A predator-prey-disease model with immune response in infected prey

作者：Bhattacharya, Souvik^*; Martcheva, Maia; Li, Xue-Zhi

来源：Journal of Mathematical Analysis and Applications, 2014, 411(1): 297-313.

DOI：10.1016/j.jmaa.2013.09.031

• Immuno-eco-epidemiology
• Prey-predator model
• Age-since-infection
• Co-existence
• Reproduction numbers
• Invasion reproduction numbers
• Global stability

In this paper, a predator-prey-disease model with immune response in the infected prey is formulated. The basic reproduction number of the within-host model is defined and it is found that there are three equilibria: extinction equilibrium, infection-free equilibrium and infection-persistent equilibrium. The stabilities of these equilibria are completely determined by the reproduction number of the within-host model. Furthermore, we define a basic reproduction number of the between-host model and two predator invasion numbers: predator invasion number in the absence of disease and predator invasion number in the presence of disease. We have predator and infection-free equilibrium, infection-free equilibrium, predator-free equilibrium and a co-existence equilibrium. We determine the local stabilities of these equilibria with conditions on the reproduction and invasion reproduction numbers. Finally, we show that the predator-free equilibrium is globally stable. Published by Elsevier Inc.

• 出版日期2014-3-1
• 单位信阳师范学院