| Hepatitis C is has become a major public health problem worldwide.According to the statistics of the World Health Organization in 2017,the number of infected people in the world exceeded 71 million,mainly in China,Brazil and other developing countries.As there is no vaccine to prevent currently,the control of hepatitis C remains one of the major global public health issues.In this paper,three kinds of dynamic models of hepatitis C are established and analyzed from the macro and micro perspectives.In the first part,according to the transmission mechanism of hepatitis C,we establish an SEICR hepatitis C model with infectious latency and relapse effect,give the basic reproduction number of the model,and study the local and global behavior of equilibrium points.By selecting the case data of hepatitis C patients in Shaanxi Province,the model is used to simulate the epidemic trend of hepatitis C in the next a few years.Finally,the sensitivity analysis of the parameters shows that the number of hepatitis C patients will continue to increase in recent years.Improving public awareness of hepatitis C detection and strengthening immunity can promote the recovery rate of hepatitis C patients and reduce the possibility of disease relapse,which can control the further spread of hepatitis C.In the second part,in order to study the influence of uncertain factors on hepatitis C in reality,we study a stochastic SICR hepatitis C model with acute and chronic infection.Firstly,the existence and uniqueness of global positive solutions are obtained using the stopping time theory.Secondly,by constructing Lyapunov function and combining Ito formula,we discuss the oscillation behavior of the solution of the stochastic model near the disease-free equilibrium point and positive equilibrium point of the corresponding determined model,and then give the sufficient conditions for the average persistence of the solution of the stochastic model and the extinction of the disease.Finally,the numerical simulations are carrying out for the influence of noise on the model.The results show that the solution of the stochastic model perturbs near the equilibrium point of the determined model,the intensity of the disturbance has a positively correlation with the noise intensity,and the noise is large enough to make the disease extinct.In the third part,in order to study the effect of DAAs treatment on the transmission mechanism of hepatitis C,a class of multi-scale age structure hepatitis C model with time delay is investigated,and the basic reproduction number of the model is given.By constructing Lyapunov functional and La Salle invariant set principle,the stability of equilibrium point is proved under certain conditions.Finally,the numerical simulations consider the therapeutic effects of different DAAs.The results show that strengthening the therapeutic effect of DAAs to a certain extent inhibits the cellular immune response,and the immune delay affects the stability of the cellular immune excitation equilibrium point.In the actual treatment,the goal of eliminating hepatitis C will be achieved by optimizing the combination of drugs and dosage. |
