Open AccessAnalysis of a stochastic HBV infection model with delayed immune response
Author(s) -
Fathalla A. Rihan,
Hebatallah J. Alsakaji
Publication year - 2021
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2021264
Subject(s) - ergodic theory , uniqueness , stationary distribution , white noise , hepatitis b virus , epidemic model , mathematics , immune system , infectious disease (medical specialty) , environmental noise , statistical physics , delay differential equation , exponential growth , control theory (sociology) , virology , disease , physics , virus , immunology , differential equation , computer science , markov chain , mathematical analysis , biology , medicine , statistics , population , artificial intelligence , environmental health , pathology , acoustics , control (management) , sound (geography)
Considering the environmental factors and uncertainties, we propose, in this paper, a higher-order stochastically perturbed delay differential model for the dynamics of hepatitis B virus (HBV) infection with immune system. Existence and uniqueness of an ergodic stationary distribution of positive solution to the system are investigated, where the solution fluctuates around the endemic equilibrium of the deterministic model and leads to the stochastic persistence of the disease. Under some conditions, infection-free can be obtained in which the disease dies out exponentially with probability one. Some numerical simulations, by using Milstein's scheme, are carried out to show the effectiveness of the obtained results. The intensity of white noise plays an important role in the treatment of infectious diseases.