A mathematical study of a prey-predator model in relevance to pest control. (English) Zbl 1279.92086
Summary: In this paper, we propose and analyze an ecological system consisting of pest and its natural enemy as predator. Here we also consider the role of infection to the pest population and the presence of some alternative source of food to the predator population. We analyze the dynamics of this system in a systemic manner, study the dependence of the dynamics on some vital parameters and discuss the global behavior and controllability of the proposed system. The investigation also includes the use of pesticide control to the system and finally we use Pontryagin’s maximum principle to derive the optimal pest control strategy. We also illustrate some of the key findings using numerical simulations.
MSC:
| 92D40 | Ecology |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 49J15 | Existence theories for optimal control problems involving ordinary differential equations |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
| 34D23 | Global stability of solutions to ordinary differential equations |
Keywords:
eco-epidemic; Hopf bifurcation; transcritical bifurcation; global stability; optimal controlReferences:
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