关于流行病的持续时间。

IF 0.8 Q3 MATHEMATICS, APPLIED

Differential Equations and Dynamical Systems Pub Date : 2022-12-28 DOI:10.1007/s12591-022-00626-7

Mario Lefebvre

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引用次数: 0

摘要

本文考虑了一种非致命疾病传播的随机 SIR（易感、感染、恢复）模型。种群的规模是恒定的。在特殊情况下，计算随机时间的时刻生成函数，直到种群中的所有成员都康复，这个问题就迎刃而解了。此外，还计算了流行病的预期持续时间，以及在每个成员都被感染之前，整个人群被治愈或免疫的概率。根据适当的边界条件，采用相似解法求解各种科尔莫哥罗夫偏微分方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the Duration of an Epidemic.

A stochastic SIR (Susceptible, Infected, Recovered) model for the spread of a non-lethal disease is considered. The size of the population is constant. The problem of computing the moment-generating function of the random time until all members of the population are recovered is solved in special cases. The expected duration of the epidemic is also computed, as well as the probability that the whole population will be either cured or immunized before every member is infected. The method of similarity solutions is used to solve the various Kolmogorov partial differential equations, subject to the appropriate boundary conditions.

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来源期刊

Differential Equations and Dynamical Systems MATHEMATICS, APPLIED-

CiteScore

3.00

自引率

0.00%

发文量

期刊介绍： Aims and Scope Differential Equations and Dynamical Systems is a multidisciplinary journal whose aim is to publish high quality original research papers in Ordinary and Partial Differential Equations, Integral and Integro-Differential Equations, Calculus of Variations, Bifurcation Theory and Dynamical Systems Theory. Articles devoted to the application of methods and techniques from the above fields of Analysis to Neural Networks, Control Theory; Physical, Biological, Medical, Social and Engineering Sciences are also welcome.In particular, for studies related to modelling aspects in all the above areas, it is essential that the mathematical results be interpreted and translated to the application domains by substantiating the usefulness of the research in solving problems in those realms. Papers dealing with computational and numerical aspects will not be considered for publication unless supported by strong theoretical results and analyses. MissionThe mission of the journal envisages to serve scientists through prompt publication of significant advances in the branches of science and technology beforehand outlined and to provide a forum for the discussion of new scientific developments.