Studies On Dynamics Of Bacterial Transmission With Resistant Genes In Different Environments

Using mathematical models to study the propagation rules in biological systems has a long history.The most widely application is to study the transmission of infectious diseases by using mathematical models.A more concise and typical quantitative description of the complicated process of epidemic can be made by mathematical models.Researchers can also find out various theoretical indicators affecting the spread of diseases,and analyze the spread rules and control measures of the diseases.Bacteria can be transmitted from person to person through contact,and antibiotic resistant bacteria with resistant genes may be tougher superbugs,which are special classes of bacteria that can be transmitted through contact.The transmission mechanism of superbugs is similar to the transmission mechanism of infectious diseases.This paper studies the transmission of two special resistant bacteria by using transmission dynamics models.The first chapter mainly introduces the research background and significance of antimicrobial resistance,and gives the important concepts and transmission mechanism of antibiotic resistance.The related research progress in domestic and international and mathematics correlative knowledge used in the subsequent studies are both introduced later.In Chapter 2,a "superbug" with a new resistance gene—NDM-1 is introduced.The researchers have found that superbugs with NDM-1 have two aspects of dynamic characteristics:firstly,NDM-1 can be horizontal transferred among bacteria,and the other is that the superbugs can be transferred between humans through direct contact.Based on these two transmission mechanisms,we study the dynamics of population in hospital environment where superbugs exist.In this section,three mathematic models are established to illustrate the dynamics of patients with bacterial resistance in hospital environment.The models are analyzed using stability theory of differential equations.Positive equilibrium points of the system are investigated and their stability analysis are carried out.The results show that when there are patients of multiple diseases in the hospital,the basic reproduction number of patients with NDM-1 in the system is the superposition of the reproduction number of each type.In Chapter 3,the research is based on mcr-1,a new type of gene that can develop strong resistance to polycolistin.Based on the characteristics that mcr-1 can transmits cross species barriers,this part combines the compartment model and predator-prey model to establish the differential models.Two differential equation models are established in this chapter.One basic model is based on the farm level,and the other is a four-population model considering human involved in the mcr-1 gene transmission.The models are analyzed with stability theory of differential equations.Positive equilibrium points of the system are investigated and the stability analyses are carried out.Moreover,the numerical simulations of the proposed model are also represented.Our results show that the fraction of animals used for human consumption and the contacting rate of animals are the most effective parameters of controlling the spread of mcr-1 gene in comparison with other parameters under closed environment.Based on the research of Chapter 3,an improved model is presented in Chapter4 to discuss the transmission of bacteria with mcr-1 gene in circulation environment.There are two possible stable states for the system:only susceptible populations exist,and populations with mcr-1 gene die out;four species co-existed which means that mcr-1 gene exist in both animals and human.Our results show that the fraction of animals used for human consumption is the most effective parameters to control the spread of mcr-1 gene,while the transmission rate of mcr-1 gene between human and the contacting rate of animals have less effect,which is significantly different from the result in Chapter3.The result shows that controlling at the source is the key to solving the problem of mcr-1 gene transmission.The thesis is then concluded in Chapter 5.