Dynamics of delayed competition model under the influence of pollution and disease

  • Naina Arya Department of Mathematics, AIAS, Amity University, Uttar Pradesh, Noida
  • Sumit Kaur Bhatia AIAS, Amity University Uttar Pradesh
  • Tripti Mittal Department of Mathematics, Dr. Akhilesh Das Gupta Institute of Technology and Management, G.G.S. Inderprastha University

Abstract

Two or more consumer species compete for a same source in a competitive model. The amount of a limiting resource in the environment reduces when two or more species compete for it. These species also confront other threats for their survival, such as health concerns, infection, pollution, and so on. Based on above, in this paper we develop a competition model where we have consider two logistically growing species competing for the same resource. Also, there is infection in one of the species. We study the influence of disease and pollutants on the competing population with delay in the transmission of infection in infective class. The characteristics of the model has been discussed to prove that the described system is bounded. The existence of infection-free equilibrium point and endemic equilibrium point of the system has been shown, in case of coexistence of the species. The stability analysis of the equilibrium points has been examined using the Routh-Hurtwiz criteria. The occurrence of hopf bifurcation considering time lag (?) as a critical parameter has been examined. The direction and stability of hopf bifurcation has been investigated. Numerical
simulations have been performed using MATLAB to prove our analytical results.

Published
2023-02-21