The stochastic bifurcation analysis and stochastic delayed optimal control for epidemic model with general incidence
1Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, People's Republic of China.
Chaos (Woodbury, N.Y.)
|January 1, 2022
Summary
This study models contagious disease spread using a delayed stochastic epidemic model. Mathematical analysis and simulations show that noise and time delays are crucial for controlling epidemics and preventing disease extinction.
Area of Science:
- Epidemiology
- Mathematical Biology
- Stochastic Processes
Background:
- Contagious diseases pose significant global health threats.
- Understanding disease dynamics requires advanced mathematical modeling.
- Time delays and stochasticity are key factors in epidemic behavior.
Purpose of the Study:
- To investigate contagious disease spread using a delayed stochastic epidemic model.
- To analyze the conditions for disease permanence and extinction.
- To explore the role of noise and time delays in epidemic control.
Main Methods:
- Developed a delayed stochastic epidemic model with general incidence and cross-immunity.
- Proved mathematical and biological well-posedness of the model.
- Derived conditions for disease permanence/extinction and existence of stationary distribution.
- Performed quantitative analysis of periodic solutions and implemented numerical simulations in MATLAB.
Main Results:
- Established conditions for disease permanence and extinction.
- Identified sufficient conditions for an ergodic stationary distribution.
- Quantitatively analyzed non-zero periodic solutions.
- Numerical simulations demonstrated the crucial role of noise in epidemic control, with extinction directly proportional to noise magnitude.
Conclusions:
- The delayed stochastic epidemic model provides a robust framework for studying chronic infections.
- Noise magnitude is directly proportional to disease extinction.
- Time delays are essential for understanding recurring epidemic dynamics.
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