After the seminal work of Lotka and Volterra [52, 1] predator-prey study becomes popular and

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After the seminal work of Lotka and Volterra [52, 1] predator-prey study becomes popular and important research area in applied sciences (population dynamics and mathematical ecology etc.). Similarly, the pioneer work of Kermack-Meckindric [53] open new door to epidemiology. After the work of [52, 1, 53] many papers published in literature (for example see [13, 16, 17, 19, 31, 34, 43, 45, 57, 3, 5, 32, 61] and references therein). All these authors study the prey-predators systems with disease dynamics and they investigate the stability results. In recent decades the combined study of ecology and epidemiology is termed as eco-epidemiology. This area is quite new, however a sucient literature is available very few of them are cited here…show more content…
Similarly some jelly sh make daily horizontal migration [22, 60]. As an example of migratory birds, we can refer to [61]. We note that in the month of October, 2013 almost 3 lakh birds include Greylag Goose, Mallards, Teals, Shovelers and Pintails Junaid Kathju come to Kashmir (India) from di erent countries including Siberia, China, Central Asia and North Europe and birds stay in wetlands of Kashmir (India)[61]. A list of animals that migrate can see in [62]. Similarly for a list of migratory Indian birds can found in [63]. From this discussion it is clear that to study the prey-predator system more scienti cally, the e ect of migration must be taken into consideration Preprint submitted to Elsevier April 6, 2014 while formulating of mathematical model of this system. As far as the data on migration is concerned, there are a very few authentic sources are available in the literature. As pointed out earlier that migration of birds to Jammu and Kashmir (India) can see in [61], but the method how they count, methodology etc. are not so well de ned. However data of human migration may be found in census reports in any of the country. Available data on human migration is more accurate and authentic as compare to other species. The reason for this is quite simple that human has documentary evidence for movements but other species not. To our knowledge, exact data on migration of other species is not available. In the present study we consider the e ect of migration on prey

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