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Qualitative Analysis of an HIV/AIDS Model with Treatment and Nonlinear Perturbation

  • Autores: Miaomiao Gao, Daqing Jiang, Tasawar Hayat
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 3, 2022
  • Idioma: inglés
  • Enlaces
  • Resumen

    • In this paper, we consider a high-dimensional stochastic HIV/AIDS model that incorporates both multiple stages treatment and higher order perturbation. Firstly, we establish sufficient criteria for the existence of a unique ergodic stationary distribution by making use of stochastic Lyapunov analysis method. Stationary distribution shows that the disease will be persistent in the long term. Then, conditions for extinction of the disease are obtained. Theoretical analysis indicates that large noise intensity can suppress the prevalence of HIV/AIDS epidemic. Finally, we provide some numerical simulations to illustrate the analytical results.

  • Referencias bibliográficas
    • 1. Toro-Zapata, H.D., Trujillo-Salazar, C.A., Carranza-Mayorga, E.M.: Mathematical model describing HIV infection with time-delayed CD4 T-Cell...
    • 2. Levy, J.A.: Pathogenesis of human immunodeficiency virus infection. Microbiol. Rev. 57, 183–289 (1993)
    • 3. Stoddart, C.A., Reyes, R.A.: Models of HIV-1 disease: a review of current status. Drug Discovery Today Dis. Models. 3, 113–119 (2006)
    • 4. Lin, X., Hethcote, H.W., van den Driessche, P.: An epidemiological model for HIV/AIDS with proportional recruitment. Math. Biosci. 118,...
    • 5. Al-Sheikh, S.A., Musali, F., Alsolami, M.: Stability Analysis of an HIV/AIDS Epidemic Model with Screening. Int. Math. Forum. 6, 3251–3273...
    • 6. World Health Organization Data on the size of the HIV/AIDS epidemic. https://www.who.int/data/ gho/data/themes/hiv-aids/GHO/hiv-aids
    • 7. Toro-Zapata, H.D., Caicedo-Casso, A., Lee, S.: The role of immune response in optimal HIV treatment interventions. Processes. 6, 102 (2018)
    • 8. Cai, L., Li, X., Ghosh, M., Guo, B.: Stability analysis of an HIV/AIDS epidemic model with treatment. J. Comput. Appl. Math. 229, 313–323...
    • 9. Cai, L., Guo, S., Wang, S.: Analysis of an extended HIV/AIDS epidemic model with treatment. Appl. Math. Comput. 236, 621–627 (2014)
    • 10. McCluskey, C.C.: A model of HIV/AIDS with staged progression and amelioration. Math. Biosci. 181, 1–16 (2003)
    • 11. Jia, J., Qin, G.: Stability analysis of HIV/AIDS epidemic model with nonlinear incidence and treatment. Adv. Differ. Equ. 2017, 136 (2017)
    • 12. Huo, H., Feng, L.: Global stability for an HIV/AIDS epidemic model with different latent stages and treatment. Appl. Math. Model. 37,...
    • 13. Huo, H., Chen, R., Wang, X.: Modelling and stability of HIV/AIDS epidemic model with treatment. Appl. Math. Model. 40, 6550–6559 (2016)
    • 14. Hove-Musekwa, S.D., Nyabadza, F.: The dynamics of an HIV/AIDS model with screened disease carriers. Comput. Math. Methods Med. 10, 287–305...
    • 15. Kretzschmar, M.E., van der Loeff, M.F.S., Birrell, P.J., Angelis, D.D., Coutinho, R.A.: Prospects of elimination of HIV with test-and-treat...
    • 16. Otunuga, O.M.: Global stability for a 2n +1 dimensional HIV/AIDS epidemic model with treatments. Math. Biosci. 299, 138–152 (2018)
    • 17. May, R.M.: Stability and Complexity in Model Ecosystems. Princeton University Press, NJ (2001)
    • 18. Imhof, L., Walcher, S.: Exclusion and persistence in deterministic and stochastic chemostat models. J. Differ. Equ. 217, 26–53 (2005)
    • 19. Zhao, Y., Jiang, D., Mao, X., Gray, A.: The threshold of a stochastic SIRS epidemic model in a population with varying size. Discrete...
