Threshold Dynamics and Probability Density Function of a Stochastic Multi-Strain Coinfection Model with Amplification and Vaccination

• Lijuan Niu ^[1] ; Qiaoling Chen ^[2] ; Zhidong Teng ^[3]
  1. [1] Xi'an Polytechnic University

     Xi'an Polytechnic University

     China

     
  2. [2] Shaanxi Normal University

     Shaanxi Normal University

     China

     
  3. [3] Xinjiang Medical University

     Xinjiang Medical University

     China

     

  Mostrar afiliaciones +
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 2, 2024
• Idioma: inglés
• DOI: 10.1007/s12346-024-00957-6
• Enlaces
  • Texto completo
• Resumen

  • Multi-strain infectious diseases, which are usually prevented from spreading widely by vaccination, have two main transmission mechanisms: competitive exclusion and coexistence. In this paper, a stochastic multi-strain coinfection model with amplification and vaccination is developed. For the deterministic model, the basic reproduction number R0 and fixed points are provided. For the stochastic model, we first prove the existence and uniqueness of the positive solution under any initial value. Then, a portion of those infected with the common strain will always become patients with the amplified strain, which increases the risk of death from the disease. Therefore, we verified that patients with common strains would become extinct if Rs 1 < 1.

    Furthermore, by constructing the Lyapunov function, we find that model (3) has a unique ergodic stationary distribution if RS 0 > 1. Particularly, we get a concrete form of the probability density of the distribution κ(·) near equilibrium E∗, where E∗ is the quasi-local equilibrium of the stochastic model. Finally, the results are verified by numerical simulation. The results show that vaccination can control disease outbreaks or even eliminate them.

