一个具有时滞的媒介传播流行病模型中的Hopt分支（英文）

文章研究的是一个具有时滞的媒介传播流行病模型.假定长期的发病率是双线性大规模行动的方式,确定了疾病是否流行的阈值R_0.当R_0≤1时,得到无病平衡点是全局稳定的,即疾病消失;当R_0〉1时,得到地方病平衡点.在具有时滞的微分模型中,时滞与载体转变成传染源的孵化期有关。我们研究了时滞对平衡点稳定性的影响,研究表明,在从寄生源到载体的传播过程中,时滞可以破坏动力系统并且得到了Hopt分支的周期解.

Hopf Bifurcation in An Epidemic Model of a Vector-Borne Disease with Time Delay

This paper considers an epidemic model of a vector-borne disease with delay.The incidence term is assumed to be of the bilinear mass-action form.The model shows that the dynamics is determined by the basic reproduction number R_0.If R_0≤1, the disease-free equilibrium is globally stable and the disease dies out.If R_0 1,a unique endemic equilibrium exists in the interior of the feasible region.The delay in the differential-delay model accounts for the incubation time the vectors need to become infectious.We study the effect of that delay on the stability of the equilibria.We show that the introduction of a time delay in the host-to-vector transmission term can destabilize the system and periodic solutions can arise through Hopf bifurcation.