{"title":"带有半马尔可夫转换和扩散的随机布鲁氏菌病模型的稳定性。","authors":"Feng Chen, Jing Hu, Yuming Chen, Qimin Zhang","doi":"10.1007/s00285-024-02139-z","DOIUrl":null,"url":null,"abstract":"<p><p>To explore the influence of state changes on brucellosis, a stochastic brucellosis model with semi-Markovian switchings and diffusion is proposed in this paper. When there is no switching, we introduce a critical value <math><msup><mi>R</mi> <mi>s</mi></msup> </math> and obtain the exponential stability in mean square when <math> <mrow><msup><mi>R</mi> <mi>s</mi></msup> <mo><</mo> <mn>1</mn></mrow> </math> by using the stochastic Lyapunov function method. Sudden climate changes can drive changes in transmission rate of brucellosis, which can be modelled by a semi-Markov process. We study the influence of stationary distribution of semi-Markov process on extinction of brucellosis in switching environment including both stable states, during which brucellosis dies out, and unstable states, during which brucellosis persists. The results show that increasing the frequencies and average dwell times in stable states to certain extent can ensure the extinction of brucellosis. Finally, numerical simulations are given to illustrate the analytical results. We also suggest that herdsmen should reduce the densities of animal habitation to decrease the contact rate, increase slaughter rate of animals and apply disinfection measures to kill brucella.</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stability of a stochastic brucellosis model with semi-Markovian switching and diffusion.\",\"authors\":\"Feng Chen, Jing Hu, Yuming Chen, Qimin Zhang\",\"doi\":\"10.1007/s00285-024-02139-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>To explore the influence of state changes on brucellosis, a stochastic brucellosis model with semi-Markovian switchings and diffusion is proposed in this paper. When there is no switching, we introduce a critical value <math><msup><mi>R</mi> <mi>s</mi></msup> </math> and obtain the exponential stability in mean square when <math> <mrow><msup><mi>R</mi> <mi>s</mi></msup> <mo><</mo> <mn>1</mn></mrow> </math> by using the stochastic Lyapunov function method. Sudden climate changes can drive changes in transmission rate of brucellosis, which can be modelled by a semi-Markov process. We study the influence of stationary distribution of semi-Markov process on extinction of brucellosis in switching environment including both stable states, during which brucellosis dies out, and unstable states, during which brucellosis persists. The results show that increasing the frequencies and average dwell times in stable states to certain extent can ensure the extinction of brucellosis. Finally, numerical simulations are given to illustrate the analytical results. We also suggest that herdsmen should reduce the densities of animal habitation to decrease the contact rate, increase slaughter rate of animals and apply disinfection measures to kill brucella.</p>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-09-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00285-024-02139-z\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00285-024-02139-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
摘要
为了探讨状态变化对布鲁氏菌病的影响,本文提出了一种具有半马尔可夫切换和扩散的随机布鲁氏菌病模型。当不存在切换时,我们引入临界值 R s,并利用随机 Lyapunov 函数方法得到 R s 1 时均方的指数稳定性。气候突变会导致布鲁氏菌病的传播率发生变化,这可以用半马尔可夫过程来模拟。我们研究了半马尔可夫过程的静态分布对布鲁氏菌病在切换环境中灭绝的影响,包括布鲁氏菌病消亡的稳定状态和布鲁氏菌病持续存在的不稳定状态。结果表明,在一定程度上增加稳定状态的频率和平均停留时间可以确保布鲁氏菌病的消亡。最后,我们给出了数值模拟来说明分析结果。我们还建议牧民减少动物居住密度以降低接触率,提高动物屠宰率,并采取消毒措施杀灭布鲁氏菌。
Stability of a stochastic brucellosis model with semi-Markovian switching and diffusion.
To explore the influence of state changes on brucellosis, a stochastic brucellosis model with semi-Markovian switchings and diffusion is proposed in this paper. When there is no switching, we introduce a critical value and obtain the exponential stability in mean square when by using the stochastic Lyapunov function method. Sudden climate changes can drive changes in transmission rate of brucellosis, which can be modelled by a semi-Markov process. We study the influence of stationary distribution of semi-Markov process on extinction of brucellosis in switching environment including both stable states, during which brucellosis dies out, and unstable states, during which brucellosis persists. The results show that increasing the frequencies and average dwell times in stable states to certain extent can ensure the extinction of brucellosis. Finally, numerical simulations are given to illustrate the analytical results. We also suggest that herdsmen should reduce the densities of animal habitation to decrease the contact rate, increase slaughter rate of animals and apply disinfection measures to kill brucella.