This paper studied a structured model by age of tuberculosis. A population divided into two parts was considered for the study. Each subpopulation is submitted to a program of vaccination. It was allowed the migration...This paper studied a structured model by age of tuberculosis. A population divided into two parts was considered for the study. Each subpopulation is submitted to a program of vaccination. It was allowed the migration of vaccinated people only between the two patches. After the determination of and , the local and global stability of the disease-free equilibrium was studied. It showed the existence of three endemic equilibrium points. The theoretical results were illustrated by a numeric simulation.展开更多
Using the sterile insect technique,in which sterile mosquitoes are released to reduce or eradicate the wild mosquito population,is an effective weapon to prevent transmission of mosquito-borne diseases. To study the i...Using the sterile insect technique,in which sterile mosquitoes are released to reduce or eradicate the wild mosquito population,is an effective weapon to prevent transmission of mosquito-borne diseases. To study the impact of the sterile insect technique on the disease transmissions,we formulate stage-structured discrete-time mathematical models,based on difference equations,for the interactive dynamics of the wild and sterile mosquitoes. We incorporate different strategies for releasing sterile mosquitoes,investigate the model dynamics,and compare the impact of the different release strategies.Numerical examples are also provided to demonstrate dynamical features of the models.展开更多
To assess the effectiveness of vaccination in contaminated environments,this study introduces a modeling framework that encompasses two transmission routes,namely direct human-to-human contact and indirect human-to-en...To assess the effectiveness of vaccination in contaminated environments,this study introduces a modeling framework that encompasses two transmission routes,namely direct human-to-human contact and indirect human-to-environment contact,as well as the implementation of new M72/AS01_(E)vaccine.Motivated by this,a coupled age-structured tuberculosis(TB)model is proposed.Its well-posedness requirement is verified using the integrated semigroup theory.Furthermore,this study presents a comprehensive analysis of threshold dynamics associated with the proposed model.Specifically,the global stability of the disease-free and positive steady states is demonstrated by employing Lyapunov functionals.Lastly,the effects of the vaccination with M72/AS01_(E)and contaminated environments on TB control are numerically simulated.Experimental results indicate that high concentrations of Mycobacterium tuberculosis in contaminated environments may somewhat impede TB control efforts,but that large-scale deployment of new vaccine could significantly reduce the prevalence of TB.展开更多
In classical mumps models,individuals are generally assumed to be uniformly mixed(homogeneous),ignoring population heterogeneity(preference,activity,etc.).Age is the key to catching mixed patterns in developing mathem...In classical mumps models,individuals are generally assumed to be uniformly mixed(homogeneous),ignoring population heterogeneity(preference,activity,etc.).Age is the key to catching mixed patterns in developing mathematical models for mumps.A continuous heterogeneous age-structured model for mumps with vaccines has been developed in this paper.The stability of age-structured models is a difficult question.An explicit formula of R0 was defined for the various mixing modes(isolation,proportional and heterogeneous mixing)with or without the vaccine.The results show that the endemic steady state is unique and locally stable if R0>1 without any additional conditions.A number of numerical examples are given to support the theory.展开更多
Insect populations,which are diverse and widespread,provide a principal area of utilization of the stage-structured modeling approach.In this paper,housefly populations incorporating a stage-structured model are inves...Insect populations,which are diverse and widespread,provide a principal area of utilization of the stage-structured modeling approach.In this paper,housefly populations incorporating a stage-structured model are investigated theoretically and graphically.First,stability charts and rightmost characteristic roots of the positive equilibrium are elucidated analytically and numerically.Furthermore,the Hopf bifurcation at the positive equilibrium is derived employing geometric stability switch criterion.Second,the properties of Hopf bifurcation are determined using the center manifold theorem and by reducing the equation to the Poincarénormal form.Finally,the correctness of the theoretical derivation is confirmed using a numerical simulation based on specific parameter values.Our results show that with an increase in delay T,the unique positive equilibrium may undergo two stability switches:from stable to unstable,and from unstable to stable.Interestingly,the characteristic equation has pure imaginary roots at the second pair and subsequent critical values,However,Hopf bifurcation theorem is not satisfied because all other characteristic roots of the characteristic equation at these critical values do not have strictly negative real parts,except the pure imaginary roots.We also simulate the unstable periodic solutions at the second pair of critical values through a bifurcation diagram.Therefore,a pair of supercritical Hopf bifurcations appear around the positive equilibrium of the housefly population stage-structured model.展开更多
