|
|
- 2016
一类包含媒体报道的SEQIHRS传染病模型的分析
|
Abstract:
摘要： 研究了一类包含媒体报道与隔离措施的SEQIHRS传染病模型的动力学行为。 首先得到了系统的有效再生数RC。 其次, 通过简单计算发现:系统总是存在无病平衡点,并且当RC<1时,它是局部渐近稳定的;当RC>1时,它是不稳定的。 然后,运用中心流形定理,发现当域值RC通过1时,系统将会发生跨临界分支,并且唯一的地方病平衡点是局部渐近稳定的。 此外, 计算结果表明,被隔离个体的传染力将影响卫生部门如何实施相应的隔离措施。
Abstract: An SEQIHRS epidemic model is proposed for the transmission dynamics of an infectious disease with quarantine and isolation control strategies. Firstly, we obtain the effective reproduction number RC of the system. Secondly, simple calculations indicate that the system always exists a disease-free equilibrium, and it is locally asymptotically stable if RC<1, whereas it is unstable if RC>1. Thirdly, by use of central manifold theory, it is established that as RC passes through unity, transcritical bifurcation occurs in the system and the unique endemic equilibrium is asymptotically stable. In addition, mathematical results indicate that infectiousness of hospitalized individuals will determine how the government takes control measures
| [1] | CASTILLO-CHAVEZ C, SONG Baojun. Dynamical models of tuberculosis and their applications[J]. Mathematical Biosciences & Engineering, 2004, 1(2):361-404. |
| [2] | CHITNIS N, HYMAN J M, CUSHING J M. Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model[J]. Bulletin of Mathematical Biology, 2008, 70(5):1272-1296. |
| [3] | KAO R R, ROBERTS M G. Quarantine-based disease control in domesticated animal herds[J]. Applied Mathematics Letters, 1998, 11(4):115-120. |
| [4] | TRACHT S M, DEL VALLE S Y, HYMAN J M. Mathematical modeling of the effectiveness of facemasks in reducing the spread of novel influenza A(H1N1)[J]. PLoS ONE, 2010, 5(2):e9018. |
| [5] | BUONOMO B, DONOFRIO A, LACITIGNOLA D. Global stability of an SIR epidemic model with information dependent vaccination[J]. Mathematical Biosciences, 2008, 216(1):9-16. |
| [6] | KISS I Z, CASSELL J, RECKER M, et al. The impact of information transmission on epidemic outbreaks[J]. Mathematical Biosciences, 2010, 225(1):1-10. |
| [7] | CUI Jingan, TAO Xin, ZHU Huaiping. An SISinfection model incorporating media coverage[J]. Rocky Mountain Journal of Mathematics, 2008, 38(5):1323-1334. |
| [8] | GREENBERG M E, LAI M H, HARTEL G F, et al. Response to a monovalent 2009 influenza A(H1N1)vaccine[J]. The New England Journal of Medicine, 2009, 361(25):2405-2413. |
| [9] | LIU Rongsong, WU Jianhong, ZHU Huaiping. Media/psychological impact on multiple outbreaks of emerging infectious diseases[J]. Computational and Mathematical Methods in Medicine, 2007, 8(3):153-164. |
| [10] | MCLEOD R G, BREWSTER J F, GUMEL A B, et al. Sensitivity and uncertainty analyses for a SARS model with time-varying inputs and output[J]. Mathematical Biosciences & Engineering, 2006, 3(3):527-544. |
| [11] | WANG Ai, XIAO Yanni. A Filippov system describing media effects on the spread of infectious diseases[J]. Nonlinear Analysis Hybrid Systems, 2014, 11:84-97. |
| [12] | WANG Yi, CAO Jinde, JIN Zhen, et al. Impact of media coverage on epidemic spreading in complex networks[J]. Physica A Statistical Mechanics & Its Applications, 2013, 392(23):5824-5835. |
| [13] | HANCOCK K, VEGUILLA V, LU Xiuhua, et al. Cross-reactive antibody responses to the 2009 pandemic H1N1 influenza virus[J]. The New England Journal of Medicine, 2009, 361(20):1945-1952. |
| [14] | LI Yongfeng, CUI Jingan. The effect of constant and pulse vaccination on SIS epidemic models incorporating media coverage[J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(5):2353-2365. |
| [15] | SAHU G P, DHAR J. Dynamics of an SEQIHRS epidemic model with media coverage, quarantine and isolation in a community with pre-existing immunity[J]. Journal of Mathematical Analysis & Applications, 2015, 421:1651-1672. |
| [16] | TCHUENCHE J M, DUBE N, BHUNU C P, et al. The impact of media coverage on the transmission dynamics of human influenza[J]. BMC Public Health, 2011, 11:S5. |
| [17] | CHAMCHOD F, BRITTON N F. On the dynamics of a two-strain influenza model with isolation[J]. Mathematical Modelling of Natural Phenomena, 2012, 7(3):49-61. |
| [18] | CUI Jingan, SUN Yonghong, ZHU Huaiping. The impact of media on the control of infectious diseases[J]. Journal of Dynamics and Differential Equations, 2007, 20(1):31-53. |
