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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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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. © 2024 Wei et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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| GB/T 7714 | Wei, F. , Zhou, R. , Jin, Z. et al. Studying the impacts of variant evolution for a generalized age-group transmission model [J]. | PLoS ONE , 2024 , 19 (7 July) . |
| MLA | Wei, F. et al. "Studying the impacts of variant evolution for a generalized age-group transmission model" . | PLoS ONE 19 . 7 July (2024) . |
| APA | Wei, F. , Zhou, R. , Jin, Z. , Sun, Y. , Peng, Z. , Cai, S. et al. Studying the impacts of variant evolution for a generalized age-group transmission model . | PLoS ONE , 2024 , 19 (7 July) . |
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Background: The structure of age groups and social contacts of the total population influenced infection scales and hospital-bed requirements, especially influenced severe infections and deaths during the global prevalence of COVID-19. Before the end of the year 2022, Chinese government implemented the national vaccination and had built the herd immunity cross the country, and announced Twenty Measures (November 11) and Ten New Measures (December 7) for further modifications of dynamic zero-COVID polity on the Chinese mainland. With the nation-wide vaccination and modified measures background, Fuzhou COVID-19 large wave (November 19, 2022–February 9, 2023) led by Omicron BA.5.2 variant was recorded and prevailed for three months in Fujian Province. Methods: A multi-age groups susceptible-exposed-infected-hospitalized-recovered (SEIHR) COVID-19 model with social contacts was proposed in this study. The main object was to evaluate the impacts of age groups and social contacts of the total population. The idea of Least Squares method was governed to perform the data fittings of four age groups against the surveillance data from Fujian Provincial Center for Disease Control and Prevention (Fujian CDC). The next generation matrix method was used to compute basic reproduction number for the total population and for the specific age group. The tendencies of effective reproduction number of four age groups were plotted by using the Epiestim R package and the SEIHR model for in-depth discussions. The sensitivity analysis by using sensitivity index and partial rank correlation coefficients values (PRCC values) were operated to reveal the differences of age groups against the main parameters. Results: The main epidemiological features such as basic reproduction number, effective reproduction number and sensitivity analysis were extensively discussed for multi-age groups SEIHR model in this study. Firstly, by using of the next generation matrix method, basic reproduction number R0 of the total population was estimated as 1.57 using parameter values of four age groups of Fuzhou COVID-19 large wave. Given age group k, the values of R0k (age group k to age group k), the values of R0k (an infected of age group k to the total population) and the values of R^0k (an infected of the total population to age group k) were also estimated, in which the explorations of the impacts of age groups revealed that the relationship R0k>R0k>R^0k was valid. Then, the fluctuating tendencies of effective reproduction number Rt were demonstrated by using two approaches (the surveillance data and the SEIHR model) for Fuzhou COVID-19 large wave, during which high-risk group (G4 group) mainly contributed the infection scale due to high susceptibility to infection and high risks to basic diseases. Further, the sensitivity analysis using two approaches (the sensitivity index and the PRCC values) revealed that susceptibility to infection of age groups played the vital roles, while the numerical simulation showed that infection scale varied with the changes of social contacts of age groups. The results of this study claimed that the high-risk group out of the total population was concerned by the local government with the highest susceptibility to infection against COVID-19. Conclusions: This study verified that the partition structure of age groups of the total population, the susceptibility to infection of age groups, the social contacts among age groups were the important contributors of infection scale. The less social contacts and adequate hospital beds for high-risk group were profitable to control the spread of COVID-19. To avoid the emergence of medical runs against new variant in the future, the policymakers from local government were suggested to decline social contacts when hospital beds were limited. © 2024 The Authors
Keyword ：
Age group Age group Contact matrix Contact matrix COVID-19 model COVID-19 model Omicron BA.5.2 variant Omicron BA.5.2 variant Social contact Social contact
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| GB/T 7714 | Lan, X. , Chen, G. , Zhou, R. et al. An SEIHR model with age group and social contact for analysis of Fuzhou COVID-19 large wave [J]. | Infectious Disease Modelling , 2024 , 9 (3) : 728-743 . |
| MLA | Lan, X. et al. "An SEIHR model with age group and social contact for analysis of Fuzhou COVID-19 large wave" . | Infectious Disease Modelling 9 . 3 (2024) : 728-743 . |
| APA | Lan, X. , Chen, G. , Zhou, R. , Zheng, K. , Cai, S. , Wei, F. et al. An SEIHR model with age group and social contact for analysis of Fuzhou COVID-19 large wave . | Infectious Disease Modelling , 2024 , 9 (3) , 728-743 . |
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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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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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A vector-host model of dengue with multiple stages and independent fluctuations is investigated in this paper. Firstly, the existence and uniqueness of the positive solution are shown by contradiction. When the death rates of aquatic mosquitoes, adult mosquitoes, and human beings respectively control the intensities of white noises, and if R-0(s)>1, then the persistence in the mean for both infective mosquitoes and infective human beings is derived. When R-0(s)>1 is valid, the existence of stationary distribution is derived through constructing several appropriate Lyapunov functions. If the intensities of white noises are controlled and phi<0 is valid, then the extinction for both infective mosquitoes and infective human beings is obtained by applying the comparison theorem and ergodic theorem. Further, the main findings are verified through numerical simulations by using the positive preserving truncated Euler-Maruyama method (PPTEM). Moreover, several numerical simulations on the infection scale of dengue in Fuzhou City were conducted using surveillance data. The main results indicate that the decrease in the transfer proportion from aquatic mosquitoes to adult mosquitoes reduces the infection scale of infective human beings with dengue virus, and the death rates of aquatic mosquitoes and adult mosquitoes affect the value of the critical threshold R0s. Further, the controls of the death rates of mosquitoes are the effective routes by the decision-makers of the Chinese mainland against the spread of dengue.
