一类具非线性传染力且潜伏期也具传染性的流行病模型

A kind of epidemic model with nonlinear infectious force in both latent period and infected period

从非线性动力学角度,运用常微分方程理论和方法,对一类具非线性传染力且潜伏期和染病期都传染的流行病模型进行了研究,讨论了在不同情况下疾病消除平衡点(零平衡点)、非零平衡点的存在性、稳定性,最后确定了各类平衡点存在的条件阈值。结果表明,通过减少染病者与易感者的接触,提高治愈率,使阈值增大到某一数值时,传染病就会从种群中根除;当阈值小于某一数值时,就会形成地方病。同时,结果揭示了潜伏期传染和染病期传染对流行病发展趋势的共同影响。

From the perspective of nonlinear dynamics, this paper, adopting the theory and method of the ordinary differential equation, studies a kind of epidemic model with nonlinear infectious force in both latent period and infected period, discusses the possibility, the stability of removing the equilibrium and Non-equilibrium of the disease, and finally gets a threshold. The results indicate that the epidemic disease will be deracinated from the group when the threshold increases by a certain numerical value by increasing the cure rate and reducing the contact between the infected and the vulnerable groups; when the threshold is less than a certain numerical value the epidemic diseases will form into endemic diseases. Meanwhile the results expose influence of the latent period and inflected period to the epidemic.