Smoking is a serious global public health problem.The ability to quit smoking is closely related to age;in addition,personal determination and education usually play an important role in quitting smoking.In order to c...Smoking is a serious global public health problem.The ability to quit smoking is closely related to age;in addition,personal determination and education usually play an important role in quitting smoking.In order to capture such characteristics,we developed a novel age-structured smoking dynamical model.By defining the smoking generation number Ro,the local stability,global stability of the boundary equilibrium and endemic equilibrium are obtained using Lyapunov functions.The uniform persistence and the well-posedness and asymptotic smoothness of the solutions are also studied.Sensitivity analyzes show that the lower the age of onset of smoking and the higher the determination to stop,the greater the likelihood of quitting smoking and numerical studies support the theoretical results.展开更多
In this paper, the existence of periodic solutions for a time dependent age-structured population model is studied. The averaged net reproductive number is introduced as the main parameter to determine the dynamical b...In this paper, the existence of periodic solutions for a time dependent age-structured population model is studied. The averaged net reproductive number is introduced as the main parameter to determine the dynamical behaviors of the model. The existence of a global parameterized branch of periodic solutions of the model is obtained by using the contracting mapping theorem in a periodic and continuous function space. The global stability of the trivial equilibrium is studied and a very practical stability criteria for the model is obtained. The dynamics of the linear time-periodic model is similar to that of the linear model.展开更多
In this paper,we propose detailed and reasonable viral dynamics by using a multi-compartment model that incorporating the age since the infection of multiple infectedcells,multiple target cells(Langerhans-cells and CD...In this paper,we propose detailed and reasonable viral dynamics by using a multi-compartment model that incorporating the age since the infection of multiple infectedcells,multiple target cells(Langerhans-cells and CD4^(+)T-cells),multiple viral strains(CCR5 and CXR4 HIV)and multiple infection routes(cell-to-cell and cell-to-virus).Thebasic reproduction number,R_(0),of the whole model is derived from two transmissionmechanisms:one is the potential trigger from the infection routes for a single target celland other is the joint effect of multiple viral infections for multi-target cells.Accordingly,we study the global stability of the steady states for the single target model.For thewhole model,we prove that the infection-free steady state is globally asymptoticallystable if R_(0)<1,whereas viruses persist uniformly if R_(0)>1.Numerical simulations arecarried out to illustrate the theoretical results.Sensitive analyses expound the effect ofmodel parameters on the comprehensive reproduction number.It is remarkable to findthat simultaneous control of HlV infection for two target cells can effectively reducethe viral loads within-host.Finally,our work suggests that the synergetic mechanism ofmulti-target cells and multi-strain cannot be ignored during treatment.展开更多
Coronavirus disease 2019 is caused by severe acute respiratory syndrome coronavirus 2.Kenya reported its first case on March 13,2020 and by March 16,2020 she instituted physical distancing strategies to reduce transmi...Coronavirus disease 2019 is caused by severe acute respiratory syndrome coronavirus 2.Kenya reported its first case on March 13,2020 and by March 16,2020 she instituted physical distancing strategies to reduce transmission and flatten the epidemic curve.An age-structured compartmental model was developed to assess the impact of the strategies on COVID-19 severity and burden.Contacts between different ages are incorporated via contact matrices.Simulation results show that 45%reduction in contacts for 60-days period resulted to 11.5e13%reduction of infections severity and deaths,while for the 190-days period yielded 18.8e22.7%reduction.The peak of infections in the 60-days mitigation was higher and happened about 2 months after the relaxation of mitigation as compared to that of the 190-days mitigation,which happened a month after mitigations were relaxed.Low numbers of cases in children under 15 years was attributed to high number of asymptomatic cases.High numbers of cases are reported in the 15e29 years and 30e59 years age bands.Two mitigation periods,considered in the study,resulted to reductions in severe and critical cases,attack rates,hospital and ICU bed demands,as well as deaths,with the 190-days period giving higher reductions.展开更多
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
Rural domestic sewage treatment is critical for environmental protection.This study defines the spatial pattern of villages from the perspective of rural sewage treatment and develops an integrated decision-making sys...Rural domestic sewage treatment is critical for environmental protection.This study defines the spatial pattern of villages from the perspective of rural sewage treatment and develops an integrated decision-making system to propose a sewage treatment mode and scheme suitable for local conditions.By considering the village spatial layout and terrain factors,a decision tree model of residential density and terrain type was constructed with accuracies of 76.47%and 96.00%,respectively.Combined with binary classification probability unit regression,an appropriate sewage treatment mode for the village was determined with 87.00%accuracy.The Analytic Hierarchy Process(AHP),combined with the Technique for Order Preference(TOPSIS)by Similarity to an Ideal Solution model,formed the basis for optimal treatment process selection under different emission standards.Verification was conducted in 542 villages across three counties of the Inner Mongolia Autonomous Region,focusing on the standard effluent effect(0.3773),low investment cost(0.3196),and high standard effluent effect(0.5115)to determine the best treatment process for the same emission standard under different needs.The annual environmental and carbon emission benefits of sewage treatment in these villages were estimated.This model matches village density,geographic feature,and social development level,and provides scientific support and a theoretical basis for rural sewage treatment decision-making.展开更多
