The importance of epidemiology in our life has stimulated researchers to extend the classic Susceptibles-Infectives-Removed (SIR) model to sophisticated models by including more factors in order to give detailed trans...The importance of epidemiology in our life has stimulated researchers to extend the classic Susceptibles-Infectives-Removed (SIR) model to sophisticated models by including more factors in order to give detailed transmission dynamics of epidemic diseases. However, the integration of the quarantine policy and age-structure is less addressed. In this work we propose an age-structured MSIQR (temporarily immune-susceptibles-infectives-quarantined-removed) model to study the impact of quarantine policies on the spread of epidemic diseases. Specifically, we investigate the existence of steady state solutions and stability property of the proposed model. The derived explicit expression of the basic reproductive number shows that the disease-free equilibrium is globally asymptotically stable if, and that the unique endemic equilibrium exists if. In addition, the stability conditions of the endemic equilibrium are derived.展开更多
The existence and uniqueness of positive steady states for the age-structured MSEIR epidemic model with age-dependent transmission coefficient is considered. Threshold results for the existence of endemic states are e...The existence and uniqueness of positive steady states for the age-structured MSEIR epidemic model with age-dependent transmission coefficient is considered. Threshold results for the existence of endemic states are established; under certain conditions, uniqueness is also shown.展开更多
Three analytic algorithms based on Adomian decomposition, homotopy perturbation and homotopy analysis methods are proposed to solve some models of nonlinear age-structured population dynamics and epidemiology. Truncat...Three analytic algorithms based on Adomian decomposition, homotopy perturbation and homotopy analysis methods are proposed to solve some models of nonlinear age-structured population dynamics and epidemiology. Truncating the resulting convergent infinite series, we obtain numerical solutions of high accuracy for these models. Three numerical examples are given to illustrate the simplicity and accuracy of the methods.展开更多
In this paper, a susceptible-vazcinated-exposed-infectious-recovered epidemic model with waning immunity and continuous age structures in vaccinated, exposed and infectious classes has been formulated. By using the Fl...In this paper, a susceptible-vazcinated-exposed-infectious-recovered epidemic model with waning immunity and continuous age structures in vaccinated, exposed and infectious classes has been formulated. By using the Fluctuation lemma and the approach of Lyapunov functionals, we establish a threshold dynamics completely determined by the basic reproduction number. When the basic reproduction number is less than one, the disease-free steady state is globally asymptotically stable, and otherwise the endemic steady state is globally asymptotically stable.展开更多
This article focuses on the study of an age structured SEIRS epidemic model with a vaccination program when the total population size is not kept at constant. We first give the explicit expression of the reproduction ...This article focuses on the study of an age structured SEIRS epidemic model with a vaccination program when the total population size is not kept at constant. We first give the explicit expression of the reproduction number in the presence of vaccine ( is the exponent of growth of total population), and show that the infection-free steady state is linearly stable if and unstable if , then we apply the theoretical results to vaccination policies to determine the optimal age or ages at which an individual should be vaccinated. It is shown that the optimal strategy can be either one- or two-age strategies.展开更多
For some infectious diseases such as mumps,HBV,there is evidence showing that vaccinated individuals always lose their immunity at different rates depending on the inoculation time.In this paper,we propose an age-stru...For some infectious diseases such as mumps,HBV,there is evidence showing that vaccinated individuals always lose their immunity at different rates depending on the inoculation time.In this paper,we propose an age-structured epidemic model using a step function to describe the rate at which vaccinated individuals lose immunity and reduce the age-structured epidemic model to the delay differential model.For the age-structured model,we consider the positivity,boundedness,and compactness of the semiflow and study global stability of equilibria by constructing appropriate Lyapunov functionals.Moreover,for the reduced delay differential equation model,we study the existence of the endemic equilibrium and prove the global stability of equilibria.Finally,some numerical simulations are provided to support our theoretical results and a brief discussion is given.展开更多
Heroin is considered as damage on the health of the individuals.In this paper,we consider a heroin epidemic model with treat age,where the inner rivalry in between the drug users for a small dose of drugs is investiga...Heroin is considered as damage on the health of the individuals.In this paper,we consider a heroin epidemic model with treat age,where the inner rivalry in between the drug users for a small dose of drugs is investigated.The influence of treatment period for a drug consumer before quitting treatment is investigated,where it is obtained that the considered model can undergo backward bifurcation,which shows the possibility of having two endemic equilibriums,this type of bifurcation is discussed in terms of the basic reproduction number R0.The bifurcation diagram is drown in the case of an age structured model.Also,we show the existence of Hopf bifurcation is shown under suitable conditions on the model parameters.The obtained mathematical results are confirmed numerically.展开更多
In this paper, a susceptible-exposed infective-recovered-susceptible （SEIRS） epidemic model with vaccination has been formulated. We studied the global stability of the corresponding single-group model, multi-group ...In this paper, a susceptible-exposed infective-recovered-susceptible （SEIRS） epidemic model with vaccination has been formulated. We studied the global stability of the corresponding single-group model, multi-group model with strongly connected network and multi-group model without strongly connected network by means of analyzing their basic reproduction numbers and the application of Lyapunov functionals. Finally, we provide some numerical simulations to illustrate our analysis results.展开更多
文摘The importance of epidemiology in our life has stimulated researchers to extend the classic Susceptibles-Infectives-Removed (SIR) model to sophisticated models by including more factors in order to give detailed transmission dynamics of epidemic diseases. However, the integration of the quarantine policy and age-structure is less addressed. In this work we propose an age-structured MSIQR (temporarily immune-susceptibles-infectives-quarantined-removed) model to study the impact of quarantine policies on the spread of epidemic diseases. Specifically, we investigate the existence of steady state solutions and stability property of the proposed model. The derived explicit expression of the basic reproductive number shows that the disease-free equilibrium is globally asymptotically stable if, and that the unique endemic equilibrium exists if. In addition, the stability conditions of the endemic equilibrium are derived.
