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学者姓名：魏凤英
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Abstract ：
本文研究具有两个年龄分组的随机传染病模型的动力学问题.该模型将人群分为易感者(S)、潜伏者(E)、感染者(I)、住院者(H)和康复者(R),并假设两个年龄组之间的衰老率为常数.首先,证明了模型全局正解的存在性和唯一性.然后,利用李雅普诺夫函数以及高维Itô公式,得到了潜伏个体和感染个体随机绝灭和随机持久的充分条件,并证明了随机绝灭指标与随机持久指标均小于基本再生数.同时,本研究的主要结果被推广至多年龄组模型.此外,利用福建省疾病预防控制中心提供的监测数据,对福州新冠疫情进行数值模拟.研究结果表明,年龄分组对研究疾病传播有着重要作用.
Keyword ：
传染病模型 传染病模型 年龄分组 年龄分组 持久性 持久性 绝灭性 绝灭性
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| GB/T 7714 | 蓝晓敏 , 陈光敏 , 周锐阳 et al. 具有年龄分组的随机传染病模型的动力学 [J]. | 应用数学 , 2025 , 38 (1) : 294-307 . |
| MLA | 蓝晓敏 et al. "具有年龄分组的随机传染病模型的动力学" . | 应用数学 38 . 1 (2025) : 294-307 . |
| APA | 蓝晓敏 , 陈光敏 , 周锐阳 , 郑奎城 , 蔡少健 , 魏凤英 et al. 具有年龄分组的随机传染病模型的动力学 . | 应用数学 , 2025 , 38 (1) , 294-307 . |
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The innate immunity helps the individuals in the exposed compartment return into the ones in the susceptible compartment when a pathogen or virus invades the local population of having four compartments: the susceptible, the exposed, the infected and the recovered. In this study, we propose a stochastic SEIR model with innate immunity and treatment. Here, Holling type II functional responses are used to describe the saturated effects of the innate immunity and treatment. Then, we obtain the extinction of the exposed and the infected when the basic reproduction number R-0 < 1 and the exponential decline rate nu < 0 are valid. Moreover, we conclude that when innate immunity and treatment increase, the time that the exposed and the infected approach zero reduces. We also find that the deterministic SEIR model reaches extinction a bit faster than the stochastic SEIR model. Further, the persistence in the mean and stationary distribution of stochastic SEIR model are obtained under suitable conditions. Finally, the numerical investigations with two methods and a case study of Fuzhou COVID-19 epidemic of 2022 are discussed.
Keyword ：
COVID-19 COVID-19 extinction and persistence extinction and persistence Holling type II functional response Holling type II functional response innate immunity innate immunity SEIR epidemic model SEIR epidemic model
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| GB/T 7714 | Chen, Lijun , Li, Wenshuang , Zhou, Ruiyang et al. STOCHASTIC SURVIVAL ANALYSIS OF AN EPIDEMIC MODEL WITH INNATE IMMUNITY AND TREATMENT [J]. | JOURNAL OF APPLIED ANALYSIS AND COMPUTATION , 2025 , 15 (4) : 1862-1881 . |
| MLA | Chen, Lijun et al. "STOCHASTIC SURVIVAL ANALYSIS OF AN EPIDEMIC MODEL WITH INNATE IMMUNITY AND TREATMENT" . | JOURNAL OF APPLIED ANALYSIS AND COMPUTATION 15 . 4 (2025) : 1862-1881 . |
| APA | Chen, Lijun , Li, Wenshuang , Zhou, Ruiyang , Wei, Fengying . STOCHASTIC SURVIVAL ANALYSIS OF AN EPIDEMIC MODEL WITH INNATE IMMUNITY AND TREATMENT . | JOURNAL OF APPLIED ANALYSIS AND COMPUTATION , 2025 , 15 (4) , 1862-1881 . |
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As of May 2024, the main strains of COVID-19 caused hundreds of millions of infection cases and millions of deaths worldwide. In this study, we consider the COVID-19 epidemics with the main strains in the Chinese mainland. We study complex interactions among hosts, non-pharmaceutical interventions, and vaccinations for the main strains by a differential equation model called SVEIR. The disease transmission model incorporates two strains and protection awareness of the susceptible population. Results of this study show that the protection awareness plays a crucial role against infection of the population, and that the vaccines are effective against the circulation of the earlier strains, but ineffective for emerging strains. By using the next generation matrix method, the basic reproduction number of the SVEIR model is firstly obtained. Our analysis by Hurwitz criterion and LaSalle's invariance principle shows that the disease free-equilibrium point is locally and globally asymptotically stable