| Infectious diseases have a huge impact on human society.It is well known that vac-cination is an effective measure to control the spread of the virus.Studies showed there is still a risk of disease after vaccination,this phenomenon is called vaccine immuniza-tion failure.The cases of vaccine immunization failure and its related problems have attracted extensive attention of public health scholars.Considering whether vaccine immunization failure will have an impact on the elimination of infectious diseases is worth further discussion and research.Therefore,three kinds of mathematical models are established in this dissertation:an infectious disease model with vaccine immuniza-tion failure,an age-structured infectious disease model with vaccine immunization fail-ure and a state-structured infectious disease model with vaccine immunization failure and quarantine.These three kinds of models not only consider the effect of vaccination for prevention and control the outbreak,but also study the effect of vaccine immuniza-tion failure on the spread of infectious diseases according to the characteristics of the infectivity and clinical symptoms of the patients with vaccine immunization failure.Therefore,the models in this dissertation can be used to describe the transmission process of virus among the population with different immune states,and they are suit-able to study some infectious diseases,such as,measles and influenza.Compared with previous research results,the models established in this dissertation are more flexible and more suitable for realistic situation.The models can study the impact of the vac-cinated population who produce specific antibodies but not permanently immunized on transmission of the virus.The models can predict the trend of infectious diseases,analyze the reasons for the persistence of the epidemic outbreaks,and give reasonable anti-epidemic measures.The structure of this dissertation are as follows:In the first chapter,we firstly introduce the research background and study mo-tivation of this dissertation,and then give a brief overview of some knowledge related to the dynamics of infectious diseases.In the second chapter,we assumed that everybody would have an immune response to vaccination.Based on the phenomenon of vaccination and vaccine immunization fail-ure,we establish an infectious disease model with the factors of vaccine immunization failure,and then analyze the dynamic behavior of this model.We use the next gen-eration matrix method to obtain the basic reproduction number R_?,and prove thatR_? is a threshold parameter through constructing a suitable Lyapunov function:when R_??1,the disease-free equilibrium is globally asymptotically stable.WhenR_?>1,the disease-free equilibrium is unstable and the endemic equilibrium is globally asymp-totically stable.Finally,we take measles outbreaks in Australia as an example,we use numerical simulation to study the impact of secondary vaccine failure caused by vaccination from herd immunity,the predicted number of new reported cases,popu-lation immune profile,and provide reasonable prevention advice for the public health department according to the discussion results.In the third chapter,we divide the population according to their age,and we establish an age-structured model with vaccine immunization failure.This model not only considers the impact of vaccination and vaccine immunization failure on infectious diseases,but also considers the heterogeneity of different age groups,so it is useful to study realistic problems.And then we analyze the dynamic behavior of this model.We use the next generation matrix method to obtain the basic reproduction numberR_?of the system,and prove thatR_?is a threshold parameter through constructing a suitable Lyapunov function:whenR_??1,the disease-free equilibrium is globally asymptotically stable.WhenR_?>1,the disease-free equilibrium is unstable and the endemic equilibrium is globally asymptotically stable.Finally,we take an infectious disease model with five age groups as an example,use numerical simulation to better illustrate the impact of vaccine immunization failure on number of new reported cases in the whole population and different age groups.According to the above results,the effects of different strategies of SIAs on epidemic prevention and control are discussed and studied.Reasonable suggestions for prevention were put forward which can provide theoretical basis for the elimination of infectious diseases.In the fourth chapter,as patients with vaccine immunization failure will lead to subclinical symptoms and weaker transmissibility,this phenomenon will increase the difficulty of clinical diagnosis.It is not possible to isolate the patients from the sus-ceptible people in time and increase the possibility of the spread of the virus.We establish a state-structured model with vaccine immunization failure and quarantine based on the situation of individuals'antibody levels.This model allows individuals to transfer among different states,which can reflect the antibody level states of different individuals at different times more accurately and depict the transmission process of virus among groups with different antibody level states.Then we analyze the dynamic behavior of this model.We use the next generation matrix method to obtain the basic reproduction numberR_?of the system,and prove thatR_?is a threshold parameter through constructing a suitable Lyapunov function:whenR_??1,the disease-free e-quilibrium is globally asymptotically stable.WhenR_?>1,the disease-free equilibrium is unstable and the endemic equilibrium is globally asymptotically stable.Finally,we take an infectious disease model with maternal immunity and quarantine as an exam-ple to illustrate the effect of vaccine immunization failure and quarantine on infectious diseases by numerical simulation.The results show that the phenomenon of vaccine immunization failure increases the difficulty of diagnosis,leads to an increase in the number of new reported cases,and has a negative impact on prevention and control work. |
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