Tongqian Zhang

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and Applied Analysis 3 From the point of biology, we only consider system 1.2 and 1.3 in the biological meaning region: D { S, I | S, I ≥ 0}. Let C { φ ( φ1 s , φ2 s ∈ C : φi 0 > 0 i 1, 2 } , 1.4 where φi s is positive, bounded, and continuous function for s ∈ −τ, 0 . Motivated by the application of systems 1.2 and 1.3 to population dynamics refer to 24 ,(More)
SIR epidemic models with distributed delay are proposed. Firstly, the dynamical behaviors of the model without vaccination are studied. Using the Jacobian matrix, the stability of the equilibrium points of the system without vaccination is analyzed. The basic reproduction number R is got. In order to study the important role of vaccination to prevent(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)
According to the different effects of biological and chemical control, we propose a model for Holling I functional response predator-prey system concerning pest control which adopts different control methods at different thresholds. By using differential equation geometry theory and the method of successor functions, we prove that the existence of order one(More)
A stochastic SIR model with vertical transmission and vaccination is proposed and investigated in this paper. The threshold dynamics are explored when the noise is small. The conditions for the extinction or persistence of infectious diseases are deduced. Our results show that large noise can lead to the extinction of infectious diseases which is conducive(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. Keywordspulse viral iufectiou;globally(More)
*Correspondence: 1College of Mathematics and Systems Science, Shandong University of Science and Technology, Qianwangang Road 579, Qingdao, 266590, P.R. China 2State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science(More)