when the threshold value is below one. The existences of endemic equilibrium points are also established, and the global asymptotic stabilities are analyzed using the Lyapunov function method. Further, the SVEIR model is confirmed to satisfy the principle of competitive exclusion, of which the strain with the larger value of the basic reproduction number is dominant. Numerically, the surveillance data with the Omicron strain and the XBB strain are split by the cubic spline interpolation method. The fitting curves against the surveillance data are plotted using the least-squares method from MATLAB. The results indicate that the XBB strain dominates in this study. Moreover, a global sensitivity analysis of the key parameters is performed by using of PRCC. The numerical simulations imply that combination control strategy positively impacts on the infection scale than what separate control strategy does, and that the earlier time producing protection awareness for the public creates less infection scale, further that the increment of protection awareness also reduces the infection scale. Therefore, the policymakers of the local government are suggested to concern the changes of protection awareness of the public. (c) 2024 The Authors. Publishing services by Elsevier B.V. on behalf of KeAi Communications Co. Ltd. This is an open access article under the CC BY-NC-ND license
Keyword ：
Competitive exclusion Competitive exclusion Protection awareness Protection awareness Stability Stability SVEIR transmission model SVEIR transmission model Two trains Two trains
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| GB/T 7714 | Chen, Kaijing , Wei, Fengying , Zhang, Xinyan et al. Dynamics of an SVEIR transmission model with protection awareness and two strains [J]. | INFECTIOUS DISEASE MODELLING , 2025 , 10 (1) : 207-228 . |
| MLA | Chen, Kaijing et al. "Dynamics of an SVEIR transmission model with protection awareness and two strains" . | INFECTIOUS DISEASE MODELLING 10 . 1 (2025) : 207-228 . |
| APA | Chen, Kaijing , Wei, Fengying , Zhang, Xinyan , Jin, Hao , Zhou, Ruiyang , Zuo, Yue et al. Dynamics of an SVEIR transmission model with protection awareness and two strains . | INFECTIOUS DISEASE MODELLING , 2025 , 10 (1) , 207-228 . |
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The epidemiological characteristics and distributions of two epidemics in Fujian Province of Southeast China were attributed to the complex interactions among variant, host, and non-pharmaceutical interventions (NPIs). All reported cases in the Putian epidemic (September 8–October 2, 2021, Delta variant B.1.617.2) and Fuzhou epidemic (October 22–November 18, 2022, Omicron variant BA.5.2) were classified by sex, age group, occupation, and location in this study. Using surveillance data from the Fujian Provincial Center for Disease Control and Prevention, we established a virus-oriented SVEIR (Susceptible–Vaccinated–Exposed–Infected–Recovered) model to investigate the dynamic evolution features of these two variants and the effects of NPIs. The optimal simulations were carried out with variants and scenario investigations. The scenario investigations showed that NPIs significantly reduced the transmission risk and infection scales of COVID-19, and that the Omicron variant was more infectious than the Delta variant. Moreover, the dynamic investigations revealed the increasing tendencies from Delta to Omicron, such as the basic reproduction number, infection rate, percentage of high-risk cases, and the growth rate. Decreasing tendencies were also identified, such as the average recovery period, the awareness delay, and the percentage of symptomatic cases. This study highlighted that NPIs played critical roles in successfully containing the two epidemics. Such interventions are strongly recommended to public health policymakers. © 2024
Keyword ：
