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The Analysis on Identifiablity and Stability of SIR Epidemic Models

Author: LiuGuanJun
Tutor: LiuHeLong
School: Xinyang Normal University
Course: Applied Mathematics
Keywords: Structure identification Impulsive Differential Age of infection Pulse period Disease - free equilibrium Optimal immunization strategy
CLC: O242.1
Type: Master's thesis
Year: 2011
Downloads: 40
Quote: 0
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Abstract


This paper studies the SIR epidemic model identification problem with medication , and has pulse immunization and class age structure SIR Epidemic Model SIR Epidemic Model with medication first structure identification , through the identification the existence of analysis can cause the same amount of output infinite dimensional parameter vector , that model is not identifiable . analysis shows that in the case of all the parameters are unknown , the model to estimate the proportion of infection between susceptible class with infection class not appropriate , but the model can still recognize the basic reproductive number R0 followed by discussion of the control of infectious diseases pulse immunization strategy rely on the individual's physiological age and infection age characteristics of the spread of the disease , the age structure of the SIR epidemic model model including susceptible individuals with the rehabilitation of individuals depends on the physiological age depends on the age of infection ( infection duration ) of infected individuals . analysis shows that , if the pulse period T and inoculation ratio p satisfies R0 ( p , T) lt ; disease-free equilibrium is globally stable . concludes with a discussion of the problem of optimal immunization strategy .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Mathematical modeling, approximate calculation > Mathematical modeling
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