Stochastic Persistence, Extinction and Stationary Distribution in HTLV-I Infection Model with CTL Immune Response

• Sovan Bera ^[2] ; Subhas Khajanchi ^[1] ; Tapan Kumar Kar ^[2]
  1. [1] Presidency University

     Presidency University

     India

     
  2. [2] Indian Institute of Engineering Science and Technology Shibpur
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº Extra 1, 2024
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • To study the impact of stochastic environmental variations on the transmission dynamics of HTLV-I infection, a stochastic HTLV-I infection model with a nonlinear CTL immune response is developed. By selecting an appropriate stochastic Lyapunov functional, we discussed the qualitative behavior of the stochastic HTLV-I infectionmodel, such as existence and uniqueness, stochastically ultimate bounded, and uniformly continuous. We find adequate criteria for the presence of a distinct ergodic stationary distribution of the HTLV-I system when the stochastic basic reproduction number is bigger than one by a careful mathematical examination of the HTLV-I infectionmodel.

    Furthermore, when the stochastic fundamental reproduction number (RE 0 ) is smaller than one, we provide sufficient circumstances for the extinction of the diseases. To illustrate our analytical conclusions, we ran numerical simulations. We also plotted the time series evolution of the CTL immune response, healthy CD4+T cells, latently infected CD4+T cells, and actively infected CD4+T cells in relation to the white noise.

    In the numerical simulation, we investigate that small intensities of a singlewhite noise can sustain a very slight fluctuation in each population. The high intensities of only one white noise can maintain the irregular recurrence of each population. Both the deterministic and stochastic models have the same solution if the random noises are too small.