The Influence of Lévy Noise and Independent Jumps on the Dynamics of a Stochastic COVID-19 Model with Immune Response and Intracellular Transmission
Abstract
1. Introduction
2. Model Formulation
3. Existence and Uniqueness
- .
- such that
- .
- for where C is a positive constant.
4. Extinction
5. Persistence
6. Numerical Analysis
6.1. Milstein Scheme with Jumps
6.2. Numerical Simulation of Extinction
6.3. Numerical Simulation of Persistence
6.4. Effects of Lévy Noise
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter | Description |
---|---|
The size of the vulnerable population at time t | |
Denote the size of the infected individuals at time t which are not yet infectious | |
Size of the infected compartment at time t | |
At time t, the quarantined individuals | |
Recovered individuals at time t | |
b | Birth rate or recruitment into the susceptible population |
Transmission rate of the infection | |
Modification factor accounting for enhanced transmission due to increased contact | |
Natural mortality rate | |
Rate of progression from infected to quarantined individuals | |
Rate of progression from exposed to quarantined individuals | |
Rate of direct transition from susceptible to quarantined individuals | |
Rate of natural immunity acquisition from susceptible individuals | |
Rate of progression from exposed to infectious individuals | |
Rate of disease-induced mortality in infected individuals | |
Recovery rate from infection | |
Transition rate from quarantined to recovered individuals | |
Total number of individuals at any time t, defined as |
Parameter | Set 1 | Set 2 |
---|---|---|
500 | 1000 | |
20 | 50 | |
10 | 30 | |
5 | 15 | |
0 | 5 | |
b | 0.02 | 0.03 |
0.5 | 0.7 | |
0.1 | 0.15 | |
0.01 | 0.02 | |
0.05 | 0.07 | |
0.03 | 0.05 | |
0.02 | 0.03 | |
0.01 | 0.02 | |
0.2 | 0.25 | |
0.03 | 0.04 | |
0.1 | 0.15 | |
0.08 | 0.1 | |
535 | 1100 |
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Song, Y.; Liu, P.; Din, A. The Influence of Lévy Noise and Independent Jumps on the Dynamics of a Stochastic COVID-19 Model with Immune Response and Intracellular Transmission. Fractal Fract. 2025, 9, 306. https://doi.org/10.3390/fractalfract9050306
Song Y, Liu P, Din A. The Influence of Lévy Noise and Independent Jumps on the Dynamics of a Stochastic COVID-19 Model with Immune Response and Intracellular Transmission. Fractal and Fractional. 2025; 9(5):306. https://doi.org/10.3390/fractalfract9050306
Chicago/Turabian StyleSong, Yuqin, Peijiang Liu, and Anwarud Din. 2025. "The Influence of Lévy Noise and Independent Jumps on the Dynamics of a Stochastic COVID-19 Model with Immune Response and Intracellular Transmission" Fractal and Fractional 9, no. 5: 306. https://doi.org/10.3390/fractalfract9050306
APA StyleSong, Y., Liu, P., & Din, A. (2025). The Influence of Lévy Noise and Independent Jumps on the Dynamics of a Stochastic COVID-19 Model with Immune Response and Intracellular Transmission. Fractal and Fractional, 9(5), 306. https://doi.org/10.3390/fractalfract9050306