IDEAS home Printed from https://ideas.repec.org/a/hin/complx/4861391.html
   My bibliography  Save this article

Dynamics of a Nonautonomous Stochastic SIS Epidemic Model with Double Epidemic Hypothesis

Author

Listed:
  • Haokun Qi
  • Lidan Liu
  • Xinzhu Meng

Abstract

We investigate the dynamics of a nonautonomous stochastic SIS epidemic model with nonlinear incidence rate and double epidemic hypothesis. By constructing suitable stochastic Lyapunov functions and using Has’minskii theory, we prove that there exists at least one nontrivial positive periodic solution of the system. Moreover, the sufficient conditions for extinction of the disease are obtained by using the theory of nonautonomous stochastic differential equations. Finally, numerical simulations are utilized to illustrate our theoretical analysis.

Suggested Citation

  • Haokun Qi & Lidan Liu & Xinzhu Meng, 2017. "Dynamics of a Nonautonomous Stochastic SIS Epidemic Model with Double Epidemic Hypothesis," Complexity, Hindawi, vol. 2017, pages 1-14, November.
    • Handle: RePEc:hin:complx:4861391
    DOI: 10.1155/2017/4861391
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2017/4861391.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2017/4861391.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2017/4861391?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Zhou, Yanli & Yuan, Sanling & Zhao, Dianli, 2016. "Threshold behavior of a stochastic SIS model with Le´vy jumps," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 255-267.
    2. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2016. "Nontrivial periodic solution of a stochastic non-autonomous SISV epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 837-845.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ruiqing Shi & Ting Lu & Cuihong Wang, 2019. "Dynamic Analysis of a Fractional-Order Model for Hepatitis B Virus with Holling II Functional Response," Complexity, Hindawi, vol. 2019, pages 1-13, August.
    2. Xinhua Wang & Rongwu Lu & Hao Yu & Dan Li, 2019. "Stability of the Evolutionary Game System and Control Strategies of Behavior Instability in Coal Mine Safety Management," Complexity, Hindawi, vol. 2019, pages 1-14, February.
    3. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "A stochastic SIRS epidemic model with logistic growth and general nonlinear incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    4. Mengnan Chi & Wencai Zhao, 2019. "Dynamical Analysis of Two-Microorganism and Single Nutrient Stochastic Chemostat Model with Monod-Haldane Response Function," Complexity, Hindawi, vol. 2019, pages 1-13, March.
    5. Zhu, Guanghu & Chen, Sixing & Shi, Benyun & Qiu, Hongjun & Xia, Shang, 2019. "Dynamics of echinococcosis transmission among multiple species and a case study in Xinjiang, China," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 103-109.
    6. Zhou, Baoquan & Zhang, Xinhong & Jiang, Daqing, 2020. "Dynamics and density function analysis of a stochastic SVI epidemic model with half saturated incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    7. Fan, Kuangang & Zhang, Yan & Gao, Shujing & Chen, Shihua, 2020. "A delayed vaccinated epidemic model with nonlinear incidence rate and Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    8. Lei Fu & Hongwei Yang, 2019. "An Application of (3+1)-Dimensional Time-Space Fractional ZK Model to Analyze the Complex Dust Acoustic Waves," Complexity, Hindawi, vol. 2019, pages 1-15, August.
    9. Boukanjime, Brahim & El Fatini, Mohamed & Laaribi, Aziz & Taki, Regragui, 2019. "Analysis of a deterministic and a stochastic epidemic model with two distinct epidemics hypothesis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    10. Selvan, T. Tamil & Kumar, M., 2023. "Dynamics of a deterministic and a stochastic epidemic model combined with two distinct transmission mechanisms and saturated incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 619(C).
    11. Tingting Ma & Xinzhu Meng & Zhengbo Chang, 2019. "Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps," Complexity, Hindawi, vol. 2019, pages 1-19, March.
    12. Liu, Guodong & Meng, Xinzhu, 2019. "Optimal harvesting strategy for a stochastic mutualism system in a polluted environment with regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    13. Rong Liu & Guirong Liu, 2018. "Asymptotic Behavior of a Stochastic Two-Species Competition Model under the Effect of Disease," Complexity, Hindawi, vol. 2018, pages 1-15, November.
    14. Qi, Haokun & Zhang, Shengqiang & Meng, Xinzhu & Dong, Huanhe, 2018. "Periodic solution and ergodic stationary distribution of two stochastic SIQS epidemic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 223-241.
