Dynamic Analysis Of Multi-scale HCV Model With Two Strains

Hepatitis C virus(HCV)infection is an infectious disease that seriously threatens human health.Direct-acting antiviral agents(DAAs)interfere with different steps of the HCV life cycle,so HCV can be treated with a higher cure rate.However,the emergence of drug-resistant variants has been a major obstacle to such treatment options.In order to accurately quantify the antiviral effect of these DAAs treatments and optimize the drug combination,we proposed a multi-scale HCV model with two-strain infection pattern and age structure using mathematical modeling method to describe the intracellular virus replication process(including the production of intracellular viral RNA,assembly/secretion in plasma,etc.)corresponding to the action mechanism,and study the dynamic behavior of HCV under DAAs treatment.The main contents are as follows:In the first chapter,introducing the background and theoretical significance of HCV infection,the status of mathematical research on HCV model,the main work of this thesis and the preliminary knowledge.In the second chapter,according to the mechanism of HCV infection,a twostrain multi-scale age-structure model including intracellular viral RNA replication and extracellular viral infection is established.Firstly,the existence,positivity and boundedness of the solution are proved,and the conditions for the existence of three steady-states(noninfectious steady-state,boundary steady-state and coexistent steady-state)of the model and their stability are calculated.Secondly,assuming that the two infected cells(sensitive and drug-resistant infected cells)are still in a stable distribution during the treatment period,we obtain an approximate solution of the decrease in viral load of the two strains(sensitive and drug-resistant strains)during the treatment period,and simulate that the long-term approximation coincide well with the solution prediction of the model.Lastly,numerical simulation is performed using the display equation of the long-term approximation to illustrate the effects of different antiviral effects of DAAs on the changes of two viral load during the treatment period,in order to study the dynamic trends of HCV infection and the dynamic effects under DAAs treatment.In the third chapter,the two-strain age-structure model proposed in Chapter 2is converted into an equivalent multi-scale ODE model,and the dynamic behavior of the ODE model is studied.Firstly,the positivity and boundedness of the solution of the transformed ODE model are proved,and the basic reproductive numbers of two virus strains are given.It is found that the existence and stability of steady-state of the transformed ODE model are completely dependent on the basic reproductive numbers of the model.Secondly,the competitive kinetics of sensitive and resistant virus strains during treatment are described.Lastly,the dynamic effects of backward mutations on sensitive and resistant virus strains during treatment are studied,which provided a theoretical framework for exploring the evolution of mutant allogeneic resistance during DAAs treatment.