We present a comprehensive description and benchmark evaluation of the global–regional chemical transport model called the Emission and Atmospheric Processes Integrated and Coupled Community(EPICC)model.The framework...We present a comprehensive description and benchmark evaluation of the global–regional chemical transport model called the Emission and Atmospheric Processes Integrated and Coupled Community(EPICC)model.The framework incorporates(1)grid configuration,(2)transport dynamics,(3)chemical mechanisms,(4)aerosol processes,(5)wet/dry deposition parameterizations,and(6)heterogeneous chemistry treatments associated with sulfate,nitrous acid(HONO)chemistry,and aerosol/cloud–photolysis interactions(APIs/CPIs).Openly shared with the atmospheric research community,the model facilitates integration of advanced physicochemical schemes to enhance simulation accuracy.Globally,the model demonstrates realistic representations of ozone(O_(3))and aerosol optical depth.The EPICC model generally demonstrates robust performance in simulating regional concentrations of O_(3) and PM_(2.5)(and its components)in China.It successfully captures vertical profiles of both global and regional O_(3).Notably,the model mitigates frequently reported sulfate underestimations in highly industrialized regions of China.The model accurately captures two regional severe pollution episodes observed in eastern China(January/June 2021).Sensitivity experiments highlight the critical roles of heterogeneous chemical mechanisms associated with sulfate,HONO chemistry,APIs,and CPIs in capturing PM_(2.5) and O_(3) concentrations in China.Improved sulfate mechanisms result in an increase of approximately 32.4%(2.8μg m^(−3))in simulated winter sulfate concentrations when observations exceed 10μg m^(−3).Enhanced HONO elevates winter O_(3) and PM_(2.5) by≤20 and≤10μg m^(−3),respectively.Overall,CPIs dominate over APIs in improving O_(3) and PM_(2.5) simulations across China.Locally,APIs mitigate PM_(2.5) and O_(3) discrepancies in the Sichuan Basin.Seasonal cloud–chemistry coupling explains the weaker impact of PM_(2.5) in summer.展开更多
Model evaluation using benchmark datasets is an important method to measure the capability of large language models(LLMs)in specific domains,and it is mainly used to assess the knowledge and reasoning abilities of LLM...Model evaluation using benchmark datasets is an important method to measure the capability of large language models(LLMs)in specific domains,and it is mainly used to assess the knowledge and reasoning abilities of LLMs.Therefore,in order to better assess the capability of LLMs in the agricultural domain,Agri-Eval was proposed as a benchmark for assessing the knowledge and reasoning ability of LLMs in agriculture.The assessment dataset used in Agri-Eval covered seven major disciplines in the agricultural domain:crop science,horticulture,plant protection,animal husbandry,forest science,aquaculture science,and grass science,and contained a total of 2283 questions.Among domestic general-purpose LLMs,DeepSeek R1 performed best with an accuracy rate of 75.49%.In the realm of international general-purpose LLMs,Gemini 2.0 pro exp 0205 standed out as the top performer,achieving an accuracy rate of 74.28%.As an LLMs in agriculture vertical,Shennong V2.0 outperformed all the LLMs in China,and the answer accuracy rate of agricultural knowledge exceeded that of all the existing general-purpose LLMs.The launch of Agri-Eval helped the LLM developers to comprehensively evaluate the model's capability in the field of agriculture through a variety of tasks and tests to promote the development of the LLMs in the field of agriculture.展开更多
We formulate an age-structured model based on a system of nonlinear partial differen- tial equations to assist the early and catch up female vaccination programs for human papillomavirus （HPV） types 6 and 11. Since ...We formulate an age-structured model based on a system of nonlinear partial differen- tial equations to assist the early and catch up female vaccination programs for human papillomavirus （HPV） types 6 and 11. Since these HPV types do not induce permanent immunity, the model, which stratifies the population based on age and gender, has a susceptible-infectious-susceptible （SIS） structure. We calculate the effective reproduction number Rv for the model and describe the local-asymptotic stability of the disease-free equilibrium using Rv. We prove the existence of an endemic equilibrium for Rv 〉 1 for the no vaccine case. However, analysis of the model for the vaccine case reveals that it undergoes the phenomenon of backward bifurcation. To support our theoretical results, we estimate the age and time solution with the given data for Toronto population, when an early and catch up female vaccine program is adopted, and when there is no vaccine. We show that early and catch up female vaccine program eliminates the infection in both male and female populations over a period of 30 years. Finally, we introduce the optimal control to an age-dependent model based on ordinary differential equations and solve it numerically to obtain the most cost-effective method for introducing the catch up vaccine into the population.展开更多
In this paper,we establish and study a single-species logistic model with impulsive age-selective harvesting.First,we prove the ultimate boundedness of the solutions of the system.Then,we obtain conditions for the asy...In this paper,we establish and study a single-species logistic model with impulsive age-selective harvesting.First,we prove the ultimate boundedness of the solutions of the system.Then,we obtain conditions for the asymptotic stability of the trivial solution and the positive periodic solution.Finally,numerical simulations are presented to validate our results.Our results show that age-selective harvesting is more conducive to sustainable population survival than non-age-selective harvesting.展开更多
