American Institute of Mathematical Sciences

Advanced
2010, 7(1): 67-81. doi: 10.3934/mbe.2010.7.67

Discrete host-parasitoid models with Allee effects and age structure in the host

Sophia R.-J. Jang 1,

1. 

Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, United States

Received  March 2009 Revised  May 2009 Published  January 2010

We study a stage-structured single species population model with Allee effects. The asymptotic dynamics of the model depend on the maximal growth rate of the population as well as on its initial population size. We also investigate two models of host-parasitoid interaction with stage-structure and Allee effects in the host. The parasitoid population may drive the host population to extinction in both models even if the initial host population is beyond the Allee threshold.
Keywords: host-parasitoid interaction., Allee effects, population threshold.
Mathematics Subject Classification: Primary: 92D25; Secondary: 39A1.
Citation: Sophia R.-J. Jang. Discrete host-parasitoid models with Allee effects and age structure in the host. Mathematical Biosciences & Engineering, 2010, 7 (1) : 67-81. doi: 10.3934/mbe.2010.7.67
[1]

Sophia R.-J. Jang. Allee effects in an iteroparous host population and in host-parasitoid interactions. Discrete & Continuous Dynamical Systems - B, 2011, 15 (1) : 113-135. doi: 10.3934/dcdsb.2011.15.113
[2]

S. R.-J. Jang. Allee effects in a discrete-time host-parasitoid model with stage structure in the host. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 145-159. doi: 10.3934/dcdsb.2007.8.145
[3]

Yunshyong Chow, Sophia Jang. Neimark-Sacker bifurcations in a host-parasitoid system with a host refuge. Discrete & Continuous Dynamical Systems - B, 2016, 21 (6) : 1713-1728. doi: 10.3934/dcdsb.2016019
[4]

Eduardo Liz, Alfonso Ruiz-Herrera. Delayed population models with Allee effects and exploitation. Mathematical Biosciences & Engineering, 2015, 12 (1) : 83-97. doi: 10.3934/mbe.2015.12.83
[5]

Nika Lazaryan, Hassan Sedaghat. Extinction and the Allee effect in an age structured Ricker population model with inter-stage interaction. Discrete & Continuous Dynamical Systems - B, 2018, 23 (2) : 731-747. doi: 10.3934/dcdsb.2018040
[6]

Jia Li. Modeling of mosquitoes with dominant or recessive Transgenes and Allee effects. Mathematical Biosciences & Engineering, 2010, 7 (1) : 99-121. doi: 10.3934/mbe.2010.7.99
[7]

Tzy-Wei Hwang, Yang Kuang. Host Extinction Dynamics in a Simple Parasite-Host Interaction Model. Mathematical Biosciences & Engineering, 2005, 2 (4) : 743-751. doi: 10.3934/mbe.2005.2.743
[8]

Erika T. Camacho, Christopher M. Kribs-Zaleta, Stephen Wirkus. Metering effects in population systems. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1365-1379. doi: 10.3934/mbe.2013.10.1365
[9]

Jim M. Cushing. The evolutionary dynamics of a population model with a strong Allee effect. Mathematical Biosciences & Engineering, 2015, 12 (4) : 643-660. doi: 10.3934/mbe.2015.12.643
[10]

Dianmo Li, Zhen Zhang, Zufei Ma, Baoyu Xie, Rui Wang. Allee effect and a catastrophe model of population dynamics. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 629-634. doi: 10.3934/dcdsb.2004.4.629
[11]

J. Leonel Rocha, Danièle Fournier-Prunaret, Abdel-Kaddous Taha. Strong and weak Allee effects and chaotic dynamics in Richards' growths. Discrete & Continuous Dynamical Systems - B, 2013, 18 (9) : 2397-2425. doi: 10.3934/dcdsb.2013.18.2397
[12]

Yongli Cai, Malay Banerjee, Yun Kang, Weiming Wang. Spatiotemporal complexity in a predator--prey model with weak Allee effects. Mathematical Biosciences & Engineering, 2014, 11 (6) : 1247-1274. doi: 10.3934/mbe.2014.11.1247
[13]

Yun Kang, Sourav Kumar Sasmal, Amiya Ranjan Bhowmick, Joydev Chattopadhyay. Dynamics of a predator-prey system with prey subject to Allee effects and disease. Mathematical Biosciences & Engineering, 2014, 11 (4) : 877-918. doi: 10.3934/mbe.2014.11.877
[14]

Peter Hinow, Philip Gerlee, Lisa J. McCawley, Vito Quaranta, Madalina Ciobanu, Shizhen Wang, Jason M. Graham, Bruce P. Ayati, Jonathan Claridge, Kristin R. Swanson, Mary Loveless, Alexander R. A. Anderson. A spatial model of tumor-host interaction: Application of chemotherapy. Mathematical Biosciences & Engineering, 2009, 6 (3) : 521-546. doi: 10.3934/mbe.2009.6.521
[15]

Miljana JovanoviĆ, Marija KrstiĆ. Extinction in stochastic predator-prey population model with Allee effect on prey. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 2651-2667. doi: 10.3934/dcdsb.2017129
[16]

Pengmiao Hao, Xuechen Wang, Junjie Wei. Global Hopf bifurcation of a population model with stage structure and strong Allee effect. Discrete & Continuous Dynamical Systems - S, 2017, 10 (5) : 973-993. doi: 10.3934/dcdss.2017051
[17]

Liman Dai, Xingfu Zou. Effects of superinfection and cost of immunity on host-parasite co-evolution. Discrete & Continuous Dynamical Systems - B, 2017, 22 (3) : 809-829. doi: 10.3934/dcdsb.2017040
[18]

Chang Gong, Jennifer J. Linderman, Denise Kirschner. A population model capturing dynamics of tuberculosis granulomas predicts host infection outcomes. Mathematical Biosciences & Engineering, 2015, 12 (3) : 625-642. doi: 10.3934/mbe.2015.12.625
[19]

Dong-Mei Zhu, Wai-Ki Ching, Robert J. Elliott, Tak-Kuen Siu, Lianmin Zhang. Hidden Markov models with threshold effects and their applications to oil price forecasting. Journal of Industrial & Management Optimization, 2017, 13 (2) : 757-773. doi: 10.3934/jimo.2016045
[20]

Edoardo Beretta, Dimitri Breda. Discrete or distributed delay? Effects on stability of population growth. Mathematical Biosciences & Engineering, 2016, 13 (1) : 19-41. doi: 10.3934/mbe.2016.13.19

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (10)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences