November  2013, 33(11&12): 5059-5066. doi: 10.3934/dcds.2013.33.5059

Prey-predator models with infected prey and predators

1. 

Mathematical Sciences Institute, Australian National University, Canberra ACT 0200, Australia

2. 

Department of Mathematics and Statistics, California State Polytechnic University, Pomona, Pomona, CA 91768, United States

Received  February 2012 Revised  March 2012 Published  May 2013

Some deterministic models for prey and predators are considered, when both may become infected, the infection of the prey being either of the SIS or SIR type. We also study a simplified model for surviving predators.
Citation: J. Gani, R. J. Swift. Prey-predator models with infected prey and predators. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 5059-5066. doi: 10.3934/dcds.2013.33.5059
References:
[1]

N. Bairagi and J. Chattopadhyay, The evolution on eco-epidemiological systems, theory and evidence, J. Physics: Conference Series, 26 (2008), 012205. doi: 10.1088/1742-6596/96/1/012205.

[2]

H. W. Hethcote, W. Wang, L. Han and Z. Ma, A predator-prey model with infected prey, Theor. Pop. Biology, 66 (2004), 258-268. doi: 10.1016/j.tpb.2004.06.010.

[3]

Y-H. Hsieh and C. K. Hsiao, Predator-prey model with disease infection in both populations, Math. Med. Biology, 25 (2008), 247-266. doi: 10.1093/imammb/dqn017.

[4]

D. G. Kendall, On the generalized "birth-and-death" process, Ann. Math. Statist, 19 (1948), 1-15. doi: 10.1214/aoms/1177730285.

[5]

X. Zhou, X. Shi and X. Song, Analysis of a delay prey-predator model with disease in the prey species only, J. Korean Math. Soc, 46 (2009), 713-791. doi: 10.4134/JKMS.2009.46.4.713.

show all references

References:
[1]

N. Bairagi and J. Chattopadhyay, The evolution on eco-epidemiological systems, theory and evidence, J. Physics: Conference Series, 26 (2008), 012205. doi: 10.1088/1742-6596/96/1/012205.

[2]

H. W. Hethcote, W. Wang, L. Han and Z. Ma, A predator-prey model with infected prey, Theor. Pop. Biology, 66 (2004), 258-268. doi: 10.1016/j.tpb.2004.06.010.

[3]

Y-H. Hsieh and C. K. Hsiao, Predator-prey model with disease infection in both populations, Math. Med. Biology, 25 (2008), 247-266. doi: 10.1093/imammb/dqn017.

[4]

D. G. Kendall, On the generalized "birth-and-death" process, Ann. Math. Statist, 19 (1948), 1-15. doi: 10.1214/aoms/1177730285.

[5]

X. Zhou, X. Shi and X. Song, Analysis of a delay prey-predator model with disease in the prey species only, J. Korean Math. Soc, 46 (2009), 713-791. doi: 10.4134/JKMS.2009.46.4.713.

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