Rosenzweig-Macaurther Model with Holling type II Predator Functional Response for Constant Delayed Migration

Apima B, Samuel; Lawi O, George; Kagendo, Nthiiri J

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dc.contributor.author	Apima B, Samuel
dc.contributor.author	Lawi O, George
dc.contributor.author	Kagendo, Nthiiri J
dc.date.accessioned	2019-09-17T06:09:52Z
dc.date.available	2019-09-17T06:09:52Z
dc.date.issued	2019-08-29
dc.identifier.citation	1] Brauer F, Chaves CC. Mathematical models in population biology and epidemiology. Second Edition, Springer, New York; 2001. [2] Murray JD. Mathematical Biology: I. An Introduction Third Edition. Springer Verlag, Berlin; 2002. [3] Abdllaoui AE, Auger PM, Kooi BW, Parra RB, Mchich R. Effects of Density - dependent migrations on stability of a two-patch predator-prey model. Mathematical Bioscience. 2007;210:335-354. [4] Mchich R, Auger PM, Poggiale JC. Effect of predator density dependent dispersal of prey on stability of a predator-prey system. Mathematical Biosciences. 2007;206:343- 356. [5] Wasike AM, Bong’ang’a AS, Lawi GO, Nyukuri MO. A predator-prey model with a time lag in the migration. Applied Mathematical Science. 2014;8-75:3721-3732. [6] Apima BS. A predator-prey model incorporating delay in migration. MSc. Thesis, Masinde Muliro University of Science and Technology, Kakamega, Kenya; 2014. [7] Pillai P, Gonzalez A, Loreau M. Evolution of dispersal in a predator-prey metacommunity. The American Naturalist. 2012;179(2):204-216. [8] Abadi, Dian S, Choirotul U. Stability analysis of Lotka-Volterra model with Holling type II functional response. Scientific Research Journal. 2013;I(V):22-26. [9] Huang Y. Predator migration in response to prey density. What are the consequences? J. Math. Biol. 2001;43:561-581. [10] Rosenzweig M, MacArthur R. Graphical representation and stability conditions of predator-prey interaction. American Naturalist. 1963;97:209-223. [11] Xu C, Li P. Oscillations for a delayed predator-prey model with Hassell- Varley type functional responses. Comptes Rendus Biologies. 2015;338(4):227-240. [12] Xu C, Li P. Bifurcation behaviors analysis on a predator-prey model with nonlinear diffusion and delay. Journal of Dynamical and Control Systems. 2014;20(1):105-122. 13Samuel et al.; ARJOM, 15(1): 1-14, 2019; Article no.ARJOM.50672 [13] Xu C, Li P. On the periodicity and global stability for a discrete delayed predatorprey model. International Journal of Mathematics 2013;24(10):1350086. [14] Xu C, Liao M. Bifurcation analysis of an autonomous epidemic predator- prey model with delay. Annali di Matematica Pura ed Applicata. 2014;193(1):23-28. [15] Xu C, Liao M. Bifurcation behaviors in a delayed three-species food-chain model with Holling type-II functional response. Applicable Analysis. 2013;92(12):2468-2486. [16] Xu C, Liao M, He X. Stability and Hopf bifurcation analysis for a Lokta-Volterra predatorprey model with two delays. International Journal of Applied Mathematics & Computer Science. 2011;21(1): 97C107. [17] Comins HN, Blatt DWE. Predator-prey models in spatially heterogeneous Environments. Journal of Theoretical Biology. 1974;48:75-83. [18] Neubert MG, Klepac P, Van Den Driessche P. Stabilizing Dispersal Delays in PredatorPrey Meta-population Models Theoretical Population Biology. 2002;61:339-347. [19] Hale JK, Lunel SV, Introduction to functional differential equations. Springer-Verlag, New York; 1993.	en_US
dc.identifier.issn	2456-477X
dc.identifier.uri	http://erepository.kafuco.ac.ke/123456789/38
dc.description.abstract	Predator-prey models describe the interaction between two species, the prey which serves as a food source to the predator. The migration of the prey for safety reasons after a predator attack and the predator in search of food, from a patch to another may not be instantaneous. In this paper, a Rosenzweig-MacAurther model with a Holling-type II predator functional response and time delay in the migration of both species is developed *Corresponding author: E-mail: sapima@kafuco.ac.ke;Samuel et al.; ARJOM, 15(1): 1-14, 2019; Article no.ARJOM.50672 and analysed. Stability analysis of the system shows that depending on the prey growth and prey migration rates either both species go to extinction or co-exist. Numerical simulations show that a longer delay in the migration of the species leads makes the model to stabilize at a slower rate compared to when the delay is shorter. Relevant agencies like the Kenya Wildlife Service should address factors that slow down migration of species,for example, destruction of natural habitats for human settlement and activities, which may cause delay in migration.	en_US
dc.language.iso	en	en_US
dc.publisher	Asian Research Journal of Mathematics	en_US
dc.subject	Rosenzweig-Mac Aurther model; delay; migration	en_US
dc.title	Rosenzweig-Macaurther Model with Holling type II Predator Functional Response for Constant Delayed Migration	en_US
dc.type	Preprint	en_US