Modeling the effects of cross-protection control in plant disease with seasonality. (English) Zbl 1371.34067
Summary: Cross-protection in plants has been widely used to control losses caused by virus diseases in the world. Here, a non-autonomous plant-virus disease model was developed including cross-protection. Global dynamics of the model was discussed. Under the quite weak assumptions, integral form conditions were resolved for permanence of the system and extinction of diseases. Furthermore, we looked into the sufficient conditions that plants could be protected against the detrimental effects of infection by an infection with the mild virus isolates. Last, we performed numerical simulations. Our investigations suggested that cross-protection played an important role in controlling the spread of the challenging virus in plants.
MSC:
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
| 37C60 | Nonautonomous smooth dynamical systems |
| 92D30 | Epidemiology |
| 92D40 | Ecology |
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