COVID-19 COVID-19 Delta variant Delta variant Non-pharmaceutical interventions Non-pharmaceutical interventions Omicron variant Omicron variant SVEIR model SVEIR model Transmission dynamics Transmission dynamics
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| GB/T 7714 | Zhou, R. , Cai, S. , Chen, G. et al. Dynamic evolution of an SVEIR model with variants and non-pharmaceutical interventions for controlling COVID-19 [J]. | Journal of Biosafety and Biosecurity , 2024 , 6 (2) : 67-75 . |
| MLA | Zhou, R. et al. "Dynamic evolution of an SVEIR model with variants and non-pharmaceutical interventions for controlling COVID-19" . | Journal of Biosafety and Biosecurity 6 . 2 (2024) : 67-75 . |
| APA | Zhou, R. , Cai, S. , Chen, G. , Huang, S. , Jin, Z. , Peng, Z. et al. Dynamic evolution of an SVEIR model with variants and non-pharmaceutical interventions for controlling COVID-19 . | Journal of Biosafety and Biosecurity , 2024 , 6 (2) , 67-75 . |
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The estimation methods of reproduction numbers and serial intervals are important in the early stages of infectious diseases. During the COVID pandemic, China implemented a dynamic zero-COVID policy on the Chinese mainland until the end of 2022. This study compares three estimation methods of basic reproduction numbers on small-scale, short-duration COVID-19 epidemics in Fujian Province. Basic reproduction numbers were investigated using a varying-strain model via a next-generation matrix method. Serial intervals were derived using the infector–infectee pairs of two epidemics from the Fujian Provincial Center for Disease Control and Prevention. Basic reproduction numbers were estimated using the maximum likelihood estimation method and the exponential growth method. The curves of the effective reproduction numbers of the three epidemics were plotted by utilizing daily cases and the EpiEstim R package. The spatial heterogeneity of infection cases was described using the Gini coefficient. This study provides significant insights on the estimation methods of reproduction numbers for policymakers in the local government. The results reveal that social contacts between infectors and susceptible individuals should be reduced to avoid an increase in deaths and to fight against the spread of infectious diseases. © 2024
Keyword ：
COVID-19 COVID-19 Estimation method Estimation method Gini coefficient Gini coefficient Reproduction number Reproduction number Serial interval Serial interval
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| GB/T 7714 | Xiong, S. , Cai, S. , Wei, F. et al. Estimation methods of reproduction numbers for epidemics of varying strains of COVID-19 [J]. | Journal of Biosafety and Biosecurity , 2024 , 6 (4) : 265-270 . |
| MLA | Xiong, S. et al. "Estimation methods of reproduction numbers for epidemics of varying strains of COVID-19" . | Journal of Biosafety and Biosecurity 6 . 4 (2024) : 265-270 . |
| APA | Xiong, S. , Cai, S. , Wei, F. , Chen, G. , Zheng, K. , Xie, J. . Estimation methods of reproduction numbers for epidemics of varying strains of COVID-19 . | Journal of Biosafety and Biosecurity , 2024 , 6 (4) , 265-270 . |
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In this study, we proposed two, symptom-dependent, HIV/AIDS models to investigate the dynamical properties of HIV/AIDS in the Fujian Province. The basic reproduction number was obtained, and the local and global stabilities of the disease-free and endemic equilibrium points were verified to the deterministic HIV/AIDS model. Moreover, the indicators R0s and Re0 were derived for the stochastic HIV/AIDS model, and the conditions for stationary distribution and stochastic extinction were investigated. By using the surveillance data from the Fujian Provincial Center for Disease Control and Prevention, some numerical simulations and future predictions on the scale of HIV/AIDS infections in the Fujian Province were conducted. © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License.
