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Predator-prey models describe the dynamics of ecological systems in which two species, the predator and the prey, interact. The objective of this study is to formulate and analyze a predator-prey mathematical model, based on a system of delay differential equations that takes into consideration time delay in migration, with a prey migration rate that depends on the predator density and other factors like availability of its food. It is shown that the population density mainly depends on both barriers during migration and the migration rate. The rates of migration may be affected by factors such as infrastructure through natural habitat, destruction of the natural habitat through logging, natural disasters like re-outbreaks among others. In view of this, relevant agencies should employ measures which will deal with factors which slow down the rate of migration or cause barriers during migration for example reducing natural habitat land allocation to human settlement, agriculture or infrastructure.
Edition, Springer, New York; 2001.
Hastings A. Population biology, concepts and models. Springer, New York; 1998.
Murray JD. Mathematical biology: I. an introduction third Edition. Springer Verlag, Berlin; 2002.
Mabwago et al.; JAMCS, 33(6): 1-11, 2019; Article no.JAMCS.51370
Abdllaoui AE, Auger PM, Kooi BW, Parra RB, Mchich R. Eects of Density - dependent migrations on stability of a two-patch predator-prey model. Mathematical Bioscience.
Pillai P, Gonzalez A, Loreau M. Evolution of dispersal in a predator-prey meta-community. The American Naturalist. 2012;179-2:204-216.
Comins HN, Blatt DWE. Predator-prey models in spatially heterogeneous environments. Journal of Theoretical Biology. 1974;48:75-83.
Mchich R, Auger PM, Poggiale JC. Eect of predator density dependent dispersal of prey on stability of a predator-prey system. Mathematical Biosciences. 2007;206:343-356.
Xu C, Chen L, Li P, Guo Y. Oscillatory dynamics in a discrete predator-prey model with distributed delays. PLoS ONE. 2018;13(12):e0208322.
Changjin Xu, Peiluan Li, Ying Guo. Global asymptotical stability of almost periodic solutions for a non-autonomous competing model with time-varying delays and feedback controls. Journal of Biological Dynamics. 2019;13(1):407-421.
Changjin Xu, Maoxin Lio. Dynamical behavior for a stochastic two-species competitive model. Open Mathemaitcs. 2017;15:1258-126.
Changjin Xu. Delay-induced oscillations in a competitor-competitor-mutualist Lotka Volterra model. Complexity. 2017:12. Article ID 2578043
Apima BS. A Predator-Prey Model incorporating delay in Migration. MSc. Thesis, Masinde Muliro University of Science and Technology, Kakamega, Kenya; 2014.
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.
Neubert MG, Klepac P, Van Den Driessche P. Stabilizing dispersal delays in predator-prey meta-population models. Theoretical Population Biology. 2002;61:339-347.
Hale JK, Lunel SV. Introduction to functional dierential equations. Springer-Verlag, NewYork; 1993.