Epidemiologic model of SIS type has a delay corresponding to the infectious period and disease related deaths,so that the population size is variable.The population dynamics structure is recruitment and natural birth...Epidemiologic model of SIS type has a delay corresponding to the infectious period and disease related deaths,so that the population size is variable.The population dynamics structure is recruitment and natural births with natural deaths.The incidence term is of the standard incidence.Here the thresholds and equilibria are detemined,and stabilities are examined.The persistence of the infectious disease and disease related deaths can lead to a new equilibrium population size below the carrying capacity.展开更多
A numerical scheme for a SIS epidemic model with a delay is constructed by applying a nonstandard finite difference (NSFD) method. The dynamics of the obtained discrete system is investigated. First we show that the d...A numerical scheme for a SIS epidemic model with a delay is constructed by applying a nonstandard finite difference (NSFD) method. The dynamics of the obtained discrete system is investigated. First we show that the discrete system has equilibria which are exactly the same as those of continuous model. By studying the distribution of the roots of the characteristics equations related to the linearized system, we can provide the stable regions in the appropriate parameter plane. It is shown that the conditions for those equilibria to be asymptotically stable are consistent with the continuous model for any size of numerical time-step. Furthermore, we also establish the existence of Neimark-Sacker bifurcation (also called Hopf bifurcation for map) which is controlled by the time delay. The analytical results are confirmed by some numerical simulations.展开更多
In this paper, an epidemic SIS model with nonlinear infectivity on heterogeneous networks and time delays is investigated. The oscillatory behavior of the solutions is studied. Two sufficient conditions are provided t...In this paper, an epidemic SIS model with nonlinear infectivity on heterogeneous networks and time delays is investigated. The oscillatory behavior of the solutions is studied. Two sufficient conditions are provided to guarantee the oscillatory behavior for the solutions. Some computer simulations are demonstrated.展开更多
Considering the antiviral drugs can act on the fusion,reverse transcription,and budding stages of HIV infected cells,in this paper,we formulate a two-periodic delay heterogeneous space diffusion HIV model with three-s...Considering the antiviral drugs can act on the fusion,reverse transcription,and budding stages of HIV infected cells,in this paper,we formulate a two-periodic delay heterogeneous space diffusion HIV model with three-stage infection process to study the effects of periodic antiviral treatment and spatial heterogeneity on HIV infection process.We first study the well-posedness of the full system and then derive the basic reproduction number R_(0),which is defined as the spectral radius of the next generation operator.We further prove that R_(0) is a threshold for the elimination and persistence of HIV infection by comparison principle and persistence theory for non-autonomous system.In the spatial homogeneous case,the explicit expression of R_(0) is derived and the global attractivity of the positive steady state is proved by using the fluctuation method.Some numerical simulations are conducted to illustrate the theoretical results and our works suggest that both spatial heterogeneity and periodic delays caused by periodic antiviral therapy have a remarkable impact on the progression of HIV infection and should not be overlooked in clinical treatment process.展开更多
This paper formulates a robust stage-structured SI eco-epidemiological model with periodic constant pulse releasing of infectious pests with pathogens. The authors show that the conditions for global attractivity of t...This paper formulates a robust stage-structured SI eco-epidemiological model with periodic constant pulse releasing of infectious pests with pathogens. The authors show that the conditions for global attractivity of the ＇pest-eradication＇ periodic solution and permanence of the system depend on time delay, hence, the authors call it ＂profitless＂. Further, the authors present a pest management strategy in which the pest population is kept under the economic threshold level （ETL） when the pest population is uniformly persistent. By numerical analysis, the authors also show that constant maturation time delay for the susceptible pests and pulse releasing of the infectious pests can bring obvious effects on the dynamics of system.展开更多
The aim of this paper is to investigate a stochastic threshold for a delayed epidemic model driven by Levy noise with a nonlinear incidence and vaccination.Mainly,we derive a stochastic threshold 77s which depends on ...The aim of this paper is to investigate a stochastic threshold for a delayed epidemic model driven by Levy noise with a nonlinear incidence and vaccination.Mainly,we derive a stochastic threshold 77s which depends on model parameters and stochastic coefficients for a better understanding of the dynamical spreading of the disease.First,we prove the well posedness of the model.Then,we study the extinction and the persistence of the disease according to the values of TZS.Furthermore,using different scenarios of Tuberculosis disease in Morocco,we perform some numerical simulations to support the analytical results.展开更多
A disease transmission model of SIS type with stage structure and a delay is formulated. Stability of the disease free equilibrium, and existence, uniqueness, and stability of an endemic equilibrium, are investigated ...A disease transmission model of SIS type with stage structure and a delay is formulated. Stability of the disease free equilibrium, and existence, uniqueness, and stability of an endemic equilibrium, are investigated for the model. The stability results arc stated in terms of a key threshold parameter. The effects of stage structure and time delay on dynamical behavior of the infectious disease are analyzed. It is shown that stage structure has no effect on the epidemic model and Hopf bifurcation can occur as the time delay increases.展开更多
