On competition of predators and prey infection |
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| Authors: | Ivo Siekmann Horst Malchow Ezio Venturino |
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| Affiliation: | 1. Mendez National Institute of Transplantation, Los Angeles, CA, United States;2. Saint Vincent Medical Center, Los Angeles, CA, United States;3. Western University of Health Sciences, Pomona, CA, United States;4. Nova Southeastern University, Miami, FL, United States;5. University of Kansas, Kansas City, KS, United States;6. University of Southern California, Los Angeles, CA, United States;7. Transplant Research Institute, Los Angeles, CA, United States;1. State Key Laboratory of Phytochemistry and Plant Resources in West China, Kunming Institute of Botany, Chinese Academy of Sciences, Kunming 650201, People''s Republic of China;2. University of Chinese Academy of Sciences, Beijing 100049, People''s Republic of China;3. Yunnan Key Laboratory of Natural Medicinal Chemistry, Kunming Institute of Botany, Chinese Academy of Sciences, Kunming 650201, People''s Republic of China |
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| Abstract: | A class of prey–predator models with infected prey is investigated. Predation terms are either of Holling type II or III, infection is either modelled by mass action or standard incidence. It is shown that the key for understanding the model behaviour is the competition of predators versus infection. In the presented models the predator is not susceptible to the infection and the infection of the prey has no influence on the ability of the predator of catching the prey. However, the prey population can be seen as a resource which both the predators and the infection depend on. The competition for this resource is strong—the principle of competitive exclusion holds for biologically meaningful choices of parameters as long as there is no destabilisation by a Hopf bifurcation. The representation of models in competition diagrams which are introduced in this article can be used for a wide range of competition models which seems to be a promising method with many potential applications. |
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