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
An infection-age structured epidemic model with a nonlinear incidence rate is investigated.We formulate the model as an abstract non-densely defined Cauchy problem and derive the condition which guarantees the existen...An infection-age structured epidemic model with a nonlinear incidence rate is investigated.We formulate the model as an abstract non-densely defined Cauchy problem and derive the condition which guarantees the existence and uniqueness for positive age-dependent equilibrium of the model.By analyzing the associated characteristic transcendental equation and applying the normal form theory presented recently for non-densely defined semilinear equations,we show that the SIR(susceptible-infected-recovered)epidemic model undergoes Zero-Hopf bifurcation at the positive equilibrium which is the main result of this paper.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
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supported by National Natural Science Foundation of China (Grant Nos. 11471044 and 11371058)the Fundamental Research Funds for the Central Universities
文摘An infection-age structured epidemic model with a nonlinear incidence rate is investigated.We formulate the model as an abstract non-densely defined Cauchy problem and derive the condition which guarantees the existence and uniqueness for positive age-dependent equilibrium of the model.By analyzing the associated characteristic transcendental equation and applying the normal form theory presented recently for non-densely defined semilinear equations,we show that the SIR(susceptible-infected-recovered)epidemic model undergoes Zero-Hopf bifurcation at the positive equilibrium which is the main result of this paper.
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.
