Effect of emergent carrying capacity in an eco‐epidemiological system. (8th June 2015)

• Record Type: Journal Article
• Authors: Saifuddin, Md.; Sasmal, Sourav Kumar; Biswas, Santanu; Sarkar, Susmita; Alquran, Marwan; Chattopadhyay, Joydev
• Is Part Of: Mathematical methods in the applied sciences. Volume 39:Number 4(2016:Mar. 15)
• Page Start: 806
• Page End: 823
• Publication Date: 2015-06-08
• Subjects: eco‐epidemiological system -- explicit carrying capacity -- emergent carrying capacity -- bi‐stability -- subclass92D25 -- 92D30 -- 92D40 -- 34D20 -- 34D23; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3523
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : The paper explores an eco‐epidemiological model of a predator–prey type, where the prey population is subject to infection. The model is basically a combination of S‐I type model and a Rosenzweig–MacArthur predator–prey model. The novelty of this contribution is to consider different competition coefficients within the prey population, which leads to the emergent carrying capacity. We explicitly separate the competition between non‐infected and infected individuals. This emergent carrying capacity is markedly different to the explicit carrying capacities that have been considered in many eco‐epidemiological models. We observed that different intra‐class and inter‐class competition can facilitate the coexistence of susceptible prey‐infected prey–predator, which is impossible for the case of the explicit carrying capacity model. We also show that these findings are closely associated with bi‐stability. The present system undergoes bi‐stability in two different scenarios: (a) bi‐stability between the planner equilibria where susceptible prey co‐exists with predator or infected prey and (b) bi‐stability between co‐existence equilibrium and the planner equilibrium where susceptible prey coexists with infected prey; have been discussed. The conditions for which the system is to be permanent and the global stability of the system around disease‐free equilibrium are worked out. Copyright © 2015 John Wiley & Sons, Ltd.