This paper considers a class of delayed renewal risk processes with a threshold dividend strategy. The main result is an expression of the Gerber-Shiu expected discounted penalty function in the delayed renewal risk m...This paper considers a class of delayed renewal risk processes with a threshold dividend strategy. The main result is an expression of the Gerber-Shiu expected discounted penalty function in the delayed renewal risk model in terms of the corresponding Cerber-Shiu function in the ordinary renewal model. Subsequently, this relationship is considered in more detail in both the stationary renewal risk model and the ruin probability.展开更多
Background Leprosy is an infectious disease caused by Mycobacterium leprae and remains a source of preventable disability if left undetected.Case detection delay is an important epidemiological indicator for progress ...Background Leprosy is an infectious disease caused by Mycobacterium leprae and remains a source of preventable disability if left undetected.Case detection delay is an important epidemiological indicator for progress in interrupting transmission and preventing disability in a community.However,no standard method exists to effectively analyse and interpret this type of data.In this study,we aim to evaluate the characteristics of leprosy case detection delay data and select an appropriate model for the variability of detection delays based on the best fitting distribution type.Methods Two sets of leprosy case detection delay data were evaluated:a cohort of 181 patients from the post exposure prophylaxis for leprosy(PEP4LEP)study in high endemic districts of Ethiopia,Mozambique,and Tanzania;and self-reported delays from 87 individuals in 8 low endemic countries collected as part of a systematic literature review.Bayesian models were fit to each dataset to assess which probability distribution(log-normal,gamma or Weibull)best describes variation in observed case detection delays using leave-one-out cross-validation,and to estimate the effects of individual factors.Results For both datasets,detection delays were best described with a log-normal distribution combined with covariates age,sex and leprosy subtype[expected log predictive density(ELPD)for the joint model:-1123.9].Patients with multibacillary(MB)leprosy experienced longer delays compared to paucibacillary(PB)leprosy,with a relative difference of 1.57[95%Bayesian credible interval(BCI):1.14-2.15].Those in the PEP4LEP cohort had 1.51(95%BCI:1.08-2.13)times longer case detection delay compared to the self-reported patient delays in the systematic review.Conclusions The log-normal model presented here could be used to compare leprosy case detection delay datasets,including PEP4LEP where the primary outcome measure is reduction in case detection delay.We recommend the application of this modelling approach to test different probability distributions and covariate effects in studies with similar outcomes in the field of leprosy and other skin-NTDs.展开更多
A disease transmission model of SI type with stage structure is formulated. The stability of disease free equilibrium, the existence and uniqueness of an endemic equilibrium, the existence of a global attractor are in...A disease transmission model of SI type with stage structure is formulated. The stability of disease free equilibrium, the existence and uniqueness of an endemic equilibrium, the existence of a global attractor are investigated.展开更多
文摘Epidemiologic model of SIS type has a delay corresponding to the infectious period and disease related deaths,so that the population size is variable.The population dynamics structure is recruitment and natural births with natural deaths.The incidence term is of the standard incidence.Here the thresholds and equilibria are detemined,and stabilities are examined.The persistence of the infectious disease and disease related deaths can lead to a new equilibrium population size below the carrying capacity.
文摘A numerical scheme for a SIS epidemic model with a delay is constructed by applying a nonstandard finite difference (NSFD) method. The dynamics of the obtained discrete system is investigated. First we show that the discrete system has equilibria which are exactly the same as those of continuous model. By studying the distribution of the roots of the characteristics equations related to the linearized system, we can provide the stable regions in the appropriate parameter plane. It is shown that the conditions for those equilibria to be asymptotically stable are consistent with the continuous model for any size of numerical time-step. Furthermore, we also establish the existence of Neimark-Sacker bifurcation (also called Hopf bifurcation for map) which is controlled by the time delay. The analytical results are confirmed by some numerical simulations.
文摘In this paper, an epidemic SIS model with nonlinear infectivity on heterogeneous networks and time delays is investigated. The oscillatory behavior of the solutions is studied. Two sufficient conditions are provided to guarantee the oscillatory behavior for the solutions. Some computer simulations are demonstrated.
基金supported by the National Natural Science Foundation of China(No.12201557)the Foundation of Zhejiang Provincial Education Department(No.Y202249921).
文摘Considering the antiviral drugs can act on the fusion,reverse transcription,and budding stages of HIV infected cells,in this paper,we formulate a two-periodic delay heterogeneous space diffusion HIV model with three-stage infection process to study the effects of periodic antiviral treatment and spatial heterogeneity on HIV infection process.We first study the well-posedness of the full system and then derive the basic reproduction number R_(0),which is defined as the spectral radius of the next generation operator.We further prove that R_(0) is a threshold for the elimination and persistence of HIV infection by comparison principle and persistence theory for non-autonomous system.In the spatial homogeneous case,the explicit expression of R_(0) is derived and the global attractivity of the positive steady state is proved by using the fluctuation method.Some numerical simulations are conducted to illustrate the theoretical results and our works suggest that both spatial heterogeneity and periodic delays caused by periodic antiviral therapy have a remarkable impact on the progression of HIV infection and should not be overlooked in clinical treatment process.
