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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
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