Exploring the Dynamics of a Three-Species  Eco-Epidemiological Model with Holling  Type-II and Type-IV Functional Responses

S Hariprasad; M A S Srinivas; N. PhaniKumar; Lavanya S; D. Manohar

doi:10.9734/bpi/mcsru/v4/4897

Authors

S Hariprasad Department of Mathematics, Anurag University, Hyderabad, Telangana, India.
M A S Srinivas Department of Mathematics, Jawaharlal Nehru Technological University, Telangana, India.
N. PhaniKumar Department of Mathematics, Vignan Institute of Technology and Science, Telangana, India.
Lavanya S Department of Humanities and Basic Sciences, Visveswaraya College of Engineering and Technology, Hyderabad, Telangana, India.
D. Manohar Department of Mathematics, Anurag University, Hyderabad, Telangana, India.

DOI:

https://doi.org/10.9734/bpi/mcsru/v4/4897

Keywords:

Infected, susceptible, boundedness, local stability, global stability, routh-Hurwitz criteria, hopf bifurcation

Abstract

In this chapter, a prey-predator eco-epidemiological model with susceptible and diseased prey is constructed and investigated. The existence, uniqueness and boundedness of the solution of the system are studied. The conditions for the local and global stability of coexistence steady state are examined. The conditions for the occurrence of Hopf bifurcation with fixed biological parameter values are investigated and also it is noticed that the bifurcation occurs by sensitive changes in the parameter values of m₃, m₀and \(\alpha\) which represents the growth rate of a predator, transmission rate from infected prey to susceptible prey and half-saturation constant of predator respectively. At last, the mathematical results are interpreted with the help of numerical simulations.

Exploring the Dynamics of a Three-Species Eco-Epidemiological Model with Holling Type-II and Type-IV Functional Responses

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