具有无症状感染者和时滞的媒介传染病模型的分析

Analysis of host-vector epidemic model with asymptomatic infectors and delay

为研究无症状感染者和时滞对媒介传染病的影响,该文探讨了一类包含无症状感染者和时滞影响的媒介传染病模型.采用第二代生成矩阵法得到了基本再生数,对平衡点的存在性以及稳定性进行了证明并对此模型进行了分支分析,以时滞τ为参数,发现当τ经过临界值时,地方病平衡点的稳定性出现了一些变化,从而导致该平衡点处Hopf分支的产生,并得到了证明Hopf分支方向和周期解稳定性的公式.

To study the effect of asymptomatic infectors and delay on host-vector epidemic model,a host-vector epidemic model with asymptomatic infectors and delay is discussed.The expression of basic reproduction number is obtained by using the second generation of generator matrix method,the existence and stability of equilibrum points is proved and bifurcation analysis to the model is performed,the delayτis used as the bifurcation parameter,when the delayτpasses through critical value,the stability of endemic equilibrium is changed,the equilibrum point will exist Hopf bifurcation and some derive formulas about the bifurcation direction and the stability of the bifurcated periodic solution are obtained.