Threshold Analysis and Stationary Distribution of a Stochastic Model with Relapse and Temporary Immunity
Abstract
:1. Introduction
2. Existence and Uniqueness of the Global Positive Solution
3. Extinction of the Disease
4. Persistence in the Mean
5. Existence of a Stationary Distribution
- If . In this case, we choose and a to be sufficiently small, such that
- If and , we choose to be sufficiently small, such that
- If and , we choose to be sufficiently close to 1, such that
- If and , we choose to be sufficiently close to 1 and a to be sufficiently small, such that
6. Numerical Simulations
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Liu, P.; Meng, X.; Qi, H. Threshold Analysis and Stationary Distribution of a Stochastic Model with Relapse and Temporary Immunity. Symmetry 2020, 12, 331. https://doi.org/10.3390/sym12030331
Liu P, Meng X, Qi H. Threshold Analysis and Stationary Distribution of a Stochastic Model with Relapse and Temporary Immunity. Symmetry. 2020; 12(3):331. https://doi.org/10.3390/sym12030331
Chicago/Turabian StyleLiu, Peng, Xinzhu Meng, and Haokun Qi. 2020. "Threshold Analysis and Stationary Distribution of a Stochastic Model with Relapse and Temporary Immunity" Symmetry 12, no. 3: 331. https://doi.org/10.3390/sym12030331