    • 20. Liu, Q., Jiang, D., Hayat, T., Ahmed, A.: Dynamics of a stochastic multigroup SIQR epidemic model with standard incidence rates. J. Franklin...
    • 21. Yang, J., Wang, X., Li, X.: Global stability of an HIV/AIDS model with stochastic perturbation. Asian-Eur. J. Math. 4, 349–358 (2011)
    • 22. Zhang, H., Xia, J., Georgescu, P.: Multigroup deterministic and stochastic SEIRI epidemic models with nonlinear incidence rates and distributed...
    • 23. Gray, A., Greenhalgh, D., Hu, L., Mao, X., Pan, J.: A stochastic differential equation SIS epidemic model. SIAM J. Appl. Math. 71, 876–902...
    • 24. Nsuami, M.U., Witbooi, P.J.: Stochastic dynamics of an HIV/AIDS epidemic model with treatment. Quaest. Math. 42, 605–621 (2019)
    • 25. Lahrouz, A., Omari, L., Kiouach, D.: Global analysis of a deterministic and stochastic nonlinear SIRS epidemic model, Nonlinear Anal....
    • 26. Cai, Y., Kang, Y., Wang, W.: A stochastic SIRS epidemic model with nonlinear incidence rate. Appl. Math. Comput. 305, 221–240 (2017)
    • 27. Feng, T., Qiu, Z.: Global analysis of a stochastic TB model with vaccination and treatment. Discrete Contin. Dyn. Syst. Ser. B. 24, 2923–2939...
    • 28. Meng, X., Zhao, S., Feng, T., Zhang, T.: Dynamics of a novel nonlinear stochastic SIS epidemic model with double epidemic hypothesis....
    • 29. Wei, F., Xue, R.: Stability and extinction of SEIR epidemic models with generalized nonlinear incidence. Math. Comput. Simulat. 170, 1–15...
    • 30. Wang, Y., Jiang, D., Hayat, T., Alsaedi, A.: Stationary distribution of an HIV model with general nonlinear incidence rate and stochastic...
    • 31. Liu, Q., Jiang, D.: Stationary distribution and extinction of a stochastic SIR model with nonlinear perturbation. Appl. Math. Lett. 73,...
    • 32. Zhang, W., Meng, X., Dong, Y.: Periodic solution and ergodic stationary distribution of stochastic SIRI epidemic systems with nonlinear...
    • 33. Lahrouz, A., Settati, A.: Asymptotic properties of switching diffusion epidemic model with varying population size. Appl. Math. Comput....
    • 34. Liu, H., Li, X., Yang, Q.: The ergodic property and positive recurrence of a multi-group Lotka-Volterra mutualistic system with regime...
    • 35. Wang, L., Jiang, D.: Ergodic property of the chemostat: A stochastic model under regime switching and with general response function....
    • 36. Wang, L., Jiang, D.: A note on the stationary distribution of the stochastic chemostat model with general response functions. Appl. Math....
    • 37. Khasminskii, R.: Stochastic Stability of Differential Equations, 2nd edn. Springer, Berlin (2012)
    • 38. Zhu, C., Yin, G.: Asymptotic properties of hybrid diffusion systems. SIAM J. Control Optim. 46, 1155–1179 (2007)
    • 39. Peng, S., Zhu, X.: Necessary and sufficient condition for comparison theorem of 1-dimensional stochastic differential equations. Stochastic...
    • 40. Kunita, H.: Ito’s stochastic calculus: its surprising power for applications. Stoch. Proc. Appl. 120, 622–652 (2010)
    • 41. Mao, X.: Stochastic Differential Equations and Applications, 2nd edn. Horwood Publishing, Chichester (2008)
    • 42. Higham, D.J.: An algorithmic introduction to numerical simulation of stochastic differential equations. SIAM Rev. 43, 525–546 (2001)
    • 43. Caraballo, T., Fatini,M.E., Khalifi,M.E., Gerlach, R., Pettersson, R.: Analysis of a stochastic distributed delay epidemic model with...
    • 44. Liu, D., Wang, B.: A novel time delayed HIV/AIDS model with vaccination and antiretroviral therapy and its stability analysis. Appl. Math....
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