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Zhang H, Xu G, Sun H. Biological control of a predator–prey system through provision of an infected predator. INT J BIOMATH 2019. [DOI: 10.1142/s179352451850105x] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Epidemic transmission has a substantial effect on the dynamics and stability of the predator–prey system, in which the transmission rate plays an important role. The probabilistic cellular automaton (PCA) approach is used to investigate the spatiotemporal dynamics of a predator–prey system with the infected predator. Remarkably, it is impossible to achieve a coexistence state of prey, susceptible predators, and infected predators in a spatial population. This is different from the analysis from a non-spatial population with the mean-field approximation, where Hopf bifurcation arises and the interior equilibrium becomes unstable, and a periodic solution appears with the increasing infection rate. The results show that the introduction of the infected predator with a high transmission rate is beneficial for the persistence of the prey population in space. However, a low transmission rate will promote the coexistence state of the prey and the susceptible predator populations. In summary, it is possible to develop management strategies to manipulate the transmission rate of the infected predator for the benefit of biological control.
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Affiliation(s)
- Hui Zhang
- Department of Applied Mathematics, School of Natural and Applied Sciences, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, P. R. China
| | - Genjiu Xu
- Department of Applied Mathematics, School of Natural and Applied Sciences, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, P. R. China
| | - Hao Sun
- Department of Applied Mathematics, School of Natural and Applied Sciences, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, P. R. China
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