Pest control through viral disease: Mathematical modeling and analysis

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,...

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Bibliographic Details
Published in:Journal of theoretical biology 2006-01, Vol.238 (1), p.177-197
Main Authors: Bhattacharyya, S., Bhattacharya, D.K.
Format: Article
Language:English
Subjects:
Agriculture
Animals
Baculoviridae
Computer Simulation
Ecosystem
Forestry
Hopf bifurcation
Insect Control - methods
Kenya
Models, Biological
Moths - virology
Pest control
Pest Control, Biological - methods
Poore's condition
Saddle–node bifurcation
Viral infection
Virus Diseases - transmission
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Summary: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 κ 0 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.
ISSN:0022-5193
1095-8541
DOI:10.1016/j.jtbi.2005.05.019