{"title":"鸟类西尼罗病毒动态的随机流行模型中疾病灭绝或爆发的概率","authors":"Milliward Maliyoni","doi":"10.1007/s10441-020-09391-y","DOIUrl":null,"url":null,"abstract":"<div><p>Thresholds for disease extinction provide essential information for the prevention and control of diseases. In this paper, a stochastic epidemic model, a continuous-time Markov chain, for the transmission dynamics of West Nile virus in birds is developed based on the assumptions of its analogous deterministic model. The branching process is applied to derive the extinction threshold for the stochastic model and conditions for disease extinction or persistence. The probability of disease extinction computed from the branching process is shown to be in good agreement with the probability approximated from numerical simulations. The disease dynamics of both models are compared to ascertain the effect of demographic stochasticity on West Nile virus dynamics. Analytical and numerical results show differences in model predictions and asymptotic dynamics between stochastic and deterministic models that are crucial for the prevention of disease outbreaks. It is found that there is a high probability of disease extinction if the disease emerges from exposed mosquitoes unlike if it emerges from infectious mosquitoes and birds. Finite-time to disease extinction is estimated using sample paths and it is shown that the epidemic duration is shortest if the disease is introduced by exposed mosquitoes.</p></div>","PeriodicalId":7057,"journal":{"name":"Acta Biotheoretica","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2020-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s10441-020-09391-y","citationCount":"15","resultStr":"{\"title\":\"Probability of Disease Extinction or Outbreak in a Stochastic Epidemic Model for West Nile Virus Dynamics in Birds\",\"authors\":\"Milliward Maliyoni\",\"doi\":\"10.1007/s10441-020-09391-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Thresholds for disease extinction provide essential information for the prevention and control of diseases. In this paper, a stochastic epidemic model, a continuous-time Markov chain, for the transmission dynamics of West Nile virus in birds is developed based on the assumptions of its analogous deterministic model. The branching process is applied to derive the extinction threshold for the stochastic model and conditions for disease extinction or persistence. The probability of disease extinction computed from the branching process is shown to be in good agreement with the probability approximated from numerical simulations. The disease dynamics of both models are compared to ascertain the effect of demographic stochasticity on West Nile virus dynamics. Analytical and numerical results show differences in model predictions and asymptotic dynamics between stochastic and deterministic models that are crucial for the prevention of disease outbreaks. It is found that there is a high probability of disease extinction if the disease emerges from exposed mosquitoes unlike if it emerges from infectious mosquitoes and birds. Finite-time to disease extinction is estimated using sample paths and it is shown that the epidemic duration is shortest if the disease is introduced by exposed mosquitoes.</p></div>\",\"PeriodicalId\":7057,\"journal\":{\"name\":\"Acta Biotheoretica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2020-09-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s10441-020-09391-y\",\"citationCount\":\"15\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Biotheoretica\",\"FirstCategoryId\":\"99\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10441-020-09391-y\",\"RegionNum\":4,\"RegionCategory\":\"生物学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICAL & COMPUTATIONAL BIOLOGY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Biotheoretica","FirstCategoryId":"99","ListUrlMain":"https://link.springer.com/article/10.1007/s10441-020-09391-y","RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICAL & COMPUTATIONAL BIOLOGY","Score":null,"Total":0}
Probability of Disease Extinction or Outbreak in a Stochastic Epidemic Model for West Nile Virus Dynamics in Birds
Thresholds for disease extinction provide essential information for the prevention and control of diseases. In this paper, a stochastic epidemic model, a continuous-time Markov chain, for the transmission dynamics of West Nile virus in birds is developed based on the assumptions of its analogous deterministic model. The branching process is applied to derive the extinction threshold for the stochastic model and conditions for disease extinction or persistence. The probability of disease extinction computed from the branching process is shown to be in good agreement with the probability approximated from numerical simulations. The disease dynamics of both models are compared to ascertain the effect of demographic stochasticity on West Nile virus dynamics. Analytical and numerical results show differences in model predictions and asymptotic dynamics between stochastic and deterministic models that are crucial for the prevention of disease outbreaks. It is found that there is a high probability of disease extinction if the disease emerges from exposed mosquitoes unlike if it emerges from infectious mosquitoes and birds. Finite-time to disease extinction is estimated using sample paths and it is shown that the epidemic duration is shortest if the disease is introduced by exposed mosquitoes.
期刊介绍:
Acta Biotheoretica is devoted to the promotion of theoretical biology, encompassing mathematical biology and the philosophy of biology, paying special attention to the methodology of formation of biological theory.
Papers on all kind of biological theories are welcome. Interesting subjects include philosophy of biology, biomathematics, computational biology, genetics, ecology and morphology. The process of theory formation can be presented in verbal or mathematical form. Moreover, purely methodological papers can be devoted to the historical origins of the philosophy underlying biological theories and concepts.
Papers should contain clear statements of biological assumptions, and where applicable, a justification of their translation into mathematical form and a detailed discussion of the mathematical treatment. The connection to empirical data should be clarified.
Acta Biotheoretica also welcomes critical book reviews, short comments on previous papers and short notes directing attention to interesting new theoretical ideas.