The proliferation of high-dimensional data and the widespread use of complex models present central challenges in contemporary statistics and data science.Dimension reduction and model checking,as two foundational pil...The proliferation of high-dimensional data and the widespread use of complex models present central challenges in contemporary statistics and data science.Dimension reduction and model checking,as two foundational pillars supporting scientific inference and data-driven decisionmaking,have evolved through the collective wisdom of generations of statisticians.This special issue,titled"Recent Developments in Dimension Reduction and Model Checking for regressions",not only aims to showcase cutting-edge advances in the field but also carries a distinct sense of academic homage to honor the groundbreaking and enduring contributions of Professor Lixing Zhu,a leading scholar whose work has profoundly shaped both areas.展开更多
In their recent paper Pereira et al.(2025)claim that validation is overlooked in mapping and modelling of ecosystem services(ES).They state that“many studies lack critical evaluation of the results and no validation ...In their recent paper Pereira et al.(2025)claim that validation is overlooked in mapping and modelling of ecosystem services(ES).They state that“many studies lack critical evaluation of the results and no validation is provided”and that“the validation step is largely overlooked”.This assertion may have been true several years ago,for example,when Ochoa and Urbina-Cardona(2017)made a similar observation.However,there has been much work on ES model validation over the last decade.展开更多
This paper presents an efficient model reduction technique for linear time-varying systems based on shifted Legendre polynomials.The approach constructs approximate low-rank decomposition factors of finite-time Gramia...This paper presents an efficient model reduction technique for linear time-varying systems based on shifted Legendre polynomials.The approach constructs approximate low-rank decomposition factors of finite-time Gramians directly from the expansion coefficients of impulse responses.Leveraging these factors,we develop two model reduction algorithms that integrate the low-rank square root method with dominant subspace projection.Our method is computationally efficient and flexible,requiring only a few matrix-vector operations and a singular value decomposition of a low-dimensional matrix,thereby avoiding the need to solve differential Lyapunov equations.Numerical experiments confirm the effectiveness of the proposed approach.展开更多
In recent years,there has been an increasing need for climate information across diverse sectors of society.This demand has arisen from the necessity to adapt to and mitigate the impacts of climate variability and cha...In recent years,there has been an increasing need for climate information across diverse sectors of society.This demand has arisen from the necessity to adapt to and mitigate the impacts of climate variability and change.Likewise,this period has seen a significant increase in our understanding of the physical processes and mechanisms that drive precipitation and its variability across different regions of Africa.By leveraging a large volume of climate model outputs,numerous studies have investigated the model representation of African precipitation as well as underlying physical processes.These studies have assessed whether the physical processes are well depicted and whether the models are fit for informing mitigation and adaptation strategies.This paper provides a review of the progress in precipitation simulation overAfrica in state-of-the-science climate models and discusses the major issues and challenges that remain.展开更多
The dissolution of MgO-refractory into the slag had an obvious influence on the steel-slag reaction and the slag property,especially for high-aluminum steels.The dissolution behavior of MgO-refractory was investigated...The dissolution of MgO-refractory into the slag had an obvious influence on the steel-slag reaction and the slag property,especially for high-aluminum steels.The dissolution behavior of MgO-refractory was investigated under various conditions,including the temperature,the initial steel composition,and the initial slag composition.A steel-slag-refractory kinetic model for high-aluminum steel was developed,which incorporated the process of MgO-refractory dissolution.The dependence of the MgO mass transfer coefficient k_(MgO)^(r)on temperature T during MgO-refractory dissolution process was established,as described by ln k_(MgO)^(r)=63,754/T+24.38524.It was indicated that the MgO dissolution rate was significantly influenced by the temperature.A higher temperature increased the dissolution rate of MgO.The initial steel composition had a slight impact on the MgO dissolution rate.Additionally,the initial slag composition strongly impacted the MgO saturation concentration and the dissolution rate.A lower initial Al_(2)O_(3)/SiO_(2)ratio increased the MgO dissolution rate.The steel-slag-refractory kinetic model accurately predicted the dissolution of MgO-refractory and the influence of dissolved MgO on the viscosity and composition change during steel-slag-refractory reactions.It was suggested that a higher temperature can hardly reduce the viscosity due to the dissolution of the MgO-refractory.展开更多
文摘This paper studied a structured model by age of tuberculosis. A population divided into two parts was considered for the study. Each subpopulation is submitted to a program of vaccination. It was allowed the migration of vaccinated people only between the two patches. After the determination of and , the local and global stability of the disease-free equilibrium was studied. It showed the existence of three endemic equilibrium points. The theoretical results were illustrated by a numeric simulation.
