| Infectious diseases have always been a threat to human health and life safety,and investigating infectious diseases and performing dynamic analysis can play a positive role in controlling the spread of diseases and provide a theoretical basis for formulating appropriate preventive measures.In this paper,three types of corresponding epidemic mathematical models are developed to reveal the effects of incubation period,early screening and population heterogeneity on hepatitis C,to seek more effective preventive and control measures.The specific study contents are shown as follows:First part,based on the long latency period of hepatitis C,the corresponding infectious disease model is constructed by using the latency period as a time delay parameter.Firstly,the control reproduction numberR_c is calculated.Secondly,the existence of disease-free equilibrium(DFE)and endemic equilibrium are proved.Furthermore,the equilibria are verified to be locally asymptotically stable using the Routh-Hurwitz criterion when the latency time delayτ=0;the Lyapunov-Lasalle theorem is used to prove that the DFE is globally asymptotically stable whenτ﹥0,and the stability of the endemic equilibrium is proved and the Hopf branch exists at the endemic equilibrium.Finally,sensitivity analysis and numerical simulation of the model show that as the time delay increases,the system destabilize and the equilibria will change from stable to unstable,and that reducing the proportion of the acute to the chronic conversion can lead to a decrease in the control reproduction number,which in turn will help control the spread of hepatitis C.Second part,to investigate the impact of early screening of the acute patients on the treatment of hepatitis C,a class of SICTR model with early screening is developed.Firstly,the control reproduction numberR_c is calculated.Secondly,the existence of the DFE and endemic equilibrium are proved,and both of them are globally asymptotically stable.Finally,sensitivity analysis and numerical simulation are performed,and optimal control theory is applied to analyze the existence of optimal solutions of the model.The results mean that early screening and timely treatment can improve the treatment rate of hepatitis C infected and can reduce the scale of transmission of hepatitis C.Final part,focusing on the influence of infection rates for different populations and rates of the acute to the chronic transition on the transmission of hepatitis C,an S_iI_iC_iR_iT(i=1,2)model incorporating population heterogeneity and early screening is proposed.Firstly,the control reproduction numberR_c is calculated.Secondly,the optimal solution of the model is obtained by the optimal control theory.Finally,sensitivity analysis and numerical simulation are carried out.The results show that increasing screening and treatment of acute infected hepatitis C in the high-risk population,and decreasing the proportion of acute to chronic conversion in both populations can effectively control the spread of hepatitis C. |
