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# A non-autonomous predator-prey model with infected prey

• 1Corresponding author
• A non-constant eco-epidemiological model with SIS-type infectious disease in prey is formulated and investigated, it is assumed that the disease is endemic in prey before the invasion of predator and that predation is more likely on infected prey than on the uninfected. Sufficient conditions for both permanence and extinction of the infected prey, and the necessary conditions for the permanence of the infected prey are established. It is shown that the predation preference to infected prey may even increase the possibility of disease endemic, and that the introduction of new resource for predator could be helpful for it to eradicate the infected prey. Numerical simulations have been performed to verify/extend our analytical results.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

 Citation:

• Figure 1.  Solutions of system (2) with different hunting rate $\eta_1(t)$ on susceptible prey $s$. Here $(a)$: $\eta_1(t) = 0$; $(b)$: $\eta_1(t) = 1.5+\cos t$; $(c)$: $\eta_1(t) = 3+\cos t$; $(d)$: $\eta_1(t) = 4.5+\cos t$

Figure 2.  Solutions of system (2) with different hunting rate $\eta_1(t)$ on susceptible prey $s$. $(a)$: $\eta_1(t) = 0$; $(b)$: $\eta_1(t) = 1.5+\cos(\sqrt{t})$; $(c)$: $\eta_1(t) = 3+\cos(\sqrt{t})$; $(d)$: $\eta_1(t) = 4.5+\cos(\sqrt{t})$

Figure 3.  Basic behavior of solutions of model (49) with different intrinsic growth rate $r(t)$ for predator $y$. $(a)$: $r(t)\equiv 0$; $(b)$: $r(t) = \sin t+13$; $(c)$: $r(t) = \sin t+19$.Here we set $\eta_1(t) = \cos t+1$, and all the other parameters are same as those for FIG. 1

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