Mathematical Analysis of the Control of the Spread of Infectious Disease in a Prey-Predator Ecosystem
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International Journal of Computer & Organization Trends (IJCOT) |  |
| © 2012 by IJCOT Journal | ||
| Volume-2 Issue-1 |
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| Year of Publication : 2012 | ||
| Authors : E.A. Bakare,Y.A Adekunle, A.Nwagwo |
Citation
E.A. Bakare,Y.A Adekunle, A.Nwagwo . "Mathematical Analysis of the Control of the Spread of Infectious Disease in a Prey-Predator Ecosystem" . International Journal of Computer & organization Trends (IJCOT), V2(1):11-16 Jan - Feb 2012, ISSN 2249-2593, www.ijcotjournal.org. Published by Seventh Sense Research Group.
Abstract
We present a model for the mathematical analysis of the control of the spread of an infectious disease in a predator-prey ecosystem. In this work, we present a compartmental mathematical model expressed by a systems of differential equations based on the dynamics of the Infection. We discuss the Disease Free Equilibrium(DFE) and the Endemic Disease Equilibrium(EDE). In this study, we realized that to eradicate or reduce the intensity of disease spread in the prey-predator ecosystem ,we apply vaccination strategies with herd immunity.
References
[1] Abulwafa, E.M., Abdou, M.A. and Mahmoud,A.A., The solution of nonlinear coagulations problem with mass loss, Chaos, Solution and Fractals,in press (2006).
[2] Beddington, J.R., Free, C.A., Lawton, J.H. Dynamic Complexity in Predator-prey Models Framed in difference equations. Journal of Nature 255, 58-60.(1975).
[3] Benyah Francis, 2006.Lecture note on Introduction to Mathematical modelingII.8th Regional College on Optimization, modeling and Simulation, University of Cape Coast, Cape Coast, Ghana.
[4] Dunbar, S.R. (1984). Traveling wave Solutions of Diffusive Lokta-Volterra equations. Journal of Mathematical Biology, 17, 11-32
[5] Dunbar, S.R. (1984). Traveling wave Solutions of diffusive Lokta-Volterra equations: A Heteroclinic connection in R4 Trans. American Mathematical Society, 268, 557-594.
[6] Francis Benyah (2008). Introduction to Epidemiological modeling.10th Regional College on Modelling, Simulation and Optimization.
[7] Hoppensteadt, F. (2006). Predator-prey Model Scholarpedia (the free peer-reviewed encyclopedia) p.5765- 5772. Available online (http://www.scholarpedia.org/article/predator-prey_model)
[8] Khaled Batiha., 2007.Numerical solutions of the Method.aspects of competition between three species. SIAM J.Appl.Math. 29:243-253.
[9] May, R.M. and Leonard W.J., 1975.Nonlinear Multispecies Predator-Prey Model by Variational Iteration
[10] Murray, J.D. (1989). Mathematical Biology, 2nd Edition. Springer-Verlag, New York 72-78.
[11] Murray, J.D. (1989). Mathematical Biology, 2nd Edition. Springer-Verlag, New York 78-83.
[12] Olek S., 1994.An accurate solution to the multispecies Lokta-Volterra equations. SIAM Review, 36:480-488.
[13] S. Pathak et al.(2010). Rich Dynamics of an SIR epidemic Model. Vol. 15 Nonlinear Analysis: Modelling and Control, 71-81.
[14] Simeon, C.I., (2008). Predator-prey mathematical model using Van Der Pol’s equation. Journal of Nigerian Association of Mathematical Physics. Volume 12 (May, 2008), 435-438
[15] Smith, H. and Waltman, P. (1997).The Mathematical Theory of Chemostats, Cambridge University Press.
[16] Volterra, V. (1926). Variations and Fluctuations of a number of individuals in animal species living together.[In R.N.Chapman: Animal Ecology, New York, McGraw Hill, 1931,409-448]
Keywords
Compartmental mathematical model, herd immunity, endemic disease equilibrium, disease free equilibrium, vaccination strategies.