According to the epidemic state, propagation mode and transformation between HBV infection states,the Hepatitis B Virus (HBV) infection with impulsive vaccination and time delay are modelled and analyzed. The contro...According to the epidemic state, propagation mode and transformation between HBV infection states,the Hepatitis B Virus (HBV) infection with impulsive vaccination and time delay are modelled and analyzed. The control methods of impulsive vaccination and active therapy are adopted. By using comparative theorem of impulsive differential equation, the sufficient conditions that Hepatitis B Virus will be eliminated eventually or be persistent are derived.展开更多
We study the application of a pulse vaccination strategy to eradicate the slowly progressing diseases that have infectiousness in latent period. We derive the condition in which eradication solution is a global attrac...We study the application of a pulse vaccination strategy to eradicate the slowly progressing diseases that have infectiousness in latent period. We derive the condition in which eradication solution is a global attractor, this condition depends on pulse vaccination proportion p. We also obtain the condition of the global asymptotic stability of the solution. The condition shows that large enough pulse vaccination proportion and relatively small interpulse time lead to the eradication of the diseases. Moreover the results of the theoretical study might be instructive to the epidemiology of HIV.展开更多
In this paper, a delayed SEIRS epidemic model with nonlinear incidence rate and impul- sive vaccination is investigated. In vaccination strategy, we perform impulsive vaccina- tion of newborn infants. Using the discre...In this paper, a delayed SEIRS epidemic model with nonlinear incidence rate and impul- sive vaccination is investigated. In vaccination strategy, we perform impulsive vaccina- tion of newborn infants. Using the discrete dynamic system determined by stroboscopic map, we obtain an infection-free periodic solution and establish conditions, on which the solution is globally attractive. We also conclude that the disease is permanent if the parameters of the model satisfy appropriate conditions. Finally, we illustrate the effec- tiveness of our theorems with numerical simulation. The results obtained in this paper are a good extension of the results obtained in [J. Hou and Z. Teng, Continuous and impulsive vaccination of SEIR epidemic models with saturation incidence rate, Math. Comput, Simulat. 79 (2009) 3038 3054] to the corresponding delayed SEIRS epidemic model with nonlinear incidence rate and impulsive vaccination.展开更多
In this paper, we discuss the SIV epidemic model with impulsive vaccination and infection-age. Bifurcation theory and Lyapunov-Schmidt series expansion are used to show the existence of the positive periodic solutions...In this paper, we discuss the SIV epidemic model with impulsive vaccination and infection-age. Bifurcation theory and Lyapunov-Schmidt series expansion are used to show the existence of the positive periodic solutions under some conditions.展开更多
Differential susceptibility SIR epidemic models with time delay and pulse vaccination is studied in this paper. We show that there exists an infection-free periodic solution by using the comparison method, which is gl...Differential susceptibility SIR epidemic models with time delay and pulse vaccination is studied in this paper. We show that there exists an infection-free periodic solution by using the comparison method, which is globally attractive provided that R1 〈 1, and that R2 〉 1 implies the disease is permanent, which means that after some period of time the disease will become endemic.展开更多
In this paper, an SEIRS epidemic model with pulse vaccination and two time delays is proposed. By using stroboscopic map and comparison principle, the disease-free periodic solution(DFPS for short) is obtained and the...In this paper, an SEIRS epidemic model with pulse vaccination and two time delays is proposed. By using stroboscopic map and comparison principle, the disease-free periodic solution(DFPS for short) is obtained and the global asymptotic stability of the DFPS is proved. The sufficient conditions for the permanence of the model are obtained. In addition, numerical simulations are done to confirm our theoretical results.展开更多
基金supported by the Fundamental Research Funds for the Central Universities,China University of Geosciences (Wuhan) CUGL1002382011CB710600 (973 Program)
文摘According to the epidemic state, propagation mode and transformation between HBV infection states,the Hepatitis B Virus (HBV) infection with impulsive vaccination and time delay are modelled and analyzed. The control methods of impulsive vaccination and active therapy are adopted. By using comparative theorem of impulsive differential equation, the sufficient conditions that Hepatitis B Virus will be eliminated eventually or be persistent are derived.
基金The research is supported by the National Science Foundation of Henan Province(No. 0611051800).
文摘We study the application of a pulse vaccination strategy to eradicate the slowly progressing diseases that have infectiousness in latent period. We derive the condition in which eradication solution is a global attractor, this condition depends on pulse vaccination proportion p. We also obtain the condition of the global asymptotic stability of the solution. The condition shows that large enough pulse vaccination proportion and relatively small interpulse time lead to the eradication of the diseases. Moreover the results of the theoretical study might be instructive to the epidemiology of HIV.
基金This work is supported by the National Natural Science Foundation of China under Grant 61174039. The authors would like to thank the editor and reviewers for their hard work to the improvement of the quality of this paper.
文摘In this paper, a delayed SEIRS epidemic model with nonlinear incidence rate and impul- sive vaccination is investigated. In vaccination strategy, we perform impulsive vaccina- tion of newborn infants. Using the discrete dynamic system determined by stroboscopic map, we obtain an infection-free periodic solution and establish conditions, on which the solution is globally attractive. We also conclude that the disease is permanent if the parameters of the model satisfy appropriate conditions. Finally, we illustrate the effec- tiveness of our theorems with numerical simulation. The results obtained in this paper are a good extension of the results obtained in [J. Hou and Z. Teng, Continuous and impulsive vaccination of SEIR epidemic models with saturation incidence rate, Math. Comput, Simulat. 79 (2009) 3038 3054] to the corresponding delayed SEIRS epidemic model with nonlinear incidence rate and impulsive vaccination.
文摘In this paper, we discuss the SIV epidemic model with impulsive vaccination and infection-age. Bifurcation theory and Lyapunov-Schmidt series expansion are used to show the existence of the positive periodic solutions under some conditions.
基金Supported by the National Natural Science Foundation of China(10971001) Supported by Henan Science and Technology Department(082102140025, 092300410228)
文摘Differential susceptibility SIR epidemic models with time delay and pulse vaccination is studied in this paper. We show that there exists an infection-free periodic solution by using the comparison method, which is globally attractive provided that R1 〈 1, and that R2 〉 1 implies the disease is permanent, which means that after some period of time the disease will become endemic.
基金The Natural Science Basic Research Plan in Shaanxi Province of China(2018JM1011)Natural Science Basic Research Plan in Shaanxi Province of China(2017JQ1014)NSF of China(11701041)
文摘In this paper, an SEIRS epidemic model with pulse vaccination and two time delays is proposed. By using stroboscopic map and comparison principle, the disease-free periodic solution(DFPS for short) is obtained and the global asymptotic stability of the DFPS is proved. The sufficient conditions for the permanence of the model are obtained. In addition, numerical simulations are done to confirm our theoretical results.