Gelugpa is the most influential extant religious sect of Tibetan Buddhism,which is the spiritual prop for Tibetans,with thousands of monasteries and followers in Tibetan areas of China.Studies on the spatial diffusion...Gelugpa is the most influential extant religious sect of Tibetan Buddhism,which is the spiritual prop for Tibetans,with thousands of monasteries and followers in Tibetan areas of China.Studies on the spatial diffusion processes of Gelugpa can not only reveal its historical geographical development but also lay the foundation for anticipating its future development trend.However,existing studies on Gelugpa lack geographical perspective,making it difficult to explore the spatial characteristics.Furthermore,the prevailing macro-perspective overlooks spatiotemporal heterogeneity in diffusion processes.Therefore,taking monastery as the carrier,this study establishes a multi-level diffusion model to reconstruct the diffusion networks of Gelugpa monasteries,as well as a framework to explore the detailed features in the spatial diffusion processes of Gelugpa in Tibetan areas of China based on a geodatabase of Gelugpa monastery.The results show that the multi-level diffusion model has a considerable applicability in the reconstruction of the diffusion networks of Gelugpa monasteries.Gelugpa monasteries in the Three Tibetan Inhabited Areas present disparate spatial diffusion processes with diverse diffusion bases,speeds,stages,as well as diffusion regions and centers.A powerful single-center diffusion-centered Gandan Monastery was rapidly formed in U-Tsang.Kham experienced a slower and more varied spatial diffusion process with multiple diffusion systems far apart from each other.The spatial diffusion process of Amdo was the most complex,with the highest diffusion intensity.Amdo possessed the most influential diffusion centers,with different diffusion shapes and diffusion ranges crossing and overlapping with each other.Multiple natural and human factors may contribute to the formation of Gelugpa monasteries.This study contributes to the understanding of the geography of Gelugpa and provides reference to studies on religion diffusion.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 study examines an optimal contraception control problem for a nonlinear competitive vermin population model that is dependent on size structure and spatial diffusion in a polluted environment.The control variable...This study examines an optimal contraception control problem for a nonlinear competitive vermin population model that is dependent on size structure and spatial diffusion in a polluted environment.The control variables are the average number of female sterilant and the input rate of exogenous toxicant.It has a good guiding effect on curbing environmental pollution and controlling the number of vermin.These results provide a theoretical basis for controlling and preventing vermin and curbing environmental pollution.The hybrid system belongs to the class of separable models,and its solution is separable in terms of size and spatial location.Therefore,we transform the system into two subsystems and prove the existence and uniqueness of non-negative solutions via the comparison principle and fixed point theorem,respectively.The necessary conditions for the optimal contraception strategy are derived by constructing an adjoint system and using tangent-normal cones.The method of characteristics and the finite difference method approximate the non-negative solutions of the two subsystems,and some numerical examples illustrate the theoretical results.展开更多
We developed a novel method for real-time monitoring of alteration of the local epithelium vessel/capillary and blood oxygenation spatial pattern in epithelium exploiting a compact fibre sensor system based on spatial...We developed a novel method for real-time monitoring of alteration of the local epithelium vessel/capillary and blood oxygenation spatial pattern in epithelium exploiting a compact fibre sensor system based on spatially and spectrally resolved diffuse reflectance.The method is based on collection of spatially resolved diffuse reflectance Re(λ)by fiber sensors.The spatial resolution is provided as a dependence of Re(λ)on a set of distancesρbetween the source and detector(attenuation curve).It is expected that the new method can reasonably extract the minor spatial deviations of oxygenation and local blood volume fraction-parameters,directly related to the local vessel density and capillary spatial patterns in the epithelium.Light scattering in visible range is naturally taken into account in the proposed method.展开更多
This paper investigates the dynamic interactions between biosurfactant-producing bacteria and their environment through pattern formations in diffusive predator-prey models.By analyzing the model’s equilibrium points...This paper investigates the dynamic interactions between biosurfactant-producing bacteria and their environment through pattern formations in diffusive predator-prey models.By analyzing the model’s equilibrium points and applying the Routh-Hurwitz criteria with bifurcation analysis,we determine the conditions for the existence of Turing patterns.Numerical simulations confirm these analytical findings and reveal diverse pattern formations influenced by diffusion and concentration zones,including both Turing and non-Turing patterns.We observe a correlation between the distribution of the two species through pattern formations and the effectiveness of biosurfactant-mediated oil recovery.More interestingly,our model focuses on the dynamics of bacterial and biosurfactant concentrations by showing that areas of high biosurfactant concentration are associated with the release of trapped oil from pores,thereby contributing to successful oil recovery.展开更多
