图  1  当$ q = 0.03,\; 0.08,\; 0.2\; $时，模型(2)解的长期行为

Figure  1.  For $ q = 0.03,\; 0.08,\; 0.2 $, the long-term behavior of the solution for model (2)

图  2  当$K = 20,\; 30,\; 50$时，模型(2)解的长期行为

注　为了解释图中的颜色，读者可以参考本文的电子网页版本，后同。

Figure  2.  For $ K = 20,\; 30,\; 50 $, the long-term behavior of the solution for model (2)

图  3  当$ \varLambda = 5 $或1时，模型(2)的非负平衡点随$ R_0 $变化的分支图：(a) $ \varLambda = 5 $； (b) $ \varLambda = 1 $

Figure  3.  For $ \varLambda = 5 $ or 1 , the bifurcation of nonnegative equilibria for model (2) with respective to $ R_0 $: (a) $\varLambda = 5$; (b) $\varLambda = 1$

图  4  模型(2)解的最终性态对初值的依赖性 (双稳定现象)

Figure  4.  Dependence of the final behavior of the solution for model (2) on the initial value (bistable phenomenon)

图  5  当$R_{0}=1.3$时，模型(2)解的长期行为，其中$\varLambda=1,\; \mu=0.008,\; K=2,\; r=0.2,\; \gamma_1=0.06,\;\gamma_2=0.3$, $d_1=0.01,\;d_2=0.001,\; a=0.7,\; \tau=0.2,\; q=0.03$，初值为$(100,5,2,10)$

Figure  5.  For $R_{0}=1.3$, the long-term behavior of the solution for model (2), where $\varLambda=1,\; \mu=0.008,\; K=2,\; r=0.2,\; \gamma_1=0.06,\;\gamma_2=0.3$, $d_1=0.01,\;d_2=0.001,\; a=0.7,\; \tau=0.2,\; q=0.03$, and the initial value is $(100,5,2,10)$