Lv Yunfei, Yuan Rong, Pei Yongzhen
School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing 100875, People's Republic of China.
School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing 100875, People's Republic of China.
Math Biosci. 2014 May;251:16-29. doi: 10.1016/j.mbs.2014.02.005. Epub 2014 Feb 15.
A two-strain epidemic model with saturating contact rate under a generalist predator is proposed. For a generalist predator which feeds on many types of prey, we assume that the predator can discriminate among susceptible and infected with each strain prey. First, mathematical analysis of the model with regard to invariance of nonnegativity, boundedness of solutions, nature of equilibria, persistence and global stability are analyzed. Second, the two strains will competitively exclude each other in the absence of predation with the strain with the larger reproduction number persisting. If predation is discriminate, then depending on the predation level, a dominant strain may occur. Thus, for some predation levels, the strain one may persist while for other predation levels strain two may persist. Furthermore, coexistence line and coexistent asymptotic-periodic solution are obtained when coexistence occur while heteroclinic is obtained when the two strains competitively exclude each other. Finally, the impact of predation is mentioned along with numerical results to provide some support to the analytical findings.
提出了一个在泛化捕食者下具有饱和接触率的双菌株流行病模型。对于以多种猎物为食的泛化捕食者，我们假设捕食者能够区分每种菌株猎物的易感个体和感染个体。首先，分析了该模型在非负性不变性、解的有界性、平衡点性质、持续性和全局稳定性方面的数学性质。其次，在没有捕食的情况下，两个菌株将相互竞争排斥，繁殖数较大的菌株持续存在。如果捕食是有区分的，那么根据捕食水平，可能会出现一个优势菌株。因此，对于某些捕食水平，菌株一可能持续存在，而对于其他捕食水平，菌株二可能持续存在。此外，当共存发生时获得共存线和共存渐近周期解，而当两个菌株相互竞争排斥时获得异宿轨。最后，提及了捕食的影响以及数值结果，为分析结果提供一些支持。
