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Pest control through viral disease: Mathematical modeling and analysis
, D.K. Bhattacharya
Published in
PMID: 16005904
Volume: 238
Issue: 1
Pages: 177 - 197
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 'κ' viruses per host, κ∈(1,∞), 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 κ0 beyond which the endemic equilibrium bifurcates from the free disease one. Still for increasing κ 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. © 2005 Elsevier Ltd. All rights reserved.
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