基金the Natural Science Foundation of Henan Province (No.994051200).
文摘The existence and uniqueness of positive steady states for the age-structured MSEIR epidemic model with age-dependent transmission coefficient is considered. Threshold results for the existence of endemic states are established; under certain conditions, uniqueness is also shown.
文摘Three analytic algorithms based on Adomian decomposition, homotopy perturbation and homotopy analysis methods are proposed to solve some models of nonlinear age-structured population dynamics and epidemiology. Truncating the resulting convergent infinite series, we obtain numerical solutions of high accuracy for these models. Three numerical examples are given to illustrate the simplicity and accuracy of the methods.
文摘In this paper, a susceptible-vazcinated-exposed-infectious-recovered epidemic model with waning immunity and continuous age structures in vaccinated, exposed and infectious classes has been formulated. By using the Fluctuation lemma and the approach of Lyapunov functionals, we establish a threshold dynamics completely determined by the basic reproduction number. When the basic reproduction number is less than one, the disease-free steady state is globally asymptotically stable, and otherwise the endemic steady state is globally asymptotically stable.
基金Supported by the NSFC (No.10371105) and the NSF of Henan Province (No.0312002000No.0211044800)
文摘This article focuses on the study of an age structured SEIRS epidemic model with a vaccination program when the total population size is not kept at constant. We first give the explicit expression of the reproduction number in the presence of vaccine ( is the exponent of growth of total population), and show that the infection-free steady state is linearly stable if and unstable if , then we apply the theoretical results to vaccination policies to determine the optimal age or ages at which an individual should be vaccinated. It is shown that the optimal strategy can be either one- or two-age strategies.
基金supported by The National Natural Science Foundation of China[12026236,12026222,12061079,11601293,12071418]Science and Technology Activities Priority Program for Overseas Researchers in Shanxi Province[20210049]The Natural Science Foundation of Shanxi Province[201901D211160,201901D211461,201901D111295]。
文摘For some infectious diseases such as mumps,HBV,there is evidence showing that vaccinated individuals always lose their immunity at different rates depending on the inoculation time.In this paper,we propose an age-structured epidemic model using a step function to describe the rate at which vaccinated individuals lose immunity and reduce the age-structured epidemic model to the delay differential model.For the age-structured model,we consider the positivity,boundedness,and compactness of the semiflow and study global stability of equilibria by constructing appropriate Lyapunov functionals.Moreover,for the reduced delay differential equation model,we study the existence of the endemic equilibrium and prove the global stability of equilibria.Finally,some numerical simulations are provided to support our theoretical results and a brief discussion is given.
基金S.Bentout and S.Djilali are partially supported by the DGRSTD of Algeria No.C00L03UN130120200004.
文摘Heroin is considered as damage on the health of the individuals.In this paper,we consider a heroin epidemic model with treat age,where the inner rivalry in between the drug users for a small dose of drugs is investigated.The influence of treatment period for a drug consumer before quitting treatment is investigated,where it is obtained that the considered model can undergo backward bifurcation,which shows the possibility of having two endemic equilibriums,this type of bifurcation is discussed in terms of the basic reproduction number R0.The bifurcation diagram is drown in the case of an age structured model.Also,we show the existence of Hopf bifurcation is shown under suitable conditions on the model parameters.The obtained mathematical results are confirmed numerically.
基金This research is supported by National Natural Science Foundation of China （No. 11371111）, Weihai Science and Technology Development Plan Project （No. 2013DXGJ06） and Shandong Provincial Natural Science Foundation of China （No. ZR2015AM018）.
文摘In this paper, a susceptible-exposed infective-recovered-susceptible （SEIRS） epidemic model with vaccination has been formulated. We studied the global stability of the corresponding single-group model, multi-group model with strongly connected network and multi-group model without strongly connected network by means of analyzing their basic reproduction numbers and the application of Lyapunov functionals. Finally, we provide some numerical simulations to illustrate our analysis results.