基金supported partially by U.S.National Science Foundation grant DMS-0931213
文摘Using the sterile insect technique,in which sterile mosquitoes are released to reduce or eradicate the wild mosquito population,is an effective weapon to prevent transmission of mosquito-borne diseases. To study the impact of the sterile insect technique on the disease transmissions,we formulate stage-structured discrete-time mathematical models,based on difference equations,for the interactive dynamics of the wild and sterile mosquitoes. We incorporate different strategies for releasing sterile mosquitoes,investigate the model dynamics,and compare the impact of the different release strategies.Numerical examples are also provided to demonstrate dynamical features of the models.
文摘To assess the effectiveness of vaccination in contaminated environments,this study introduces a modeling framework that encompasses two transmission routes,namely direct human-to-human contact and indirect human-to-environment contact,as well as the implementation of new M72/AS01_(E)vaccine.Motivated by this,a coupled age-structured tuberculosis(TB)model is proposed.Its well-posedness requirement is verified using the integrated semigroup theory.Furthermore,this study presents a comprehensive analysis of threshold dynamics associated with the proposed model.Specifically,the global stability of the disease-free and positive steady states is demonstrated by employing Lyapunov functionals.Lastly,the effects of the vaccination with M72/AS01_(E)and contaminated environments on TB control are numerically simulated.Experimental results indicate that high concentrations of Mycobacterium tuberculosis in contaminated environments may somewhat impede TB control efforts,but that large-scale deployment of new vaccine could significantly reduce the prevalence of TB.
基金supported by the Natural Science Foundation of Xinjiang(2022D01A198,2022D03027)the National Natural Science Foundation of China(12071382).
文摘In classical mumps models,individuals are generally assumed to be uniformly mixed(homogeneous),ignoring population heterogeneity(preference,activity,etc.).Age is the key to catching mixed patterns in developing mathematical models for mumps.A continuous heterogeneous age-structured model for mumps with vaccines has been developed in this paper.The stability of age-structured models is a difficult question.An explicit formula of R0 was defined for the various mixing modes(isolation,proportional and heterogeneous mixing)with or without the vaccine.The results show that the endemic steady state is unique and locally stable if R0>1 without any additional conditions.A number of numerical examples are given to support the theory.
基金partially supported by the National Natural Science Foundation of China(Nos.12201271 and 12361101)the Tianyou Youth Talent Lift Program of Lanzhou Jiaotong University.
文摘Insect populations,which are diverse and widespread,provide a principal area of utilization of the stage-structured modeling approach.In this paper,housefly populations incorporating a stage-structured model are investigated theoretically and graphically.First,stability charts and rightmost characteristic roots of the positive equilibrium are elucidated analytically and numerically.Furthermore,the Hopf bifurcation at the positive equilibrium is derived employing geometric stability switch criterion.Second,the properties of Hopf bifurcation are determined using the center manifold theorem and by reducing the equation to the Poincarénormal form.Finally,the correctness of the theoretical derivation is confirmed using a numerical simulation based on specific parameter values.Our results show that with an increase in delay T,the unique positive equilibrium may undergo two stability switches:from stable to unstable,and from unstable to stable.Interestingly,the characteristic equation has pure imaginary roots at the second pair and subsequent critical values,However,Hopf bifurcation theorem is not satisfied because all other characteristic roots of the characteristic equation at these critical values do not have strictly negative real parts,except the pure imaginary roots.We also simulate the unstable periodic solutions at the second pair of critical values through a bifurcation diagram.Therefore,a pair of supercritical Hopf bifurcations appear around the positive equilibrium of the housefly population stage-structured model.
基金supported by the National Natural Science Foundation of China(NSFC:11961024,11801047)the Natural Science Foundation of Chongqing under Grant(cstc2019jcyj-msxmX0755,cstc2018jcyjAX0606)+1 种基金the Team Building Project for Graduate Tutors in Chongqing(JDDSTD201802)Group Building Scientific Innovation Project for universities in Chongqing(CXQT21021).
