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Qualitative Analyses and Numerical Simulation of Epidemic Dynamic Models by Pulse Effects

Author: WeiWei
Tutor: LiuShaoPing
School: Huazhong University of Science and Technology
Course: Computational Mathematics
Keywords: Impulsive Differential Epidemic Models Pulse Vaccination Pulse Remove Stability Periodic solution Numerical Simulation
CLC: R181.3
Type: Master's thesis
Year: 2006
Downloads: 153
Quote: 0
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Abstract


This paper considers the role of several infectious diseases in the pulse dynamics model discussed Pulse Vaccination Infectious Existence of Periodic Solutions and Stability , get the pulse removes Epidemic Model periodic solution under sufficient conditions for stability by numerical simulation conclusions full text of chapters divided into two parts , the first part consists of the second, third and fourth chapters discuss the pulse vaccination epidemic model under the second part consists of the fifth chapters discuss the role of the pulse removed epidemic model . article first consider a continuous and pulse immunization immunization SIQR epidemic model , were given their respective basic reproduction number ; utilization Dulac function method proved a continuous immune vaccination SIQR model of disease-free equilibrium global stability ; pulse immunization in infectious diseases under the SIQR model, discussed the existence of periodic solutions disease resistance, prove the global asymptotic stability of periodic solutions , and is continuous and pulse vaccination under SIQR epidemic Models compare the efficiency of vaccination . then studied pulse Vaccination with vertical transmission of SIR epidemic model , the model has been disease-free basic reproduction number and global stability of periodic solution a sufficient condition , and verified by numerical simulation of the conclusion . Moreover, also studied with pulse vaccination groups more susceptible epidemic model DS-IR analysis of the model without the existence of periodic solutions disease given for the spread of disease have important implications for the basic reproductive number , disease-free periodic solution obtained sufficient conditions for global stability . Finally, consider the effect of having a vertical pulse removing infected SIS epidemic model , the model proved the presence of disease-free equilibrium , access to basic reproductive number of the model , and analyzes the effect of pulsed with vertical transmission removed SIS Epidemic model infected individuals and populations of the total amount of asymptotic properties .

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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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