基金the National Natural Science Foundation of China under Grant No.10471117,10771179the Natural Science and Development Foundation of Shandong University of Science and Technology under Grant No.05g016
文摘This paper formulates a robust stage-structured SI eco-epidemiological model with periodic constant pulse releasing of infectious pests with pathogens. The authors show that the conditions for global attractivity of the ＇pest-eradication＇ periodic solution and permanence of the system depend on time delay, hence, the authors call it ＂profitless＂. Further, the authors present a pest management strategy in which the pest population is kept under the economic threshold level （ETL） when the pest population is uniformly persistent. By numerical analysis, the authors also show that constant maturation time delay for the susceptible pests and pulse releasing of the infectious pests can bring obvious effects on the dynamics of system.
文摘The aim of this paper is to investigate a stochastic threshold for a delayed epidemic model driven by Levy noise with a nonlinear incidence and vaccination.Mainly,we derive a stochastic threshold 77s which depends on model parameters and stochastic coefficients for a better understanding of the dynamical spreading of the disease.First,we prove the well posedness of the model.Then,we study the extinction and the persistence of the disease according to the values of TZS.Furthermore,using different scenarios of Tuberculosis disease in Morocco,we perform some numerical simulations to support the analytical results.
基金the K.C. Wong Education Foundation, Hong Kong and Partly by the China Postdoctoral Science Foundation.
文摘A disease transmission model of SIS type with stage structure and a delay is formulated. Stability of the disease free equilibrium, and existence, uniqueness, and stability of an endemic equilibrium, are investigated for the model. The stability results arc stated in terms of a key threshold parameter. The effects of stage structure and time delay on dynamical behavior of the infectious disease are analyzed. It is shown that stage structure has no effect on the epidemic model and Hopf bifurcation can occur as the time delay increases.
基金Supported by the Natural Science Foundation of Hunan (No. 08JJ3004)
文摘This paper considers a class of delayed renewal risk processes with a threshold dividend strategy. The main result is an expression of the Gerber-Shiu expected discounted penalty function in the delayed renewal risk model in terms of the corresponding Cerber-Shiu function in the ordinary renewal model. Subsequently, this relationship is considered in more detail in both the stationary renewal risk model and the ruin probability.
基金the European Union awarded to NLR/LM(grant number RIA2017NIM-1839-PEP-4LEP),and the Leprosy Research Initiative(LRIwww.lepro syres earch.org)awarded to NLR/LM(grant number 707.19.58.).
文摘Background Leprosy is an infectious disease caused by Mycobacterium leprae and remains a source of preventable disability if left undetected.Case detection delay is an important epidemiological indicator for progress in interrupting transmission and preventing disability in a community.However,no standard method exists to effectively analyse and interpret this type of data.In this study,we aim to evaluate the characteristics of leprosy case detection delay data and select an appropriate model for the variability of detection delays based on the best fitting distribution type.Methods Two sets of leprosy case detection delay data were evaluated:a cohort of 181 patients from the post exposure prophylaxis for leprosy(PEP4LEP)study in high endemic districts of Ethiopia,Mozambique,and Tanzania;and self-reported delays from 87 individuals in 8 low endemic countries collected as part of a systematic literature review.Bayesian models were fit to each dataset to assess which probability distribution(log-normal,gamma or Weibull)best describes variation in observed case detection delays using leave-one-out cross-validation,and to estimate the effects of individual factors.Results For both datasets,detection delays were best described with a log-normal distribution combined with covariates age,sex and leprosy subtype[expected log predictive density(ELPD)for the joint model:-1123.9].Patients with multibacillary(MB)leprosy experienced longer delays compared to paucibacillary(PB)leprosy,with a relative difference of 1.57[95%Bayesian credible interval(BCI):1.14-2.15].Those in the PEP4LEP cohort had 1.51(95%BCI:1.08-2.13)times longer case detection delay compared to the self-reported patient delays in the systematic review.Conclusions The log-normal model presented here could be used to compare leprosy case detection delay datasets,including PEP4LEP where the primary outcome measure is reduction in case detection delay.We recommend the application of this modelling approach to test different probability distributions and covariate effects in studies with similar outcomes in the field of leprosy and other skin-NTDs.
基金This work is supported by National Natural Science Foundation of China (10171106)the Special Fund for Major State Basic Research Projects (G1999032805)
文摘A disease transmission model of SI type with stage structure is formulated. The stability of disease free equilibrium, the existence and uniqueness of an endemic equilibrium, the existence of a global attractor are investigated.