Keyword ：
Cell proliferation Cell proliferation Disease control Disease control Diseases Diseases Stochastic models Stochastic models Stochastic systems Stochastic systems Transmissions Transmissions
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| GB/T 7714 | Li, Wenshuang , Cai, Shaojian , Zhai, Xuanpei et al. Transmission dynamics of symptom-dependent HIV/AIDS models [J]. | Mathematical Biosciences and Engineering , 2024 , 21 (2) : 1819-1843 . |
| MLA | Li, Wenshuang et al. "Transmission dynamics of symptom-dependent HIV/AIDS models" . | Mathematical Biosciences and Engineering 21 . 2 (2024) : 1819-1843 . |
| APA | Li, Wenshuang , Cai, Shaojian , Zhai, Xuanpei , Ou, Jianming , Zheng, Kuicheng , Wei, Fengying et al. Transmission dynamics of symptom-dependent HIV/AIDS models . | Mathematical Biosciences and Engineering , 2024 , 21 (2) , 1819-1843 . |
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This work develops a novel approximation for a class of superlinear stochastic Kol-mogorov equations with positive global solutions. On the one hand, most existing explicit methods that work for the superlinear stochastic differential equations (SDEs), e.g. various modified Euler-Maruyama (EM) methods, fail to preserve positivity of the solution. On the other hand, methods that preserve positivity are mostly implicit, or fail to cope with the multi-dimensional scenario. This work aims to construct an advanced numerical method which is not only naturally structure preserving but also cost effective. A strong convergence framework is then developed with an almost optimal convergence rate of order arbitrarily close to 1/2. To make the arguments concise, we elaborate our theory with the generalised stochastic Lotka-Volterra model, though the method is applicable to a wide bunch of multi-dimensional superlinear stochastic Kolmogorov systems in various fields including finance and epidemiology.& COPY; 2023 Published by Elsevier B.V.
Keyword ：
Convergence rate Convergence rate Exponential Euler-Maruyama method Exponential Euler-Maruyama method Kolmogorov equation Kolmogorov equation Stochastic differential equation Stochastic differential equation Structure preserving numerical method Structure preserving numerical method
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| GB/T 7714 | Cai, Yongmei , Mao, Xuerong , Wei, Fengying . An advanced numerical scheme for multi-dimensional stochastic Kolmogorov equations with superlinear coefficients [J]. | JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS , 2024 , 437 . |
| MLA | Cai, Yongmei et al. "An advanced numerical scheme for multi-dimensional stochastic Kolmogorov equations with superlinear coefficients" . | JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 437 (2024) . |
| APA | Cai, Yongmei , Mao, Xuerong , Wei, Fengying . An advanced numerical scheme for multi-dimensional stochastic Kolmogorov equations with superlinear coefficients . | JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS , 2024 , 437 . |
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The differences of SARS-CoV-2 variants brought the changes of transmission characteristics and clinical manifestations during the prevalence of COVID-19. In order to explore the evolution mechanisms of SARS-CoV-2 variants and the impacts of variant evolution, the classic SIR (Susceptible-Infected-Recovered) compartment model was modified to a generalized SVEIR (Susceptible-Vaccinated-Exposed-Infected-Recovered) compartment model with age-group and varying variants in this study. By using of the SVEIR model and least squares method, the optimal fittings against the surveillance data from Fujian Provincial Center for Disease Control and Prevention were performed for the five epidemics of Fujian Province. The main epidemiological characteristics such as basic reproduction number, effective reproduction number, sensitivity analysis, and cross-variant scenario investigations were extensively investigated during dynamic zero-COVID policy. The study results showed that the infectivities of the variants became fast from wild strain to the Delta variant, further to the Omicron variant. Meanwhile, the cross-variant investigations showed that the average incubation periods were shortened, and that the infection scales quickly enhanced. Further, the risk estimations with the new variants were performed without implements of the non-pharmaceutical interventions, based on the dominant variants XBB.1.9.1 and EG.5. The results of the risk estimations suggested that non-pharmaceutical interventions were necessary on the Chinese mainland for controlling severe infections and deaths, and also that the regular variant monitors were still workable against the aggressive variant evolution and the emergency of new transmission risks in the future.
