The global dynamics for a stochastic SIS epidemic model with isolation
Yiliang Chen1, Buyu Wen1, Zhidong Teng1
1College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, People's Republic of China.
Physica A
|April 15, 2020
Summary
This study analyzes a stochastic Susceptible-Infectious-Susceptible (SIS) epidemic model with isolation. Results show a critical threshold determines disease extinction or persistence, with a unique stationary distribution proven to exist.
Area of Science:
- Epidemiology
- Mathematical Biology
- Stochastic Processes
Background:
- Infectious disease modeling is crucial for public health.
- Isolation is a key strategy for disease control.
- Stochastic effects can significantly alter epidemic dynamics.
Purpose of the Study:
- To investigate the dynamical behavior of a stochastic SIS epidemic model incorporating isolation.
- To analyze the impact of stochastic fluctuations on disease transmission and control.
Main Methods:
- Stochastic differential equations were used to model the epidemic.
- Lyapunov function method was employed to establish conditions for stability.
- Analysis of threshold dynamics for disease extinction and persistence.
Main Results:
- A critical threshold value determines disease extinction or persistence in the mean.
- If the threshold is below a certain value, the disease dies out.
- If the threshold exceeds this value, the disease persists stochastically.
- Existence and uniqueness of a stationary distribution were proven.
Conclusions:
- The stochastic SIS model with isolation exhibits predictable dynamics based on a threshold.
- Isolation strategy effectiveness is influenced by stochastic fluctuations.
- The model provides insights into disease control under uncertainty.
Keywords:
ExtinctionPersistence in the meanStationary distributionStochastic SIQS epidemic modelThreshold valueMore Related Videos
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