    15. Liu, Qiong & Zhang, Meng & Chen, Lansun, 2019. "State feedback impulsive therapy to SIS model of animal infectious diseases," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 222-232.
    16. Shi, Ruiqing & Lu, Ting & Wang, Cuihong, 2021. "Dynamic analysis of a fractional-order model for HIV with drug-resistance and CTL immune response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 509-536.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cao, Zhongwei & Shi, Yuee & Wen, Xiangdan & Liu, Liya & Hu, Jingwei, 2020. "Analysis of a hybrid switching SVIR epidemic model with vaccination and Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    2. Alkhazzan, Abdulwasea & Wang, Jungang & Nie, Yufeng & Khan, Hasib & Alzabut, Jehad, 2023. "An effective transport-related SVIR stochastic epidemic model with media coverage and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    3. Bao, Kangbo & Zhang, Qimin & Rong, Libin & Li, Xining, 2019. "Dynamics of an imprecise SIRS model with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 489-506.
    4. RabieiMotlagh, Omid & Soleimani, Leila, 2023. "Effect of mutations on stochastic dynamics of infectious diseases, a probability approach," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    5. Rifhat, Ramziya & Wang, Lei & Teng, Zhidong, 2017. "Dynamics for a class of stochastic SIS epidemic models with nonlinear incidence and periodic coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 176-190.
    6. Gao, Miaomiao & Jiang, Daqing, 2019. "Analysis of stochastic multimolecular biochemical reaction model with lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 601-613.
    7. Cao, Zhongwei & Feng, Wei & Wen, Xiangdan & Zu, Li & Gao, Jinyao, 2020. "Nontrivial periodic solution of a stochastic seasonal rabies epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    8. Liu, Chao & Xun, Xinying & Zhang, Qingling & Li, Yuanke, 2019. "Dynamical analysis and optimal control in a hybrid stochastic double delayed bioeconomic system with impulsive contaminants emission and Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 99-118.
    9. Liu, Chao & Xun, Xinying & Zhang, Guilai & Li, Yuanke, 2020. "Stochastic dynamics and optimal control in a hybrid bioeconomic system with telephone noise and Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    10. Ruichao Li & Xiurong Guo, 2024. "Dynamics of a Stochastic SEIR Epidemic Model with Vertical Transmission and Standard Incidence," Mathematics, MDPI, vol. 12(3), pages 1-17, January.
    11. Zhang, Xinhong & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Dynamics of a stochastic SIS model with double epidemic diseases driven by Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 767-777.
    12. Zeng, Ting & Teng, Zhidong & Li, Zhiming & Hu, Junna, 2018. "Stability in the mean of a stochastic three species food chain model with general Le´vy jumps," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 258-265.
    13. Liu, Chao & Wang, Luping & Zhang, Qingling & Li, Yuanke, 2018. "Modeling and dynamical analysis of a triple delayed prey–predator–scavenger system with Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1216-1239.
    14. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "Periodic solution and stationary distribution of stochastic SIR epidemic models with higher order perturbation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 209-217.
    15. Tingting Ma & Xinzhu Meng & Zhengbo Chang, 2019. "Dynamics and Optimal Harvesting Control for a Stochastic One-Predator-Two-Prey Time Delay System with Jumps," Complexity, Hindawi, vol. 2019, pages 1-19, March.
    16. Sun, Shulin & Sun, Yaru & Zhang, Guang & Liu, Xinzhi, 2017. "Dynamical behavior of a stochastic two-species Monod competition chemostat model," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 153-170.
    17. Ali, Ishtiaq & Ullah Khan, Sami, 2020. "Analysis of stochastic delayed SIRS model with exponential birth and saturated incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    18. Gao, Miaomiao & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Threshold behavior of a stochastic Lotka–Volterra food chain chemostat model with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 191-203.
    19. Cao, Zhongwei & Wen, Xiangdan & Su, Huishuang & Liu, Liya & Ma, Qiang, 2020. "Stationary distribution of a stochastic chemostat model with Beddington–DeAngelis functional response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:complx:4861391. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.