• Referencias bibliográficas
  • 1. Overview of the Epidemic of National Statutory Infectious Diseases in 2021. National Health Commission
  • 2. Bonhoeffer, S., Nowak, M.A.: Mutation and the evolution of virulence. Proc. R. Soc. Lond. B. 258(1352), 133–140 (1994)
  • 3. Martcheva, M.: A non-autonomous multi-strain SIS epidemic model. J. Biol. Dyn. 3(2–3), 235–251 (2009)
  • 4. Kuddus, M.A., McBryde, E.S., Adekunle, A.I., White, L.J., Meehan, M.T.: Mathematical analysis of a two-strain disease model with amplification....
  • 5. He, D.H., Ali, S.T., Fan, G.H., Gao, D.Z., Song, H.T., Lou, Y.J., Zhao, S., Cowling, B.J., Stone, L.: Evaluation of effectiveness of global...
  • 6. Kaur, S.P., Gupta, V.: COVID-19 vaccine: a comprehensive status report. Virus Res. 288, 198114 (2020). https://doi.org/10.1016/j.virusres.2020.198114
  • 7. Yavuz, M., Co¸sar, F.Ö., Günay, F., Özdemir, F.N.: A new mathematical modeling of the COVID-19 pandemic including the vaccination campaign....
  • 8. Wang, X.Y., Yang, J.Y., Han, Y.: Threshold dynamics of a chronological age and infection age structured cholera model with Neumann boundary...
  • 9. Yang, J.Y., Yang, L., Jin, Z.: Optimal strategies of the age-specific vaccination and antiviral treatment against influenza. Chaos Soliton...
  • 10. Saha, S., Samanta, G., Nieto, J.J.: Epidemic model of COVID-19 outbreak by inducing behavioural response in population. Nonlinear Dyn....
  • 11. Saha, S., Samanta, G., Nieto, J.J.: Impact of optimal vaccination and social distancing on COVID-19 pandemic. Math. Comput. Simul. 200,...
  • 12. Wu, H., Zhang, L., Li, H.L., Teng, Z.D.: Stability analysis and optimal control on a multi-strain coinfection model with amplification...
  • 13. Khajanchi, S., Bera, S., Roy, T.K.: Mathematical analysis of the global dynamics of a HTLV-I infection model, considering the role of...
  • 14. Bera, S., Khajanchi, S., Roy, T.K.: Stability analysis of fuzzy HTLV-I infection model: a dynamic approach. J. Appl. Math. Comput. 69(1),...
  • 15. Han, B.T., Jiang, D.Q., Zhou, B.Q., Hayat, T., Alsaedi, A.: Stationary distribution and probability density function of a stochastic SIRSI...
  • 16. Omame, A., Abbas, M., Din, A.: Global asymptotic stability, extinction and ergodic stationary distribution in a stochastic model for dual...
  • 17. Zhang, X.H., Jiang, D.Q., Alsaedi, A., Hayat, T.: Stationary distribution of stochastic SIS epidemic model with vaccination under regime...
  • 18. Zhao, Y.N., Jiang, D.Q., O’Regan, D.: The extinction and persistence of the stochastic SIS epidemic model with vaccination. Physica A...
  • 19. Li, Z.M., Zhang, T.L., Li, X.Q.: Threshold dynamics of stochastic models with time delays: A case study for Yunnan, China. Electron Res....
  • 20. Cai, Y.L., Kang, Y., Wang, W.M.: A stochastic SIRS epidemic model with nonlinear incidence rate. Appl. Math. Comput. 305, 221–240 (2017)....
  • 21. Rao, F., Wang, W.M., Li, Z.B.: Stability analysis of an epidemic model with diffusion and stochastic perturbation. Commun. Nonlinear Sci....
  • 22. Zhang, S.Q., Yuan, S.L., Zhang, T.H.: Dynamic analysis of a stochastic eco-epidemiological model with disease in predators. Stud. Appl....
  • 23. Silver, S.D., Driessche, P., Khajanchi, S.: A dynamic multistate and control model of the COVID-19 pandemic. J. Public Health, 1–14 (2023)....
  • 24. Mollah, S., Biswas, S., Khajanchi, S.: Impact of awareness program on diabetes mellitus described by fractional-order model solving by...
  • 25. Sarkar, K., Mondal, J., Khajanchi, S.: How do the contaminated environment influence the transmission dynamics of COVID-19 pandemic? Eur....
  • 26. Sardar, M., Khajanchi, S.: Is the Allee effect relevant to stochastic cancer model? J. Appl. Math. Comput. 68(4), 2293–2315 (2022)
  • 27. Dwivedi, A., Keval, R., Khajanchi, S.: Modeling optimal vaccination strategy for dengue epidemic model: a case study of India. Phys. Scr....
  • 28. Saha, S., Dutta, P., Samanta, G.: Dynamical behavior of SIRS model incorporating government action and public response in presence of...
  • 29. Zhao, Y.N., Jiang, D.Q.: The threshold of a stochastic SIS epidemic model with vaccination. Appl. Math. Comput. 243, 718–727 (2014). https://doi.org/10.1016/j.amc.2014.05.124
  • 30. Ma, Z.E., Zhou, Y.C., Li, C.Z.: Qualitative and Stability Methods for Ordinary Differential Equations. Science Press, Beijing (2015)
  • 31. Hasminskii, R.: Stochastic Stability of Differential Equations. Sijthoff and Noordhoff. Alphen aan den Rijn, NetherBlands (1980)
  • 32. Shi, Z.F., Jiang, D.Q., Zhang, X.H., Alsaedi, A.: A stochastic SEIRS rabies model with population dispersal: stationary distribution and...
  • 33. Zuo, W.J., Jiang, D.Q.: Stationary distribution and periodic solution for stochastic predator-prey systems with nonlinear predator harvesting....
  • 34. Zhang, G., Li, Z.M., Din, A.: A stochastic SIQR epidemic model with lévy jumps and three-time delays. Appl. Math. Comput. 431, 127329...
  • 35. Zhao, S.N., Yuan, S.L., Zhang, T.H.: The impact of environmental fluctuations on a plankton model with toxin-producing phytoplankton and...
  • 36. Zhang, S.Q., Yuan, S.L., Zhang, T.H.: A predator–prey model with different response functions to juvenile and adult prey in deterministic...
  • 37. Samantaa, G., Bera, S.P.: Analysis of a Chlamydia epidemic model with pulse vaccination strategy in a random environment. Nonlinear Anal-Model....
  • 38. Nguyen, D.H., Yin, G., Zhu, C.: Long-term analysis of a stochastic SIRS model with general incidence rates. SIAM J. Appl. Math. 80(2),...
  • 39. Liu, Q., Shi, Z.F.: Analysis of a stochastic HBV infection model with DNA-containing capsids and virions. J. Nonlinear Sci. 33(2), 23...
  • 40. Zhou, B.Q., Jiang, D.Q., Dai, Y.C., Hayat, T.: Threshold dynamics and probability density function of a stochastic avian influenza epidemic...
  • 41. Gardiner, C.W., et al.: Handbook of Stochastic Methods. Springer, Berlin (1985)
  • 42. Roozen, H.: An asymptotic solution to a two-dimensional exit problem arising in population dynamics. SIAM J. Appl. Math. 49(6), 1793–1810...
  • 43. Higham, D.J.: An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev. 43(3), 525–546 (2001)