文摘Smoking is a serious global public health problem.The ability to quit smoking is closely related to age;in addition,personal determination and education usually play an important role in quitting smoking.In order to capture such characteristics,we developed a novel age-structured smoking dynamical model.By defining the smoking generation number Ro,the local stability,global stability of the boundary equilibrium and endemic equilibrium are obtained using Lyapunov functions.The uniform persistence and the well-posedness and asymptotic smoothness of the solutions are also studied.Sensitivity analyzes show that the lower the age of onset of smoking and the higher the determination to stop,the greater the likelihood of quitting smoking and numerical studies support the theoretical results.
文摘In this paper, the existence of periodic solutions for a time dependent age-structured population model is studied. The averaged net reproductive number is introduced as the main parameter to determine the dynamical behaviors of the model. The existence of a global parameterized branch of periodic solutions of the model is obtained by using the contracting mapping theorem in a periodic and continuous function space. The global stability of the trivial equilibrium is studied and a very practical stability criteria for the model is obtained. The dynamics of the linear time-periodic model is similar to that of the linear model.
基金This research was supported by the National Natural Science Foundation of China(11971013,11571170).
文摘In this paper,we propose detailed and reasonable viral dynamics by using a multi-compartment model that incorporating the age since the infection of multiple infectedcells,multiple target cells(Langerhans-cells and CD4^(+)T-cells),multiple viral strains(CCR5 and CXR4 HIV)and multiple infection routes(cell-to-cell and cell-to-virus).Thebasic reproduction number,R_(0),of the whole model is derived from two transmissionmechanisms:one is the potential trigger from the infection routes for a single target celland other is the joint effect of multiple viral infections for multi-target cells.Accordingly,we study the global stability of the steady states for the single target model.For thewhole model,we prove that the infection-free steady state is globally asymptoticallystable if R_(0)<1,whereas viruses persist uniformly if R_(0)>1.Numerical simulations arecarried out to illustrate the theoretical results.Sensitive analyses expound the effect ofmodel parameters on the comprehensive reproduction number.It is remarkable to findthat simultaneous control of HlV infection for two target cells can effectively reducethe viral loads within-host.Finally,our work suggests that the synergetic mechanism ofmulti-target cells and multi-strain cannot be ignored during treatment.
文摘Coronavirus disease 2019 is caused by severe acute respiratory syndrome coronavirus 2.Kenya reported its first case on March 13,2020 and by March 16,2020 she instituted physical distancing strategies to reduce transmission and flatten the epidemic curve.An age-structured compartmental model was developed to assess the impact of the strategies on COVID-19 severity and burden.Contacts between different ages are incorporated via contact matrices.Simulation results show that 45%reduction in contacts for 60-days period resulted to 11.5e13%reduction of infections severity and deaths,while for the 190-days period yielded 18.8e22.7%reduction.The peak of infections in the 60-days mitigation was higher and happened about 2 months after the relaxation of mitigation as compared to that of the 190-days mitigation,which happened a month after mitigations were relaxed.Low numbers of cases in children under 15 years was attributed to high number of asymptomatic cases.High numbers of cases are reported in the 15e29 years and 30e59 years age bands.Two mitigation periods,considered in the study,resulted to reductions in severe and critical cases,attack rates,hospital and ICU bed demands,as well as deaths,with the 190-days period giving higher reductions.
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supported by the Central Government Guiding Local Science and Technology Development Fund Project(No.2024SZY0343)the Joint Research Program for Ecological Conservation and High Quality Development of the Yellow River Basin(No.2022-YRUC-01-050205)+2 种基金the Higher Education Scientific Research Project of Inner Mongolia Autonomous Region(No.NJZZ23078)the project of Inner Mongolia"Prairie Talents"Engineering Innovation Entrepreneurship Talent Team,the Major Projects of Erdos Science and Technology(No.2022EEDSKJZDZX015)the Innovation Team of the Inner Mongolia Academy of Science and Technology(No.CXTD2023-01-016).
文摘Rural domestic sewage treatment is critical for environmental protection.This study defines the spatial pattern of villages from the perspective of rural sewage treatment and develops an integrated decision-making system to propose a sewage treatment mode and scheme suitable for local conditions.By considering the village spatial layout and terrain factors,a decision tree model of residential density and terrain type was constructed with accuracies of 76.47%and 96.00%,respectively.Combined with binary classification probability unit regression,an appropriate sewage treatment mode for the village was determined with 87.00%accuracy.The Analytic Hierarchy Process(AHP),combined with the Technique for Order Preference(TOPSIS)by Similarity to an Ideal Solution model,formed the basis for optimal treatment process selection under different emission standards.Verification was conducted in 542 villages across three counties of the Inner Mongolia Autonomous Region,focusing on the standard effluent effect(0.3773),low investment cost(0.3196),and high standard effluent effect(0.5115)to determine the best treatment process for the same emission standard under different needs.The annual environmental and carbon emission benefits of sewage treatment in these villages were estimated.This model matches village density,geographic feature,and social development level,and provides scientific support and a theoretical basis for rural sewage treatment decision-making.
