Sveir epidemiological model with varying infectivity and distributed delays
Jinliang Wang1, Gang Huang, Yasuhiro Takeuchi
1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China. jinliangwang@hit.edu.cn
Mathematical Biosciences and Engineering : MBE
|June 17, 2011
Summary
This study introduces a vaccination compartment into an SEIR model, creating an SVEIR model. Mathematical analysis shows vaccination can control disease spread by reducing the basic reproduction number, but successful eradication depends on vaccine efficacy timelines.
Area of Science:
- Epidemiology
- Mathematical Biology
- Public Health Modeling
Background:
- SEIR (Susceptible-Exposed-Infectious-Recovered) models are foundational in understanding infectious disease dynamics.
- Incorporating vaccination is crucial for evaluating disease control strategies.
- Distributed delays are essential for accurately modeling varying infectivity periods.
Purpose of the Study:
- To develop an SVEIR (Susceptible-Vaccinated-Exposed-Infectious-Recovered) epidemiological model.
- To analyze the global asymptotic stability of disease-free and endemic equilibria.
- To investigate the impact of vaccination on disease eradication.
Main Methods:
- Utilized direct Lyapunov method and LaSalle's invariance principle.
- Constructed functionals integrating over past states for stability analysis.
- Determined stability conditions based on the basic reproduction number R(V)(0).
Main Results:
- Established conditions for global asymptotic stability of both disease-free and endemic equilibria.
- Demonstrated that R(V)(0) ≤ 1 leads to disease eradication, while R(V)(0) > 1 results in a stable endemic state.
- Indicated that vaccination effectively decreases the basic reproduction number.
Conclusions:
- Vaccination is a valuable tool for infectious disease control.
- Successful disease elimination requires specific conditions related to vaccine immunity acquisition time and pre-immunity infection risk.
- Overestimation of vaccination's impact may occur if these conditions are simplified.
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