Analysis of infected single species population model with delay in polluted environment

Analysis of Infected Single Species Population Model

  • Naina Arya Department of Mathematics, AIAS, Amity University, Uttar Pradesh, Noida
  • Sumit Kaur Bhatia Department of Mathematics, Amity Institute of Applied Sciences, Amity University Uttar Pradesh, Noida, India
  • Deeksha Singhal Department of Mathematics, AIAS, Amity University, Uttar Pradesh, Noida
  • Rishika Chanian Department of Mathematics, AIAS, Amity University, Uttar Pradesh, Noida
  • Sudipa Chauhan Department of Mathematics, AIAS, Amity University, Uttar Pradesh, Noida

Abstract

We propose a non-linear population model in which the simultaneous effects of disease and toxicants are studied. Boundedness and positivity of the model is discussed. Existence of infection free equilibrium point has been established and its stability is analyzed on the basis of reproduction number. Also, existence of the endemic equilibrium point has been established. Further, we study the existence of Hopf-Bifurcation and derive a threshold ?0, below which the endemic equilibrium point is asymptotically stable and at ?0 it undergoes Hopf-Bifurcation. We also discuss the direction of Hopf-Bifurcation. Using Lyapunov functional approach, sufficient conditions for global stability of the endemic equilibrium point are obtained. Lastly, numerical simulations are carried out to support our analytic results and to investigate the influence of key parameter like pollution on the spread of disease.

Published
2024-02-16
Issue
Vol 31 No 1 (2024): Nonlinear Studies (NS)
Section
Articles