一类具有非线性感染率的随机SIQS传染病模型解的渐近行为
Asymptotic Behavior of the Solution of a Random SIQS Epidemic Model with Nonlinear Infection Rate
摘要: 本文研究了一类带有非线性感染率的随机SIQS传染病模型。 首先证明了该随机SIQS传染病模型对正的初始条件存在着唯一的全局正解。 然后，通过构造适当的Lyapunov函数并结合伊藤公式的应用，对该随机SIQS传染病模型的解在无病平衡点以及地方病平衡点附近的渐进行为进行了分析讨论。
Abstract: This paper studies a kind of random SIQS infectious disease model with nonlinear infection rate. First, it is proved that the random SIQS infectious disease model has a unique global positive solution to the initial conditions of the positive. Then, by constructing an appropriate Lyapunov Function and combined with the application of Ito’s formula, the gradual behavior of the solution of the random SIQS infectious disease model near the disease-free balance point and the endemic disease balance point is analyzed and discussed.
文章引用：刘向荣. 一类具有非线性感染率的随机SIQS传染病模型解的渐近行为[J]. 应用数学进展, 2021, 10(7): 2359-2368. https://doi.org/10.12677/AAM.2021.107247

参考文献

[1] 周瑶, 吕贵臣. 具有人传人的登革热传染病模型的动力学分析[J]. 重庆理工大学学报: 自然科学版, 2021, 35(2): 258-267.
[2] Liu, Q. and Jiang, D. (2016) The Threshold of a Stochastic Delayed SIR Epidemic Model with Vaccination. Physica A: Statistical Mechanics and Its Applications, 461, 140-147.
https://doi.org/10.1016/j.physa.2016.05.036
[3] Liu, Q., Jiang, D., Hayat, T., et al. (2018) Analysis of a Delayed Vaccinated SIR Epidemic Model with Temporary Immunity and L´evy Jumps. Nonlinear Analysis: Hybrid Systems, 27, 29-43.
https://doi.org/10.1016/j.nahs.2017.08.002
[4] Wen, B.Y., Teng, Z.D., Li, Z.M., et al. (2018) The Threshold of a Periodic Stochastic SIVS Epi- demic Model with Nonlinear Incidence. Physica A: Statistical Mechanics and Its Applications, 508, 532-549.
https://doi.org/10.1016/j.physa.2018.05.056
[5] Wang, L., Zhang, X. and Liu, Z. (2018) An SEIR Epidemic Model with Relapse and General Nonlinear Incidence Rate with Application to Media Impact. Qualitative Theory of Dynamical Systems, 17, 1309-329.
[6] 杨俊仙, 徐丽. 一类具有非线性发生率和时沛的SIQS传染病模型的全局稳定性[J]. 山东大学学报理学版, 2014, 49(5): 67-74.
[7] Xiang, H., Tang, Y.L. and Huo, H.F. (2016) A Viral Model with Intracellular Delay and Humoral Immunity. Bulletin of the Malaysian Mathematical Sciences Society, 40, 1011-1023.
https://doi.org/10.1007/s40840-016-0326-2
[8] Jiang, D., Yu, J., Ji, C., et al. (2011) Asymptotic Behavior of Global Positive Solution to a Stochastic SIR Model. Mathematical and Computer Modelling, 54, 221-232.
https://doi.org/10.1016/j.mcm.2011.02.004
[9] Carletti, M. (2002) On the Stability Properties of a Stochastic Model for Phage-Bacteria Interaction in Open Marine Environment. Mathematical Biosciences, 175, 117-131.
https://doi.org/10.1016/S0025-5564(01)00089-X
[10] Jiang, D., Yu, J., Ji, C., et al. (2011) Asymptotic Behavior of Global Positive Solution to a Stochastic SIR Model. Mathematical and Computer Modelling, 54, 221-232.
https://doi.org/10.1016/j.mcm.2011.02.004
[11] 赵彦军, 李辉来, 李文轩. 一类具有饱和发生率和心理作用的随机SIR传染病模型[J]. 吉林大学 学报理学版, 2021, 59(1): 20-26.
[12] Amir, K., Ghulam, H., Mostafa, Z., et al. (2020) A Stochastic SACR Epidemic Model for HBV Transmission. Journal of Biological Dynamics, 14, 788-801.
https://doi.org/10.1080/17513758.2020.1833993

为你推荐