Beretta E, Capasso V, Rinaldi F
Istituto di Biomatematica, Università di Urbino, Italy.
J Math Biol. 1988;26(6):661-88. doi: 10.1007/BF00276147.
The paper contains an extension of the general ODE system proposed in previous papers by the same authors, to include distributed time delays in the interaction terms. The new system describes a large class of Lotka-Volterra like population models and epidemic models with continuous time delays. Sufficient conditions for the boundedness of solutions and for the global asymptotic stability of nontrivial equilibrium solutions are given. A detailed analysis of the epidemic system is given with respect to the conditions for global stability. For a relevant subclass of these systems an existence criterion for steady states is also given.
本文包含了同一作者在之前论文中提出的一般常微分方程系统的扩展，以在相互作用项中纳入分布时滞。新系统描述了一大类具有连续时滞的类似Lotka-Volterra的种群模型和流行病模型。给出了解的有界性以及非平凡平衡解的全局渐近稳定性的充分条件。针对全局稳定性条件对流行病系统进行了详细分析。对于这些系统的一个相关子类，还给出了稳态的存在准则。
