Exploring the Dynamics of a Three-Species Eco-Epidemiological Model with Holling Type-II and Type-IV Functional Responses | Chapter 9 | Mathematics and Computer Science: Research Updates Vol. 4

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 , m₀ and α 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.

 

Author (s) Details

 

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.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcsru/v4/4897

Stability and Optimal Control of an Mathematical Model of Tuberculosis/AIDS Co-infection with Vaccination | Chapter 3 | New Ideas Concerning Science and Technology Vol. 11

 The analysis and control of a nonlinear mathematical epidemic model (S S_vih V E LI ) based on a system of ordinary differential equations modelling the spread of tuberculosis infectious with VIH/AIDS coinfection are the subject of this paper. The existence of both disease-free and endemic equilibrium is debated. R₀ is the reproduction number that has been calculated. We investigate the stability of epidemic systems around equilibriums using Lyapunov-Lasalle methods (Disease free and endemic equilibrium). The disease-free equilibrium's global asymptotic stability is proven whenever R_vac < 1, where R₀ is the reproduction number. We also show that Tuberculosis can be eradicated when R0 is less than one. To validate analytic data, numerical simulations are used. To achieve disease prevention by reducing the infectious group to the lowest level of vaccine coverage possible. There is a formulation of a control problem. The optimal control is defined using the Pontryagin's maximum theory. The Runge Kutta fourth method is used to extract and solve the optimality system numerically.

Author (s) Details

Leontine Nkague Nkamba
Department of Mathematics, University of Yaound´e I, Higher Teacher Training College, P.O. Box 47 Yaound´ e, Cameroon and AIDEPY Association des Ing ´enieurs Diplom´es de l’Ecole Polytechnique de Yaound´ e, Cameroon.

Thomas Timothee Manga
AIDEPY Association des Ing ´enieurs Diplom´es de l’Ecole Polytechnique de Yaound´ e, Cameroon.

View Book :- https://stm.bookpi.org/NICST-V11/article/view/677

Ammensalism Model with Distributed Type Delay | Chapter 4 | Recent Studies in Mathematics and Computer Science Vol. 3

 

We describe a mathematical model for the interaction between three species ecological model consists of first
(N1), second (N2) and third species (N3). The first species is preying on second, second species is ammensal on
the third. Distributed type delay is included in the interaction of first and second species. The system is
explained by couple of integro differential equations. The co-existing state is identified and also characterizes
the local, global stability analysis at this state. We provide a numerical simulation in support of stability analysis
using MATLAB and shown that the system is asymptotically stable.

Author(s) Details
Mrs. G. A. L. Satyavathi
Jawaharlal Nehru Technological University (JNTU), Kakinada, A.P., India.

Dr. A. V. Paparao
Department of Mathematics, Jawaharlal Nehru Technological University (JNTU), UCE, Vizianagaram, A.P., India.

Dr. K. Sobhan Babu
Department of Mathematics, Jawaharlal Nehru Technological University (JNTU), UCE, Narasaraopet, A.P., India.

View Book :- http://bp.bookpi.org/index.php/bpi/catalog/book/233