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Stationary distribution and bifurcation analysis for a stochastic SIS model with nonlinear incidence and degenerate diffusion

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  • Wang, Lei
  • Gao, Chunjie
  • Rifhat, Ramziya
  • Wang, Kai
  • Teng, Zhidong

Abstract

In this paper, a stochastic SIS model with nonlinear incidence and degenerate diffusion is investigated. Firstly, the existence of a uniquely stable stationary distribution of this model is obtained by applying Markov semigroup theory, Fokker–Planck equation and Khasminskiĭ function. In addition, the bifurcation for this two-dimensional stochastic SIS model is discussed. Specifically, phenomenological bifurcation (P-bifurcation) is analyzed by approximately solving the stationary probability density of Fokker–Planck equation for linearizing system of the model. Subsequently, dynamical bifurcation (D-bifurcation) is thoroughly investigated by utilizing the method of Lyapunov exponent. At last, numerical simulations are performed to elaborate the dynamics and the characteristics of distribution for solutions of the model under the variations of different parameters. These findings demonstrate that: (i) appropriate parameters could cause the shape of a stationary probability distribution to shift from monotonic to unimodal; (ii) P-bifurcation caused by the alteration of transmission rate seem to be more obvious than those caused by the change of recovery rate; (iii) P-bifurcation induced by noises also exists even if D-bifurcation would not occur.

Suggested Citation

  • Wang, Lei & Gao, Chunjie & Rifhat, Ramziya & Wang, Kai & Teng, Zhidong, 2024. "Stationary distribution and bifurcation analysis for a stochastic SIS model with nonlinear incidence and degenerate diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:chsofr:v:182:y:2024:i:c:s0960077924004247
    DOI: 10.1016/j.chaos.2024.114872
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    1. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2010. "Stochastic stability for roommate markets," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2218-2240, November.
    2. Cai, Liming & Guo, Shumin & Li, XueZhi & Ghosh, Mini, 2009. "Global dynamics of a dengue epidemic mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2297-2304.
    3. Wen, Buyu & Rifhat, Ramziya & Teng, Zhidong, 2019. "The stationary distribution in a stochastic SIS epidemic model with general nonlinear incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 258-271.
    4. Lin, Yuguo & Jiang, Daqing & Wang, Shuai, 2014. "Stationary distribution of a stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 187-197.
    5. Chiarella, Carl & He, Xue-Zhong & Wang, Duo & Zheng, Min, 2008. "The stochastic bifurcation behaviour of speculative financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3837-3846.
    6. Zhang, Xiaofeng & Yuan, Rong, 2022. "Stochastic bifurcation and density function analysis of a stochastic logistic equation with distributed delay and weak kernel," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 195(C), pages 56-70.
    7. Rudnicki, Ryszard, 2003. "Long-time behaviour of a stochastic prey-predator model," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 93-107, November.
    8. Cai, Yongli & Jiao, Jianjun & Gui, Zhanji & Liu, Yuting & Wang, Weiming, 2018. "Environmental variability in a stochastic epidemic model," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 210-226.
    9. Boukanjime, Brahim & Caraballo, Tomás & El Fatini, Mohamed & El Khalifi, Mohamed, 2020. "Dynamics of a stochastic coronavirus (COVID-19) epidemic model with Markovian switching," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    10. Cai, Yongli & Kang, Yun & Wang, Weiming, 2017. "A stochastic SIRS epidemic model with nonlinear incidence rate," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 221-240.
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