Prey-predator models with infected prey and predators

Previous Article
On a class of model Hilbert spaces
DCDS Home
This Issue
Next Article
On the Ornstein Uhlenbeck operator perturbed by singular potentials in $L^p$--spaces

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

Prey-predator models with infected prey and predators

J. Gani ^1, and R. J. Swift ^2,

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

Abstract
Related Papers

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.

Keywords: non-homogeneous birth-death process., SIS and SIR epidemics, Deterministic and stochastic models, predator-prey models.

Mathematics Subject Classification: Primary: 92D25; Secondary: 34A3.

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.

[1]	Zhenquan Zhang, Meiling Chen, Jiajun Zhang, Tianshou Zhou. Analysis of non-Markovian effects in generalized birth-death models. Discrete and Continuous Dynamical Systems - B, 2021, 26 (7) : 3717-3735. doi: 10.3934/dcdsb.2020254
[2]	Hongxiao Hu, Liguang Xu, Kai Wang. A comparison of deterministic and stochastic predator-prey models with disease in the predator. Discrete and Continuous Dynamical Systems - B, 2019, 24 (6) : 2837-2863. doi: 10.3934/dcdsb.2018289
[3]	Christian Kuehn, Thilo Gross. Nonlocal generalized models of predator-prey systems. Discrete and Continuous Dynamical Systems - B, 2013, 18 (3) : 693-720. doi: 10.3934/dcdsb.2013.18.693
[4]	Nhu N. Nguyen, George Yin. Stochastic partial differential equation models for spatially dependent predator-prey equations. Discrete and Continuous Dynamical Systems - B, 2020, 25 (1) : 117-139. doi: 10.3934/dcdsb.2019175
[5]	Cheng-Hsiung Hsu, Jian-Jhong Lin. Existence and non-monotonicity of traveling wave solutions for general diffusive predator-prey models. Communications on Pure and Applied Analysis, 2019, 18 (3) : 1483-1508. doi: 10.3934/cpaa.2019071
[6]	Benjamin Leard, Catherine Lewis, Jorge Rebaza. Dynamics of ratio-dependent Predator-Prey models with nonconstant harvesting. Discrete and Continuous Dynamical Systems - S, 2008, 1 (2) : 303-315. doi: 10.3934/dcdss.2008.1.303
[7]	Wei Feng, Michael T. Cowen, Xin Lu. Coexistence and asymptotic stability in stage-structured predator-prey models. Mathematical Biosciences & Engineering, 2014, 11 (4) : 823-839. doi: 10.3934/mbe.2014.11.823
[8]	Henri Berestycki, Alessandro Zilio. Predator-prey models with competition, Part Ⅲ: Classification of stationary solutions. Discrete and Continuous Dynamical Systems, 2019, 39 (12) : 7141-7162. doi: 10.3934/dcds.2019299
[9]	Wan-Tong Li, Yong-Hong Fan. Periodic solutions in a delayed predator-prey models with nonmonotonic functional response. Discrete and Continuous Dynamical Systems - B, 2007, 8 (1) : 175-185. doi: 10.3934/dcdsb.2007.8.175
[10]	Aniello Buonocore, Luigia Caputo, Enrica Pirozzi, Amelia G. Nobile. A non-autonomous stochastic predator-prey model. Mathematical Biosciences & Engineering, 2014, 11 (2) : 167-188. doi: 10.3934/mbe.2014.11.167
[11]	Changrong Zhu, Lei Kong. Bifurcations analysis of Leslie-Gower predator-prey models with nonlinear predator-harvesting. Discrete and Continuous Dynamical Systems - S, 2017, 10 (5) : 1187-1206. doi: 10.3934/dcdss.2017065
[12]	Seong Lee, Inkyung Ahn. Diffusive predator-prey models with stage structure on prey and beddington-deangelis functional responses. Communications on Pure and Applied Analysis, 2017, 16 (2) : 427-442. doi: 10.3934/cpaa.2017022
[13]	Laurent Denis, Anis Matoussi, Jing Zhang. The obstacle problem for quasilinear stochastic PDEs with non-homogeneous operator. Discrete and Continuous Dynamical Systems, 2015, 35 (11) : 5185-5202. doi: 10.3934/dcds.2015.35.5185
[14]	Demetris Hadjiloucas. Stochastic matrix-valued cocycles and non-homogeneous Markov chains. Discrete and Continuous Dynamical Systems, 2007, 17 (4) : 731-738. doi: 10.3934/dcds.2007.17.731
[15]	Ching-Hui Wang, Sheng-Chen Fu. Traveling wave solutions to diffusive Holling-Tanner predator-prey models. Discrete and Continuous Dynamical Systems - B, 2021, 26 (4) : 2239-2255. doi: 10.3934/dcdsb.2021007
[16]	Julián López-Gómez, Eduardo Muñoz-Hernández, Fabio Zanolin. On the applicability of the poincaré–Birkhoff twist theorem to a class of planar periodic predator-prey models. Discrete and Continuous Dynamical Systems, 2020, 40 (4) : 2393-2419. doi: 10.3934/dcds.2020119
[17]	Hao Zhang, Hirofumi Izuhara, Yaping Wu. Asymptotic stability of two types of traveling waves for some predator-prey models. Discrete and Continuous Dynamical Systems - B, 2021, 26 (4) : 2323-2342. doi: 10.3934/dcdsb.2021046
[18]	Tahani Mtar, Radhouane Fekih-Salem, Tewfik Sari. Mortality can produce limit cycles in density-dependent models with a predator-prey relationship. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022049
[19]	Guanqi Liu, Yuwen Wang. Stochastic spatiotemporal diffusive predator-prey systems. Communications on Pure and Applied Analysis, 2018, 17 (1) : 67-84. doi: 10.3934/cpaa.2018005
[20]	P. Bai, H.T. Banks, S. Dediu, A.Y. Govan, M. Last, A.L. Lloyd, H.K. Nguyen, M.S. Olufsen, G. Rempala, B.D. Slenning. Stochastic and deterministic models for agricultural production networks. Mathematical Biosciences & Engineering, 2007, 4 (3) : 373-402. doi: 10.3934/mbe.2007.4.373

2020 Impact Factor: 1.392

Tools

Metrics

Other articles
by authors

on AIMS
J. Gani R. J. Swift
on Google Scholar
J. Gani R. J. Swift

[Back to Top]