基金National Key Scientific and Technological Infrastructure project “Earth System Science Numerical Simulator Facility” (EarthLab)supported by the National Natural Science Foundation of China (Grant No. 92044302)the National Key Research Development Program of China (Grant No. 2022YFC3700703)
文摘We present a comprehensive description and benchmark evaluation of the global–regional chemical transport model called the Emission and Atmospheric Processes Integrated and Coupled Community(EPICC)model.The framework incorporates(1)grid configuration,(2)transport dynamics,(3)chemical mechanisms,(4)aerosol processes,(5)wet/dry deposition parameterizations,and(6)heterogeneous chemistry treatments associated with sulfate,nitrous acid(HONO)chemistry,and aerosol/cloud–photolysis interactions(APIs/CPIs).Openly shared with the atmospheric research community,the model facilitates integration of advanced physicochemical schemes to enhance simulation accuracy.Globally,the model demonstrates realistic representations of ozone(O_(3))and aerosol optical depth.The EPICC model generally demonstrates robust performance in simulating regional concentrations of O_(3) and PM_(2.5)(and its components)in China.It successfully captures vertical profiles of both global and regional O_(3).Notably,the model mitigates frequently reported sulfate underestimations in highly industrialized regions of China.The model accurately captures two regional severe pollution episodes observed in eastern China(January/June 2021).Sensitivity experiments highlight the critical roles of heterogeneous chemical mechanisms associated with sulfate,HONO chemistry,APIs,and CPIs in capturing PM_(2.5) and O_(3) concentrations in China.Improved sulfate mechanisms result in an increase of approximately 32.4%(2.8μg m^(−3))in simulated winter sulfate concentrations when observations exceed 10μg m^(−3).Enhanced HONO elevates winter O_(3) and PM_(2.5) by≤20 and≤10μg m^(−3),respectively.Overall,CPIs dominate over APIs in improving O_(3) and PM_(2.5) simulations across China.Locally,APIs mitigate PM_(2.5) and O_(3) discrepancies in the Sichuan Basin.Seasonal cloud–chemistry coupling explains the weaker impact of PM_(2.5) in summer.
文摘Model evaluation using benchmark datasets is an important method to measure the capability of large language models(LLMs)in specific domains,and it is mainly used to assess the knowledge and reasoning abilities of LLMs.Therefore,in order to better assess the capability of LLMs in the agricultural domain,Agri-Eval was proposed as a benchmark for assessing the knowledge and reasoning ability of LLMs in agriculture.The assessment dataset used in Agri-Eval covered seven major disciplines in the agricultural domain:crop science,horticulture,plant protection,animal husbandry,forest science,aquaculture science,and grass science,and contained a total of 2283 questions.Among domestic general-purpose LLMs,DeepSeek R1 performed best with an accuracy rate of 75.49%.In the realm of international general-purpose LLMs,Gemini 2.0 pro exp 0205 standed out as the top performer,achieving an accuracy rate of 74.28%.As an LLMs in agriculture vertical,Shennong V2.0 outperformed all the LLMs in China,and the answer accuracy rate of agricultural knowledge exceeded that of all the existing general-purpose LLMs.The launch of Agri-Eval helped the LLM developers to comprehensively evaluate the model's capability in the field of agriculture through a variety of tasks and tests to promote the development of the LLMs in the field of agriculture.
文摘We formulate an age-structured model based on a system of nonlinear partial differen- tial equations to assist the early and catch up female vaccination programs for human papillomavirus （HPV） types 6 and 11. Since these HPV types do not induce permanent immunity, the model, which stratifies the population based on age and gender, has a susceptible-infectious-susceptible （SIS） structure. We calculate the effective reproduction number Rv for the model and describe the local-asymptotic stability of the disease-free equilibrium using Rv. We prove the existence of an endemic equilibrium for Rv 〉 1 for the no vaccine case. However, analysis of the model for the vaccine case reveals that it undergoes the phenomenon of backward bifurcation. To support our theoretical results, we estimate the age and time solution with the given data for Toronto population, when an early and catch up female vaccine program is adopted, and when there is no vaccine. We show that early and catch up female vaccine program eliminates the infection in both male and female populations over a period of 30 years. Finally, we introduce the optimal control to an age-dependent model based on ordinary differential equations and solve it numerically to obtain the most cost-effective method for introducing the catch up vaccine into the population.
