Journal
JOURNAL OF THEORETICAL BIOLOGY
Volume 238, Issue 1, Pages 177-197Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jtbi.2005.05.019
Keywords
pest control; viral infection; saddle-node bifurcation; hopf bifurcation; Poore's condition
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This paper deals with the mathematical modeling of pest management under viral infection (i.e. using viral pesticide) and analysis of its essential mathematical features. As the viral infection induces host lysis which releases more virus into the environment, on the average 'kappa' viruses per host, kappa is an element of (1, infinity), the 'virus replication parameter' is chosen as the main parameter on which the dynamics of the infection depends. We prove that there exists a threshold value kappa(0) beyond which the endemic equilibrium bifurcates from the free disease one. Still for increasing K values, the endemic equilibrium bifurcates towards a periodic solution. We further analyse the orbital stability of the periodic orbits arising from bifurcation by applying Poor's condition. A concluding discussion with numerical simulation of the model is then presented. (c) 2005 Elsevier Ltd. All rights reserved.
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