Eco-epidemiology model with age structure and prey-dependent consumption for pest management. (English) Zbl 1179.34049

From the introduction: The prey-dependent consumption predator-prey (natural enemy-pest) model with age structure for the predators and infectious disease in the prey,
\[ \begin{cases} \left.\begin{aligned} & S'(t)=rS(t) \left(1-\frac{S(t)}{K}\right)-\frac{\alpha(t)S(t)}{1+\omega S(t)}-\beta S(t)y_2(t),\\ & I'(t)=\frac{\alpha I(t)S(t)}{1+\omega S(t)}-d_1I(t),\\ & y_1'(t)=\frac{\lambda\beta S(t)y_2(t)}{1+\beta hS(t)}-d_2y_1(t)=my_1(t),\\ &y_2'(t)=my_1(t)-d_2y_2(t),\end{aligned}\right\}\ t\neq nT,\\ \left.\begin{aligned} & \Delta S(t)=0,\quad \Delta I(t)=p,\\ & \Delta y_1(t)=q_1,\quad \Delta y_2(t)=q_2,\end{aligned}\right\}\;t=nT,\quad n=1,2,\dots,\end{cases} \]
is considered. Infectious pests, immature natural enemies and mature natural enemies are released impulsively. By using Floquet’s theorem, small-amplitude perturbation skills and comparison theorem, we obtain both sufficient conditions for the global asymptotical stability of the susceptible pest-eradication periodic solution and the permanence of the system. The results provide a reliable theoretical tactics for pest management.


34C60 Qualitative investigation and simulation of ordinary differential equation models
92D30 Epidemiology
92D40 Ecology
34D05 Asymptotic properties of solutions to ordinary differential equations
34A37 Ordinary differential equations with impulses
34C25 Periodic solutions to ordinary differential equations
Full Text: DOI


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