一类随机系统基本再生数的计算与应用
Calculation and Application of Basic Regeneration Number for a Class of Stochastic Systems
摘要: 本文考虑了随机噪声在SIR、SEIR、SEIAR传染病模型中的影响，建立了的具有受随机扰动的SIR、SEIR、SEIAR模型，并利用Itô公式推导出均值意义下的随机传染病模型的基本再生数的计算公式。通过数值模拟系统演化过程验证了基本再生数计算方法的有效性。
Abstract: Considering the influence of random noise on SIR, SEIR and SEIAR infectious disease models, we establish SIR, SEIR and SEIAR models with random disturbance, and deduce the calculation formu-la of the basic regeneration number of the random infectious disease model in the sense of mean value by using Itô formula. The effectiveness of the basic regeneration number calculation method is verified by numerical simulation of the system evolution process.
文章引用：石佳欣, 黄东卫. 一类随机系统基本再生数的计算与应用[J]. 应用数学进展, 2022, 11(6): 3849-3859. https://doi.org/10.12677/AAM.2022.116412

参考文献

[1] Feng, Z.L. and Velasco-Hernández, J.X. (1997) Competitive Exclusion in a Vector-Host Model for the Dengue Fever. Journal of Mathematical Biology, 35, 523-544. [Google Scholar] [CrossRef] [PubMed]
[2] Small, M., Tse, C.K. and Walker, D.M. (2006) Super-Spreaders and the Rate of Transmission of the SARS Virus. Physica D: Nonlinear Phenomena, 215, 146-158. [Google Scholar] [CrossRef] [PubMed]
[3] Castillo-Chavez, C. and Feng, Z.L. (1997) To Treat or Not to Treat: The Case of Tuberculosis. Journal of Mathematical biology, 35, 629-656. [Google Scholar] [CrossRef] [PubMed]
[4] Kermack, W.O. and Mckendrick, A.G. (1927) Contributions to the Mathematical Theory of Epidemics. Proceedings of the Royal Society A, 115, 700-721. [Google Scholar] [CrossRef] 
[5] Cui, J.A., Sun, Y.H. and Zhu, H.P. (2007) The Impact of Media on the Control of Infectious Diseases. Journal of Dynamics and Differential Equations, 20, 31-53. [Google Scholar] [CrossRef] [PubMed]
[6] Ji, C.Y., Jiang, D.Q. and Shi, N.Z. (2012) The Behavior of an SIR Epidemic Model with Stochastic Perturbation. Stochastic Analysis and Applications, 30, 755-773. [Google Scholar] [CrossRef] 
[7] Lahrouz, A., Omari, L., Kiouach, D., et al. (2012) Complete Global Stability for an SIRS Epidemic Model with Generalized Non-Linear Incidence and Vaccination. Applied Mathe-matics and Computation, 218, 6519-6525. [Google Scholar] [CrossRef] 
[8] Side, S., Mulbar, U., Sidjara, S. and Sanusi, W. (2017) A SEIR Model for Transmission of Tuberculosis. AIP Conference Proceedings, 1830, 020004. [Google Scholar] [CrossRef] 
[9] Diekmann, O., Heesterbeek, J.A.P. and Metz, J.A.J. (1990) On the Defini-tion and the Computation of the Basic Reproduction Ratio R0 in Models for Infectious Diseases in Heterogeneous Popu-lations. Journal of Mathematical Biology, 28, 365-382. [Google Scholar] [CrossRef] 

为你推荐