Liu W M, Levin S A, Iwasa Y
J Math Biol. 1986;23(2):187-204. doi: 10.1007/BF00276956.
When the traditional assumption that the incidence rate is proportional to the product of the numbers of infectives and susceptibles is dropped, the SIRS model can exhibit qualitatively different dynamical behaviors, including Hopf bifurcations, saddle-node bifurcations, and homoclinic loop bifurcations. These may be important epidemiologically in that they demonstrate the possibility of infection outbreak and collapse, or autonomous periodic coexistence of disease and host. The possible mechanisms leading to nonlinear incidence rates are discussed. Finally, a modified general criterion for supercritical or subcritical Hopf bifurcation of 2-dimensional systems is presented.
当传统假设即发病率与感染者数量和易感者数量的乘积成正比被摒弃时，SIRS模型可以展现出定性上不同的动力学行为，包括霍普夫分岔、鞍结分岔和同宿环分岔。这些在流行病学上可能很重要，因为它们证明了感染爆发和崩溃的可能性，或者疾病与宿主的自主周期性共存。讨论了导致非线性发病率的可能机制。最后，给出了二维系统超临界或亚临界霍普夫分岔的修正通用准则。