Keyword ：
dengue dengue multi stage multi stage persistence and extinction persistence and extinction PPTEM method PPTEM method stationary distribution stationary distribution stochastic vector-host model stochastic vector-host model
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| GB/T 7714 | Wang, Zuwen , Cai, Shaojian , Chen, Guangmin et al. Dynamics of a Dengue Transmission Model with Multiple Stages and Fluctuations [J]. | MATHEMATICS , 2024 , 12 (16) . |
| MLA | Wang, Zuwen et al. "Dynamics of a Dengue Transmission Model with Multiple Stages and Fluctuations" . | MATHEMATICS 12 . 16 (2024) . |
| APA | Wang, Zuwen , Cai, Shaojian , Chen, Guangmin , Zheng, Kuicheng , Wei, Fengying , Jin, Zhen et al. Dynamics of a Dengue Transmission Model with Multiple Stages and Fluctuations . | MATHEMATICS , 2024 , 12 (16) . |
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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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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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The complex interactions were performed among non-pharmaceutical interventions, vaccinations, and hosts for all epidemics in mainland China during the spread of COVID-19. Specially, the small-scale epidemic in the city described by SVEIR model was less found in the current studies. The SVEIR model with control was established to analyze the dynamical and epidemiological features of two epidemics in Jinzhou City led by Omicron variants before and after Twenty Measures. In this study, the total population (N) of Jinzhou City was divided into five compartments: the susceptible (S), the vaccinated (V), the exposed (E), the infected (I), and the recovered (R). By surveillance data and the SVEIR model, three methods (maximum likelihood method, exponential growth rate method, next generation matrix method) were governed to estimate basic reproduction number, and the results showed that an increasing tendency of basic reproduction number from Omicron BA.5.2 to Omicron BA.2.12.1. Meanwhile, the effective reproduction number for two epidemics were investigated by surveillance data, and the results showed that Jinzhou wave 1 reached the peak on November 1 and was controlled 7 days later, and that Jinzhou wave 2 reached the peak on November 28 and was controlled 5 days later. Moreover, the impacts of non-pharmaceutical interventions (awareness delay, peak delay, control intensity) were discussed extensively, the variations of infection scales for Omicron variant and EG.5 variant were also discussed. Furthermore, the investigations on peaks and infection scales for two epidemics in dynamic zero-COVID policy were operated by the SVEIR model with control. The investigations on public medical requirements of Jinzhou City and Liaoning Province were analyzed by using SVEIR model without control, which provided a possible perspective on variant evolution in the future. (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 (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keyword ：
Control strategy Control strategy COVID-19 COVID-19 SVEIR model SVEIR model Twenty measures Twenty measures Variant evolution Variant evolution
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| GB/T 7714 | Chen, Kaijing , Wei, Fengying , Zhang, Xinyan et al. Epidemiological feature analysis of SVEIR model with control strategy and variant evolution [J]. | INFECTIOUS DISEASE MODELLING , 2024 , 9 (3) : 689-700 . |
| MLA | Chen, Kaijing et al. "Epidemiological feature analysis of SVEIR model with control strategy and variant evolution" . | INFECTIOUS DISEASE MODELLING 9 . 3 (2024) : 689-700 . |
| APA | Chen, Kaijing , Wei, Fengying , Zhang, Xinyan , Jin, Hao , Wang, Zuwen , Zuo, Yue et al. Epidemiological feature analysis of SVEIR model with control strategy and variant evolution . | INFECTIOUS DISEASE MODELLING , 2024 , 9 (3) , 689-700 . |
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