A competitive LotkaVolterra reactiondiffusion system with two delays subject to Neumann boundary conditions is considered. It is well known that the positive con stant steady state of the system is globally asymptotic...A competitive LotkaVolterra reactiondiffusion system with two delays subject to Neumann boundary conditions is considered. It is well known that the positive con stant steady state of the system is globally asymptotically stable if the interspecies competition is weaker than the intraspecies one and is unstable if the interspecies com petition dominates over the intraspecies one. If the latter holds, then we show that Hopf bifurcation can occur as the parameters （delays） in the system cross some critical val ues. In particular, we prove that these Hopf bifurcations are all spatially homogeneous if the diffusive rates are suitably large, which has the same properties as Hopf bifur cation of the corresponding delayed system without diffusion. However, if the diffusive rates are suitably small, then the system generates the spatially nonhomogeneous Hopf bifurcation. Furthermore, we derive conditions for determining the direction of spatially nonhomogeneous Hopf bifurcations and the stability of bifurcating periodic solutions. These results indicate that the diffusion plays an important role for deriving the complex spatiotemporal dynamics.展开更多
Background:The ongoing transmission of the Middle East respiratory syndrome coronavirus(MERS-CoV)in the Middle East and its expansion to other regions are raising concerns of a potential pandemic.An in-depth analysis ...Background:The ongoing transmission of the Middle East respiratory syndrome coronavirus(MERS-CoV)in the Middle East and its expansion to other regions are raising concerns of a potential pandemic.An in-depth analysis about both population and molecular epidemiology of this pathogen is needed.Methods:MERS cases reported globally as of June 2020 were collected mainly from World Health Organization official reports,supplemented by other reliable sources.Determinants for case fatality and spatial diffusion of MERS were assessed with Logistic regressions and Cox proportional hazard models,respectively.Phylogenetic and phylogeographic analyses were performed to examine the evolution and migration history of MERS-CoV.Results:A total of 2562 confirmed MERS cases with 150 case clusters were reported with a case fatality rate of 32.7%(95%Cl:30.9-34.6%).Saudi Arabia accounted for 83.6%of the cases.Age of>65 years old,underlying conditions and>5 days delay in diagnosis were independent risk factors for death.However,a history of animal contact was associated with a higher risk(adjusted OR=297,95%Cl:1」0-7.98)among female cases<65 years but with a lower risk(adjusted OR=0.31,95%Cl:0.18-0.51)among male cases>65 years old.Diffusion of the disease was fastest from its origin in Saudi Arabia to the east,and was primarily driven by the transportation network.The most recent subclade C5.1(since 2013)was associated with non-synonymous mutations and a higher mortality rate.Phylogeographic analyses pointed to Riyadh of Saudi Arabia and Abu Dhabi of the United Arab Emirates as the hubs for both local and international spread of MERS-CoV.Conclusions:MERS-CoV remains primarily locally transmitted in the Middle East,with opportunistic exportation to other continents and a potential of causing transmission clusters of human cases.Animal contact is associated with a higher risk of death,but the association differs by age and sex.Transportation network is the leading driver for the spatial diffusion ofthe disease.These findings how this pathogen spread are helpful for targeting public health surveillance and interventions to control endemics and to prevent a potential pandemic.展开更多
Weibo,China’s largest microblogging platform,has become one of the key information-sharing platforms in modern society.This study examines topic propagation in relation to microblogging from the perspective of the“p...Weibo,China’s largest microblogging platform,has become one of the key information-sharing platforms in modern society.This study examines topic propagation in relation to microblogging from the perspective of the“peer effect.”Using data of hot topics from Weibo,we analyze how the social effect and propagation pathway influence the topic propagation process.We propose a spatial and temporal heterogeneity diffusion model that includes endogenous and exogenous social effects and is based on but different from the Bass diffusion model.We find that most propagation pathways end after a single level of propagation.The endogenous social effect in microblogs primarily influences the inflow of topics.Such endogenous social effect,combined with the multiplier effect,motivates most users to share a microblog topic in a short period of time.The exogenous social effect primarily influences the outflow of topics,and therefore,the microblog topics of a small number of popular users’account for most of the share volume.Our results are robust to potential serial correlation,reflection problem,and potential self-selection due to user status.The findings reveal that group characteristics affect individuals’behaviors and choices in relation to the topic propagation process on microblogging platforms.The use of a spatial and temporal heterogeneity diffusion model and the robustness of the analysis process provide new information for scholars in this field.展开更多
基金supported by the Humanities and Social Sciences Foundation of the Ministry of Education of China(Grant No.18YJAZH140).
