Global stability mathematical analysis for virus transmission model with latent age structure
1School of Mathematics and Big Data, Guizhou Education University, Guiyang 550018, China.
Mathematical Biosciences and Engineering : MBE
|March 28, 2022
Summary
Mathematical models incorporating fast and slow disease progression aid in understanding transmission. Vaccination reduces the disease threshold, proving effective for controlling epidemics like Coronavirus.
Area of Science:
- Epidemiology
- Mathematical Biology
- Disease Modeling
Background:
- Mathematical models are crucial for disease control.
- Incorporating fast and slow disease progression enhances transmission mechanism representation.
- Understanding disease dynamics requires advanced modeling techniques.
Purpose of the Study:
- To propose and analyze an age-structured epidemic model with fast and slow progression.
- To investigate the dynamic properties of infectious disease transmission.
- To evaluate the impact of disease progression rates on epidemiological thresholds.
Main Methods:
- Development of an age-structured epidemic model.
- Application of stability theory for differential equations.
- Analysis of global stability for disease-free and endemic equilibria using Lyapunov functions.
- Numerical simulations to validate theoretical findings.
Main Results:
- Calculation of the basic reproduction number (R₀).
- Demonstration of global asymptotic stability for disease-free equilibrium when R₀ < 1.
- Proof of global stability for endemic equilibrium when R₀ > 1.
- Finding that a higher slow progression rate reduces the epidemiological threshold.
Conclusions:
- Vaccination, while not providing lifelong immunity, reduces mortality and the disease threshold.
- Vaccination effectively controls disease transmission, including Coronavirus.
- Mathematical models provide theoretical evidence for epidemic prevention and control strategies.
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