-3

Cite this article as:
Su, M., Hui, C., Zhang, Y. et al. Bull. Math. Biol. (2008) 70: 2195. doi:10.1007/s11538-008-9340-3

Abstract

Epidemic transmission is one of the critical density-dependent mechanisms that affect species viability and dynamics. In a predator-prey system, epidemic transmission can strongly affect the success probability of hunting, especially for social animals. Predators, therefore, will suffer from the positive density-dependence, i.e., Allee effect, due to epidemic transmission in the population. The rate of species contacting the epidemic, especially for those endangered or invasive, has largely increased due to the habitat destruction caused by anthropogenic disturbance. Using ordinary differential equations and cellular automata, we here explored the epidemic transmission in a predator-prey system. Results show that a moderate Allee effect will destabilize the dynamics, but it is not true for the extreme Allee effect (weak or strong). The predator-prey dynamics amazingly stabilize by the extreme Allee effect. Predators suffer the most from the epidemic disease at moderate transmission probability. Counter-intuitively, habitat destruction will benefit the control of the epidemic disease. The demographic stochasticity dramatically influences the spatial distribution of the system. The spatial distribution changes from oil-bubble-like (due to local interaction) to aggregated spatially scattered points (due to local interaction and demographic stochasticity). It indicates the possibility of using human disturbance in habitat as a potential epidemic-control method in conservation.

Keywords

Eco-epidemiology Cellular automaton Ordinary differential equations Probability transition model Discrete event model 

Copyright information

© Society for Mathematical Biology 2008

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsLanzhou UniversityLanzhouPeople’s Republic of China
  2. 2.Center of Excellence for Invasion Biology, Department of Botany and ZoologyUniversity of StellenboschMatielandSouth Africa
  3. 3.Key Laboratory of Arid and Grassland Agroecology of the Ministry of EducationLanzhou UniversityLanzhouPeople’s Republic of China

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