文摘Gelugpa is the most influential extant religious sect of Tibetan Buddhism,which is the spiritual prop for Tibetans,with thousands of monasteries and followers in Tibetan areas of China.Studies on the spatial diffusion processes of Gelugpa can not only reveal its historical geographical development but also lay the foundation for anticipating its future development trend.However,existing studies on Gelugpa lack geographical perspective,making it difficult to explore the spatial characteristics.Furthermore,the prevailing macro-perspective overlooks spatiotemporal heterogeneity in diffusion processes.Therefore,taking monastery as the carrier,this study establishes a multi-level diffusion model to reconstruct the diffusion networks of Gelugpa monasteries,as well as a framework to explore the detailed features in the spatial diffusion processes of Gelugpa in Tibetan areas of China based on a geodatabase of Gelugpa monastery.The results show that the multi-level diffusion model has a considerable applicability in the reconstruction of the diffusion networks of Gelugpa monasteries.Gelugpa monasteries in the Three Tibetan Inhabited Areas present disparate spatial diffusion processes with diverse diffusion bases,speeds,stages,as well as diffusion regions and centers.A powerful single-center diffusion-centered Gandan Monastery was rapidly formed in U-Tsang.Kham experienced a slower and more varied spatial diffusion process with multiple diffusion systems far apart from each other.The spatial diffusion process of Amdo was the most complex,with the highest diffusion intensity.Amdo possessed the most influential diffusion centers,with different diffusion shapes and diffusion ranges crossing and overlapping with each other.Multiple natural and human factors may contribute to the formation of Gelugpa monasteries.This study contributes to the understanding of the geography of Gelugpa and provides reference to studies on religion diffusion.
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supported by the National Natural Science Foundation of China(No.11561041)the Young Doctor Support Foundation of Gansu Education Department(No.2023QB-077)the Start-Up Foundation of Doctoral Research of Hexi University(No.KYQD2023011).
文摘This study examines an optimal contraception control problem for a nonlinear competitive vermin population model that is dependent on size structure and spatial diffusion in a polluted environment.The control variables are the average number of female sterilant and the input rate of exogenous toxicant.It has a good guiding effect on curbing environmental pollution and controlling the number of vermin.These results provide a theoretical basis for controlling and preventing vermin and curbing environmental pollution.The hybrid system belongs to the class of separable models,and its solution is separable in terms of size and spatial location.Therefore,we transform the system into two subsystems and prove the existence and uniqueness of non-negative solutions via the comparison principle and fixed point theorem,respectively.The necessary conditions for the optimal contraception strategy are derived by constructing an adjoint system and using tangent-normal cones.The method of characteristics and the finite difference method approximate the non-negative solutions of the two subsystems,and some numerical examples illustrate the theoretical results.
基金The authors gratefully acknowledge funding of the Erlangen Graduate School in Advanced Optical Technologies(SAOT)by the German National Science Foundation(DFG)in the framework of the excellence initiative for support of this study.
文摘We developed a novel method for real-time monitoring of alteration of the local epithelium vessel/capillary and blood oxygenation spatial pattern in epithelium exploiting a compact fibre sensor system based on spatially and spectrally resolved diffuse reflectance.The method is based on collection of spatially resolved diffuse reflectance Re(λ)by fiber sensors.The spatial resolution is provided as a dependence of Re(λ)on a set of distancesρbetween the source and detector(attenuation curve).It is expected that the new method can reasonably extract the minor spatial deviations of oxygenation and local blood volume fraction-parameters,directly related to the local vessel density and capillary spatial patterns in the epithelium.Light scattering in visible range is naturally taken into account in the proposed method.
文摘This paper investigates the dynamic interactions between biosurfactant-producing bacteria and their environment through pattern formations in diffusive predator-prey models.By analyzing the model’s equilibrium points and applying the Routh-Hurwitz criteria with bifurcation analysis,we determine the conditions for the existence of Turing patterns.Numerical simulations confirm these analytical findings and reveal diverse pattern formations influenced by diffusion and concentration zones,including both Turing and non-Turing patterns.We observe a correlation between the distribution of the two species through pattern formations and the effectiveness of biosurfactant-mediated oil recovery.More interestingly,our model focuses on the dynamics of bacterial and biosurfactant concentrations by showing that areas of high biosurfactant concentration are associated with the release of trapped oil from pores,thereby contributing to successful oil recovery.
