Studies On Dynamics Of Within-host Malaria Infection Models In Mixed Infection

Malaria is one of the most important public health issues of global concern,which is widespread all over the world.Now employing antimalarial drugs is an important mean to treat malaria,but it will also lead to the occurrence and spread of drug resistance of malaria parasites,which will greatly reduce the service life of antimalarial drugs.Recent experiments have shown that for mixed infection,different doses of antimalarial drug treatment regimens will affect the spread and evolution of drug resistance: high doses of antimalarial drug treatment regimen will lead to the competitive release of drug-resistant parasites,on the contrary,moderate doses of antimalarial drug treatment regimen will delay the spread and evolution of drug resistance to some extent,which is mainly due to the competitive inhibition of drug-sensitive parasite on drug-resistant parasites.In this thesis,the development process of malaria parasite within a host and the evolution of drug resistance within a host in the case of mixed infection are studied by mathematical models.Then,the dynamic properties of the model and the sensitivity of parameters are further analyzed.The main contents of this thesis are as follows:1.For the case of mixed infection,in order to measure the competition between drug-sensitive parasites and drug-resistant parasites,two host dynamics models with and without competition are established to describe and predict the evolution of drug resistance during drug treatment.In order to estimate the unknown parameters of the model,the model included the competition is fitted with the experimental data of Huijben et al.,and the uncertainty of the estimated parameters is further analyzed.Then,by analyzing the dynamics of the model,the existence and stability of the equilibrium and the existence of the bistable solution are proved,and the initial value region tending to the bistable solution is divided numerically.In addition,from the perspective of numerical simulation,the thesis also studies the effect of different competition intensity and drug treatment regimen on drug resistance.2.Since some chemical sensitizers can reverse the drug resistance of malaria parasite,that is,they can reverse the chloroquine resistant parasite to chloroquine sensitive parasite,which has far-reaching significance for drug resistance management.Therefore,this factor is incorporated into the within-host dynamical model,and the significance of this parameter is verified by global sensitivity analysis.Then,the influence of competitionand drug treatment on drug resistance is further studied.By analyzing the dynamics of the model,the existence and stability of equilibrium and the existence of fixed point branch are proved.In the numerical simulation,it is found that the boundary equilibrium and interior equilibrium can be stable simultaneously when the model considers the competition,which shows the bistable phenomenon of the model.Then,we study the influence of the initial value of drug-resistant parasites on drug resistance.3.Since the host immunity is conducive to the elimination of malaria parasites,hence,in order to study the influence of immune response,we formulate two within-host malaria infection models that are with and without the immune response.Firstly,the global sensitivity of the model parameters is analyzed.Then,the model with immune response is analyzed in detail,and the existence and stability of equilibrium as well as the existence of Hopf bifurcation are proved.From the perspective of numerical simulation,we also investigate the effects of different competition intensity,drug treatment level and immune level on drug resistance.4.We explore the within-host dynamical model considering the development delay of malaria parasites that was proposed by Schneider et al.Firstly,the global sensitivity of the model parameters is analyzed.Then,by analyzing the dynamics of the model,the existence and stability of equilibrium and Hopf bifurcation are proved.The local Hopf branch is globally extended by numerical simulation.It is found that there are multiple turning points of the global Hopf branch,which make the model have multiple periodic solutions in some intervals of parameters.Finally,by calculating the Floquet factor distribution of periodic solution on the Hopf branch,the existence of the periodic doubling branch is found,and the key parameters affecting the existence of the periodic doubling branch are found based on the results of global sensitivity analysis.To summarize,by establishing malaria infection models within a host and considering the proportion of drug-resistant parasite reverts to drug-sensitive parasite,immunity and development delay of parasite,this thesis mainly studies the influence of drug treatment and competition between drug-resistant parasite population and drug-sensitive parasite population on drug resistance.Both sensitivity analysis and dynamical analysis of the model are carried out to identify the significant factors affecting malaria infection,and to prove the existence and stability of the equilibrium,as well as the existence and stability of the branches.Finally,the results of theoretical analysis are verified by numerical simulation.The results obtained in this thesis are consistent with the experimental resultsof Huijben and Read et al,which also provide a good theoretical basis for controlling the spread and evolution of malaria resistance.