Haque Mainul, Rahman Md Sabiar, Venturino Ezio
Division of Anaesthesia & Intensive Care, School of Clinical Sciences, Queen's Medical Centre, University of Nottingham, UK.
Biosystems. 2013 Nov;114(2):98-117. doi: 10.1016/j.biosystems.2013.06.002. Epub 2013 Jul 30.
The current paper deals with the mathematical models of predator-prey system where a transmissible disease spreads among the predator species only. Four mathematical models are proposed and analysed with several popular predator functional responses in order to show the influence of functional response on eco-epidemic models. The existence, boundedness, uniqueness of solutions of all the models are established. Mathematical analysis including stability and bifurcation are observed. Comparison among the results of these models allows the general conclusion that relevant behaviour of the eco-epidemic predator-prey system, including switching of stability, extinction, persistence and oscillations for any species depends on four important parameters viz. the rate of infection, predator interspecies competition and the attack rate on susceptible predator. The paper ends with a discussion of the biological implications of the analytical and numerical results.
本文研究了捕食者 - 猎物系统的数学模型，其中一种可传播疾病仅在捕食者物种中传播。提出并分析了四个数学模型，并结合几种常见的捕食者功能反应，以展示功能反应对生态 - 流行病模型的影响。建立了所有模型解的存在性、有界性和唯一性。观察了包括稳定性和分岔在内的数学分析。这些模型结果之间的比较得出一个普遍结论，即生态 - 流行病捕食者 - 猎物系统的相关行为，包括任何物种的稳定性切换、灭绝、持久性和振荡，取决于四个重要参数，即感染率、捕食者种间竞争以及对易感捕食者的攻击率。本文最后讨论了分析和数值结果的生物学意义。
