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Threshold dynamics of a time periodic and two--group epidemic model with distributed delay
Lin Zhao1, Zhi-Cheng Wang1, Liang Zhang1
1School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China
Mathematical Biosciences and Engineering : MBE
|November 23, 2017
Summary
This study introduces a reaction-diffusion epidemic model with distributed delay. The basic reproduction number (R0) determines disease persistence or extinction, with R0>1 leading to uniform persistence.
Area of Science:
- Mathematical epidemiology
- Reaction-diffusion systems
- Epidemic modeling
Background:
- Epidemic models are crucial for understanding disease dynamics.
- Reaction-diffusion models incorporate spatial spread.
- Distributed delays add complexity to disease transmission.
Purpose of the Study:
- To propose and investigate a time-periodic, two-group reaction-diffusion epidemic model with distributed delay.
- To analyze the threshold dynamics governing disease persistence and extinction.
Main Methods:
- Introduction of the basic reproduction number (R0) using the next-generation operator method.
- Establishment of threshold dynamics based on R0 values.
- Analysis of global dynamics in a special case with constant coefficients.
Main Results:
- The basic reproduction number (R0) was successfully introduced.
- Uniform persistence of the disease is established for R0 > 1.
- Disease extinction is proven for R0 < 1.
Conclusions:
- The model exhibits clear threshold dynamics determined by R0.
- The findings provide insights into the spatial and temporal spread of diseases.
- The study contributes to the theoretical understanding of complex epidemic models.
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