A nonlinear HCV model in deterministic and randomly fluctuating environments

Two novel deterministic and stochastic nonlinear hepatitis C virus (HCV) models with nonlinear incidence rates as beta SpE,beta SpI$$ \beta {S}<^>pE,\beta {S}<^>pI $$, and beta SpCq$$ \beta {S}<^>p{C}<^>q $$, containing acute and chronic infections, are developed, and an endeavor to understand their dynamics has been accomplished. For the former model, both the existence of unique equilibria and the sharp sufficient conditions of globally stable equilibria under different cases are established. Whereafter, the efforts taken to detect the asymptotic behaviors around equilibria, the existence of ergodic stationary distribution, and stochastic extinction of the latter model have been supplemented with meticulous theoretical proofs. At last, several numerical examples and discussions are illustrated to sustain and visualize our theoretical results. Compared and analyzed the numerical and theoretical results, we can find that the noise can influence the dynamics of disease and turn the disease from persistence to extinction. Moreover, several control measures are suggested based on our study.