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In this paper, by using impulsive delay differential equation, we investigate the dynamics of an SIR epidemic disease model with distributed times delay and pulse vaccination.We show that the conditions for global attractivity of “infection-free” periodic solution and permanence of the “infection” depend on time delay and pulse… (More)
The cure effect of a virus model with both cell-to-cell transmission and cell-to-virus transmission is studied. By the method of next generation matrix, the basic reproduction number is obtained. The locally asymptotic stability of the virus-free equilibrium and the endemic equilibrium is considered by investigating the characteristic equation of the model.… (More)
In this paper, by using impulsive differential equa tion, we investigate the dynamics of a new predator-prey model with puIse viral infection .We show that the conditions for glob ally asymptotical stability of pest-eradication periodic solution and permanence of the periodic solution depend on pulse viral infection.
In this paper, an SEIRS epidemic disease model with double delays of latent period and immune period is formulated, and the global dynamics behaviors of the model under pulse input and vaccination are analyzed. By use of the stroboscopic map, an `infection-free' periodic solution is obtained, and the global attractivity of the `infection-free' periodic… (More)
According to the integrated pest management strategies, we propose a model for pest control which adopts different control methods at different thresholds. By using differential equation geometry theory and the method of successor functions, we prove the existence of order one periodic solution of such system, and further, the attractiveness of the order… (More)