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The role of viral infection in pest control: a mathematical study. (English) Zbl 1245.92054
Summary: We propose a mathematical model of viral infection in pest control. As the viral infection induces host lysis which releases more viruses into the environment, on the average ‘$$\kappa$$’ viruses per host, $$\kappa \in (1,\infty)$$, the ‘virus replication parameter’ is chosen as the main parameter on which the dynamics of the infection depends. There exists a threshold value $$\kappa_{0}$$ beyond which the infection persists in the system. Still for increasing the value of $$\kappa$$, the endemic equilibrium bifurcates towards a periodic solution, which essentially indicates that the viral pesticide has a density-dependent ‘numerical response’ component to its action. The investigations also include the dependence of the process on predation of natural enemies in the system. A concluding discussion with numerical simulations of the model is also presented.

##### MSC:
 92D30 Epidemiology 92C60 Medical epidemiology 34C60 Qualitative investigation and simulation of ordinary differential equation models 65C20 Probabilistic models, generic numerical methods in probability and statistics
##### Keywords:
Hopf bifurcations; orbital stability
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