基金Supported by the National Natural Science Foundation of China(12261018)Universities Key Laboratory of Mathematical Modeling and Data Mining in Guizhou Province(2023013)。
文摘In this paper,we establish and study a single-species logistic model with impulsive age-selective harvesting.First,we prove the ultimate boundedness of the solutions of the system.Then,we obtain conditions for the asymptotic stability of the trivial solution and the positive periodic solution.Finally,numerical simulations are presented to validate our results.Our results show that age-selective harvesting is more conducive to sustainable population survival than non-age-selective harvesting.
文摘The proliferation of high-dimensional data and the widespread use of complex models present central challenges in contemporary statistics and data science.Dimension reduction and model checking,as two foundational pillars supporting scientific inference and data-driven decisionmaking,have evolved through the collective wisdom of generations of statisticians.This special issue,titled"Recent Developments in Dimension Reduction and Model Checking for regressions",not only aims to showcase cutting-edge advances in the field but also carries a distinct sense of academic homage to honor the groundbreaking and enduring contributions of Professor Lixing Zhu,a leading scholar whose work has profoundly shaped both areas.
文摘In their recent paper Pereira et al.(2025)claim that validation is overlooked in mapping and modelling of ecosystem services(ES).They state that“many studies lack critical evaluation of the results and no validation is provided”and that“the validation step is largely overlooked”.This assertion may have been true several years ago,for example,when Ochoa and Urbina-Cardona(2017)made a similar observation.However,there has been much work on ES model validation over the last decade.
文摘This paper presents an efficient model reduction technique for linear time-varying systems based on shifted Legendre polynomials.The approach constructs approximate low-rank decomposition factors of finite-time Gramians directly from the expansion coefficients of impulse responses.Leveraging these factors,we develop two model reduction algorithms that integrate the low-rank square root method with dominant subspace projection.Our method is computationally efficient and flexible,requiring only a few matrix-vector operations and a singular value decomposition of a low-dimensional matrix,thereby avoiding the need to solve differential Lyapunov equations.Numerical experiments confirm the effectiveness of the proposed approach.
基金the World Climate Research Programme(WCRP),Climate Variability and Predictability(CLIVAR),and Global Energy and Water Exchanges(GEWEX)for facilitating the coordination of African monsoon researchsupport from the Center for Earth System Modeling,Analysis,and Data at the Pennsylvania State Universitythe support of the Office of Science of the U.S.Department of Energy Biological and Environmental Research as part of the Regional&Global Model Analysis(RGMA)program area。
文摘In recent years,there has been an increasing need for climate information across diverse sectors of society.This demand has arisen from the necessity to adapt to and mitigate the impacts of climate variability and change.Likewise,this period has seen a significant increase in our understanding of the physical processes and mechanisms that drive precipitation and its variability across different regions of Africa.By leveraging a large volume of climate model outputs,numerous studies have investigated the model representation of African precipitation as well as underlying physical processes.These studies have assessed whether the physical processes are well depicted and whether the models are fit for informing mitigation and adaptation strategies.This paper provides a review of the progress in precipitation simulation overAfrica in state-of-the-science climate models and discusses the major issues and challenges that remain.
基金support from the National Key R&D Program of China(Grant No.2023YFB3709901)the National Natural Science Foundation of China(Grant No.U22A20171)+1 种基金China Baowu Low Carbon Metallurgy Innovation Foundation(Grant No.BWLCF202315)the High Steel Center(HSC)at North China University of Technology and University of Science and Technology Beijing,China.
文摘The dissolution of MgO-refractory into the slag had an obvious influence on the steel-slag reaction and the slag property,especially for high-aluminum steels.The dissolution behavior of MgO-refractory was investigated under various conditions,including the temperature,the initial steel composition,and the initial slag composition.A steel-slag-refractory kinetic model for high-aluminum steel was developed,which incorporated the process of MgO-refractory dissolution.The dependence of the MgO mass transfer coefficient k_(MgO)^(r)on temperature T during MgO-refractory dissolution process was established,as described by ln k_(MgO)^(r)=63,754/T+24.38524.It was indicated that the MgO dissolution rate was significantly influenced by the temperature.A higher temperature increased the dissolution rate of MgO.The initial steel composition had a slight impact on the MgO dissolution rate.Additionally,the initial slag composition strongly impacted the MgO saturation concentration and the dissolution rate.A lower initial Al_(2)O_(3)/SiO_(2)ratio increased the MgO dissolution rate.The steel-slag-refractory kinetic model accurately predicted the dissolution of MgO-refractory and the influence of dissolved MgO on the viscosity and composition change during steel-slag-refractory reactions.It was suggested that a higher temperature can hardly reduce the viscosity due to the dissolution of the MgO-refractory.
