Fan Guihong, Lou Yijun, Thieme Horst R, Wu Jianhong
Department of Mathematics and Philosophy, Columbus State University, Columbus, Georgia 31907, United States.
Math Biosci Eng. 2015 Aug;12(4):661-86. doi: 10.3934/mbe.2015.12.661.
A model of ordinary differential equations is formulated for populations which are structured by many stages. The model is motivated by ticks which are vectors of infectious diseases, but is general enough to apply to many other species. Our analysis identifies a basic reproduction number that acts as a threshold between population extinction and persistence. We establish conditions for the existence and uniqueness of nonzero equilibria and show that their local stability cannot be expected in general. Boundedness of solutions remains an open problem though we give some sufficient conditions.
针对由多个阶段构成结构的种群，构建了一个常微分方程模型。该模型的灵感来源于作为传染病传播媒介的蜱虫，但具有足够的通用性，可应用于许多其他物种。我们的分析确定了一个基本繁殖数，它作为种群灭绝和持续存在之间的阈值。我们建立了非零平衡点存在性和唯一性的条件，并表明一般情况下不能期望它们具有局部稳定性。尽管我们给出了一些充分条件，但解的有界性仍然是一个未解决的问题。