文摘A competitive LotkaVolterra reactiondiffusion system with two delays subject to Neumann boundary conditions is considered. It is well known that the positive con stant steady state of the system is globally asymptotically stable if the interspecies competition is weaker than the intraspecies one and is unstable if the interspecies com petition dominates over the intraspecies one. If the latter holds, then we show that Hopf bifurcation can occur as the parameters （delays） in the system cross some critical val ues. In particular, we prove that these Hopf bifurcations are all spatially homogeneous if the diffusive rates are suitably large, which has the same properties as Hopf bifur cation of the corresponding delayed system without diffusion. However, if the diffusive rates are suitably small, then the system generates the spatially nonhomogeneous Hopf bifurcation. Furthermore, we derive conditions for determining the direction of spatially nonhomogeneous Hopf bifurcations and the stability of bifurcating periodic solutions. These results indicate that the diffusion plays an important role for deriving the complex spatiotemporal dynamics.
基金supported by China Mega-Project on Infectious Disease Prevention(No.2017ZX10303401,2018ZX10713002,2018ZX10101003 and 2018ZX10201001)National Natural Science Foundation of China(No.81825019),and the National Institutes of Health of United States(R01 All 39761 and R01 AI116770)YY was supported by US National Institutes of Health grants R01 Al 139761 and R56 Al 148284.
文摘Background:The ongoing transmission of the Middle East respiratory syndrome coronavirus(MERS-CoV)in the Middle East and its expansion to other regions are raising concerns of a potential pandemic.An in-depth analysis about both population and molecular epidemiology of this pathogen is needed.Methods:MERS cases reported globally as of June 2020 were collected mainly from World Health Organization official reports,supplemented by other reliable sources.Determinants for case fatality and spatial diffusion of MERS were assessed with Logistic regressions and Cox proportional hazard models,respectively.Phylogenetic and phylogeographic analyses were performed to examine the evolution and migration history of MERS-CoV.Results:A total of 2562 confirmed MERS cases with 150 case clusters were reported with a case fatality rate of 32.7%(95%Cl:30.9-34.6%).Saudi Arabia accounted for 83.6%of the cases.Age of>65 years old,underlying conditions and>5 days delay in diagnosis were independent risk factors for death.However,a history of animal contact was associated with a higher risk(adjusted OR=297,95%Cl:1」0-7.98)among female cases<65 years but with a lower risk(adjusted OR=0.31,95%Cl:0.18-0.51)among male cases>65 years old.Diffusion of the disease was fastest from its origin in Saudi Arabia to the east,and was primarily driven by the transportation network.The most recent subclade C5.1(since 2013)was associated with non-synonymous mutations and a higher mortality rate.Phylogeographic analyses pointed to Riyadh of Saudi Arabia and Abu Dhabi of the United Arab Emirates as the hubs for both local and international spread of MERS-CoV.Conclusions:MERS-CoV remains primarily locally transmitted in the Middle East,with opportunistic exportation to other continents and a potential of causing transmission clusters of human cases.Animal contact is associated with a higher risk of death,but the association differs by age and sex.Transportation network is the leading driver for the spatial diffusion ofthe disease.These findings how this pathogen spread are helpful for targeting public health surveillance and interventions to control endemics and to prevent a potential pandemic.
基金the National Natural Science Foundation of China(Grant Nos.70801066,71071167,7107168,71371200)Sun Yat-sen University Basic Research Funding(Grant Nos.1009028,1109115,16wkjc13)。
文摘Weibo,China’s largest microblogging platform,has become one of the key information-sharing platforms in modern society.This study examines topic propagation in relation to microblogging from the perspective of the“peer effect.”Using data of hot topics from Weibo,we analyze how the social effect and propagation pathway influence the topic propagation process.We propose a spatial and temporal heterogeneity diffusion model that includes endogenous and exogenous social effects and is based on but different from the Bass diffusion model.We find that most propagation pathways end after a single level of propagation.The endogenous social effect in microblogs primarily influences the inflow of topics.Such endogenous social effect,combined with the multiplier effect,motivates most users to share a microblog topic in a short period of time.The exogenous social effect primarily influences the outflow of topics,and therefore,the microblog topics of a small number of popular users’account for most of the share volume.Our results are robust to potential serial correlation,reflection problem,and potential self-selection due to user status.The findings reveal that group characteristics affect individuals’behaviors and choices in relation to the topic propagation process on microblogging platforms.The use of a spatial and temporal heterogeneity diffusion model and the robustness of the analysis process provide new information for scholars in this field.