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| GB/T 7714 | Wei, Fengying , Zhou, Ruiyang , Jin, Zhen et al. Studying the impacts of variant evolution for a generalized age-group transmission model [J]. | PLOS ONE , 2024 , 19 (7) . |
| MLA | Wei, Fengying et al. "Studying the impacts of variant evolution for a generalized age-group transmission model" . | PLOS ONE 19 . 7 (2024) . |
| APA | Wei, Fengying , Zhou, Ruiyang , Jin, Zhen , Sun, Yamin , Peng, Zhihang , Cai, Shaojian et al. Studying the impacts of variant evolution for a generalized age-group transmission model . | PLOS ONE , 2024 , 19 (7) . |
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We propose single-species population models with the psychological effects and time delay in a toxicant environment in this study, of which the concentrations of toxicant nonlinearly affect the density of adults, linearly affect the density of juveniles. The models, consisting of a system of stochastic differential equations, govern the dynamics of juveniles and adults, as well as the concentrations of toxicant in the environment and organisms. First of all, the existence and uniqueness of the global solution to the models are derived, the sufficient conditions of the extinction and the time that the densities of adults and juveniles approach zero are investigated. Further, the sufficient conditions for the weak persistence in the mean are obtained around the pollution-free equilibrium point, and the stochastic permanence of adults and juveniles occurs around the pollution equilibrium points under moderate conditions. As a consequence, the corresponding numerical simulations reveal that higher psychological effects and less time delay create larger densities of juveniles and adults in the sense of weak persistence and stochastic permanence, and that less fluctuations of white noises and less psychological effects produce the earlier extinction time for adults and juveniles.
Keyword ：
psychological effects psychological effects Single-species population model Single-species population model stochastic permanence stochastic permanence time delay time delay toxicant environment toxicant environment weak persistence in the mean weak persistence in the mean
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| GB/T 7714 | Mo, Rongli , Wu, Xingmin , Wei, Fengying . Population-toxicant models with stage structure and the psychological effects [J]. | INTERNATIONAL JOURNAL OF BIOMATHEMATICS , 2024 . |
| MLA | Mo, Rongli et al. "Population-toxicant models with stage structure and the psychological effects" . | INTERNATIONAL JOURNAL OF BIOMATHEMATICS (2024) . |
| APA | Mo, Rongli , Wu, Xingmin , Wei, Fengying . Population-toxicant models with stage structure and the psychological effects . | INTERNATIONAL JOURNAL OF BIOMATHEMATICS , 2024 . |
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This paper proposes the symptom-based SEMIR compartmental model with age groups and fluctuations from the perspective of the managers of the local government. The basic reproduction number of the total population is given by the next generation matrix method, the group-based basic reproduction number are then followed. The unique global positive solution is derived by using the Lyapunov function. Furthermore, the sufficient conditions of the stochastic extinction and the stochastic persistence of the SEMIR model are studied. When Fuzhou COVID-19 epidemic is chosen from the surveillance data for the further numerical investigation, the data fittings of the SEMIR model reveal that age groups are profitable to control the infection scale of intensive cases, and that the susceptibility to infection of age groups are higher than those within the total population. Alternatively, the scenario investigations show that the prompt treatments are conducive to the reduction of infection scale for intensive cases.
Keyword ：
Age groups Age groups Basic reproduction number Basic reproduction number Persistence and extinction Persistence and extinction Stochastic epidemic model Stochastic epidemic model Symptom Symptom
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| GB/T 7714 | Chen, Shijing , Lan, Xiaomin , Chen, Guangmin et al. Dynamical analysis on symptom-based SEMIR compartmental model with age groups [J]. | JOURNAL OF APPLIED MATHEMATICS AND COMPUTING , 2024 , 71 (2) : 1459-1484 . |
| MLA | Chen, Shijing et al. "Dynamical analysis on symptom-based SEMIR compartmental model with age groups" . | JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 71 . 2 (2024) : 1459-1484 . |
| APA | Chen, Shijing , Lan, Xiaomin , Chen, Guangmin , Zheng, Kuicheng , Cai, Shaojian , Wei, Fengying et al. Dynamical analysis on symptom-based SEMIR compartmental model with age groups . | JOURNAL OF APPLIED MATHEMATICS AND COMPUTING , 2024 , 71 (2) , 1459-1484 . |
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