具有孵化期时滞和潜伏期时滞的登革热病毒传播动力学模型研究

The Dynamical Behavior of Dengue Virus Transmission Model with Maturation Delay and Incubation Delay

考虑到登革热病毒传播过程中在蚊子和人体内都具有一定的潜伏期,以及相对于蚊子的生命周期来说蚊子有一个较长的孵化期,本文考虑了一类具有潜伏期时滞和孵化期时滞的登革热病毒传播动力学模型。利用反证法证明了模型解的正性,通过线性化方法得到模型无病平衡点和地方病平衡点的局部渐近稳定性,给出了刻画疾病消除或流行的阈值条件。进一步,通过构造合适的李雅普诺夫泛函,得到模型无病平衡点和地方病平衡点的全局渐近稳定性的判别准则。

The dynamical behavior of dengue virus transmission model with incubation delay and relatively long maturation delay compared to the average life span of adult mosquito is investigated. The positivity of solutions is showed by using contradiction. The local stability of the disease free equilibrium and endemic equilibrium are obtained by using the linearization method. Further, the global asymptotic stability of the positive equilibrium is proved by using Lyapunov functional method.