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Research on Age-structured Epidemic Models

Author: SuXiRong
Tutor: LiuSheng
School: Beijing Forestry University
Course: Biophysics
Keywords: Age structure Epidemic Model Reproduction number Stability
CLC: R181.3
Type: Master's thesis
Year: 2010
Downloads: 139
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Abstract


In this thesis epidemic model with age structure . The main purpose of the establishment of infectious disease model is a clear description of the impact of the spread of the disease biology and sociology mechanism . Use of the model , and then through the study of the model to reveal the laws of epidemics , predict trends , for the detection, prevention and control of the prevalence of the disease in accordance with policy. In this paper, the different characteristics of the spread of infectious diseases , the establishment of three categories epidemic model with age structure , are : the age and quarantine measures SEIQR model , the age structure of the hand, foot and mouth disease model and age structure and constant mobility SIR model . The three types of models are partial differential equations , this article use in infectious disease dynamics method and the theory of functions of a real variable theory model , model disease-free equilibrium and endemic equilibrium existence and stability conditions , and prove the basic reproduction number is less than 1 , the disease-free equilibrium is locally asymptotically stable ( or globally asymptotically stable ) , when the basic reproduction number greater than 1 , the endemic equilibrium under certain conditions locally asymptotically stable ( or model in the endemic equilibrium at the characteristic equation of the linearized system is nothing more than a negative real roots ) . Finally , on the basis of the above theoretical results , the solution of partial differential equations , numerical simulation model differential format , then the difference scheme of the model Matlab programming . Finally, the simulation model susceptible and infected trends . Process during the computer test , looking for greater impact of infectious diseases development by changing the values ??of various parameters , for later in life practice provides a good basis . The test results show that the two equilibrium states of the infectious disease model is closely related to the basic reproduction number . The basic reproduction number depends on the model parameters , we can control certain parameters to control the spread of infectious diseases . The innovation of this paper is reflected in the dynamics of infectious disease successfully applied to the age structure of the infectious disease model , and a more in-depth analysis of the endemic equilibrium model .

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CLC: > Medicine, health > Preventive Medicine,Health > Epidemiology and Prevention of Disease > Epidemiology of the basic theory and methods > Special epidemiological each
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