Dynamical Analysis and Numerical Simulation of a Stochastic Influenza Transmission Model with Human Mobility and Ornstein–Uhlenbeck Process

• Tan Su ^[1] ; Xinhong Zhang ^[1] ; Yonggui Kao ^[1] ; Daqing Jiang ^[1]
  1. [1] China University of Petroleum

     China University of Petroleum

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 2, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • With the inevitable environmental perturbations and complex population movements, the analysis of troublesome influenza is harder to proceed. Studies about the epidemic mathematical models can not only forecast the development trend of influenza, but also have a beneficial influence on the protection of health and the economy. Motivated by this, a stochastic influenza model incorporating human mobility and the Ornstein– Uhlenbeck process is established in this paper. Based on the existence of the unique global positive solution, we obtain sufficient conditions for influenza extinction and persistence, which are related to the basic reproduction number in the corresponding deterministic model. Notably, the analytical expression of the probability density function of stationary distribution near the quasi-endemic equilibrium is obtained by solving the challenging Fokker–Planck equation. Finally, numerical simulations are performed to support the theoretical conclusions, and the effect of main parameters and environmental perturbations on influenza transmission are also investigated.

• Referencias bibliográficas
  • 1. Kilbourne, E.D.: Influenza. Springer Science and Business Media, Berlin (2012)
  • 2. Taubenberger, J.K., Reid, A.H., Krafft, A.E., Bijwaard, K.E., Fanning, T.G.: Initial genetic characterization of the: “Spanish” influenza...
  • 3. Reid, A.H., Taubenberger, J.K., Fanning, T.G.: The Spanish influenza: integrating history and biology. Microbes Infect. 1(2001), 81–87...
  • 4. Cockburn, W.C., Delon, P.J., Ferreira, W.: Origin and progress of the 1968–69 Hong Kong influenza epidemic. Bull. World Health Organ. 41,...
  • 5. Jordan, J.R., William, S.: The mechanism of spread of Asian influenza. Am. Rev. Respir. Dis. 83, 29–40 (1961)
  • 6. Kermack, W.O., Mckendrick, A.G.: Contributions to the mathematical theory of epidemics. Bull. Math. Biol. 53, 33–55 (1991)
  • 7. Tchuenche, J.M., Khamis, S.A., Agusto, F.B., Mpeshe, S.C.: Optimal control and sensitivity analysis of an influenza model with treatment...
  • 8. Lucchetti, J., Roy, M., Martcheva, M.: An avian influenza model and its fit to human avian influenza cases. Adv. Dis. Epidemiol. 1, 1–30...
  • 9. Zhao, Y., Zhang, L., Yuan, S.: The effect of media coverage on threshold dynamics for a stochastic SIS epidemic model. Phys. A 512, 248–260...
  • 10. Yang, Q., Zhang, X., Jiang, D., Shao, M.: Analysis of a stochastic predator–prey model with weak Allee effect and Holling-(n+1) functional...
  • 11. Adnani, J., Hattaf, K., Yousfi, N.: Stability analysis of a stochastic SIR epidemic model with specific nonlinear incidence rate. Int....
  • 12. Lv, X., Hui, H., Liu, F., Bai, Y.: Stability and optimal control strategies for a novel epidemic model of COVID-19. Nonlinear Dyn. 106,...
  • 13. Epstein, J.M., Parker, J., Cummings, D., Hammond, R.A.: Coupled contagion dynamics of fear and disease: mathematical and computational...
  • 14. d’Onofrio, A., Manfredi, P.: Information-related changes in contact patterns may trigger oscillations in the endemic prevalence of infectious...
  • 15. Wang, W.: Modeling adaptive behavior in influenza transmission. Math. Modell. Nat. Phenom. 7, 253–262 (2012)
  • 16. Mao, X.: Stochastic Differential Equations and Applications. Horwood Publishing, Chichester (1997)
  • 17. Meng, X., Li, F., Gao, S.: Global analysis and numerical simulations of a novel stochastic ecoepidemiological model with time delay. Appl....
  • 18. Sadki, M., Allali, K.: Stochastic two-strain epidemic model with saturated incidence rates driven by Lévy noise. Math. Biosci. 375, 109262...
  • 19. Mohammad, K.M., Tisha, M.S., Kamrujjaman, Md.: Wiener and Lévy processes to prevent disease outbreaks: predictable vs stochastic analysis....
  • 20. Chen, C., Kang, Y.: Dynamics of a stochastic multi-strain SIS epidemic model driven by Lévy noise. Commun. Nonlinear Sci. Numer. Simul....
  • 21. Zhu, Y., Wang, L., Qiu, Z.: Dynamics of a stochastic cholera epidemic model with Lévy process. Phys. A 595, 127069 (2022)
  • 22. Zhao, D., Yuan, S.: Threshold dynamics of the stochastic epidemic model with jump-diffusion infection force. J. Appl. Anal. Comput. 2,...
  • 23. May, R.: Stability and Complexity in Model Ecosystems. Princeton University Press, Princeton (2001)
  • 24. Cai, Y., Li, J., Kang, Y., Wang, K., Wang, W.: The fluctuation impact of human mobility on the influenza transmission. J. Frankl. Inst....
  • 25. Allen, E.: Environmental variability and mean-reverting processes. Discret. Contin. Dyn. Syst. Ser. B 21, 2073–2089 (2016)
  • 26. Zhou, B., Jiang, D., Han, B., Hayat, T.: Threshold dynamics and density function of a stochastic epidemic model with media coverage and...
  • 27. Mu, X., Jiang, D., Hayat, T., Alsaedi, A., Ahmad, B.: Dynamical behavior of a stochastic Nicholson’s blowflies model with distributed...
  • 28. Ayoubi, T., Bao, H.: Persistence and extinction in stochastic delay logistic equation by incorporating Ornstein–Uhlenbeck process. Appl....
  • 29. Zhang, X., Yuan, R.: A stochastic chemostat model with mean-reverting Ornstein–Uhlenbeck process and Monod–Haldane response function....
  • 30. Song, Y., Zhang, X.: Stationary distribution and extinction of a stochastic SVEIS epidemic model incorporating Ornstein–Uhlenbeck process....
  • 31. Chen, X., Tian, B., Xu, X., Yang, R., Zhong, S.: A stochastic SIS epidemic model with Ornstein– Uhlenbeck process and Brown motion. Research...
  • 32. Zhang, X., Yang, Q., Su, T.: Dynamical behavior and numerical simulation of a stochastic ecoepidemiological model with Ornstein–Uhlenbeck...
  • 33. Cai, Y., Jiao, J., Gui, Z., Liu, Y., Wang, W.: Environmental variability in a stochastic epidemic model. Appl. Math. Comput. 329, 210–226...
  • 34. Meyn, S.P., Tweedi, R.L.: Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes. Adv. Appl. Probab....
  • 35. Ma, Z., Zhou, Y.: Qualitative and Stability Methods for Ordinary Differential Equations. Science Press, Beijing (2015)
  • 36. Zhou, B., Jiang, D., Dai, Y., Hayat, T.: Stationary distribution and density function expression for a stochastic SIQRS epidemic model...
  • 37. Gardiner, C.W.: Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences. Springer, Berlin (1983)
  • 38. Roozen, H.: An asymptotic solution to a two-dimensional exit problem arising in population dynamics. SIAM J. Appl. Math. 49, 1793–1810...
  • 39. Higham, D.J.: An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev. 43, 525–546 (2001)
  • 40. Mandal, M., Jana, S., Nandi, S.K., Khatua, A., Adak, S., Kar, T.K.: A model based study on the dynamics of COVID-19: prediction and control....