TY - JOUR
T1 - Stochastic SIRC epidemic model with time-delay for COVID-19
AU - Rihan, F. A.
AU - Alsakaji, H. J.
AU - Rajivganthi, C.
N1 - Funding Information:
This work is generously funded by PhD Program and UPAR Project (G00003440), United Arab Emirates University (UAE). Acknowledgements Availability of data and materials
Publisher Copyright:
© 2020, The Author(s).
PY - 2020/12/1
Y1 - 2020/12/1
N2 - Environmental factors, such as humidity, precipitation, and temperature, have significant impacts on the spread of the new strain coronavirus COVID-19 to humans. In this paper, we use a stochastic epidemic SIRC model, with cross-immune class and time-delay in transmission terms, for the spread of COVID-19. We analyze the model and prove the existence and uniqueness of positive global solution. We deduce the basic reproduction number R0s for the stochastic model which is smaller than R of the corresponding deterministic model. Sufficient conditions that guarantee the existence of a unique ergodic stationary distribution, using the stochastic Lyapunov function, and conditions for the extinction of the disease are obtained. Our findings show that white noise plays an important part in controlling the spread of the disease; When the white noise is relatively large, the infectious diseases will become extinct; Re-infection and periodic outbreaks can occur due to the existence of feedback time-delay (or memory) in the transmission terms.
AB - Environmental factors, such as humidity, precipitation, and temperature, have significant impacts on the spread of the new strain coronavirus COVID-19 to humans. In this paper, we use a stochastic epidemic SIRC model, with cross-immune class and time-delay in transmission terms, for the spread of COVID-19. We analyze the model and prove the existence and uniqueness of positive global solution. We deduce the basic reproduction number R0s for the stochastic model which is smaller than R of the corresponding deterministic model. Sufficient conditions that guarantee the existence of a unique ergodic stationary distribution, using the stochastic Lyapunov function, and conditions for the extinction of the disease are obtained. Our findings show that white noise plays an important part in controlling the spread of the disease; When the white noise is relatively large, the infectious diseases will become extinct; Re-infection and periodic outbreaks can occur due to the existence of feedback time-delay (or memory) in the transmission terms.
KW - Brownian motion
KW - COVID-19
KW - Cross-immunity
KW - Extinction
KW - Stationary distribution
KW - Stochastic SIRC model
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U2 - 10.1186/s13662-020-02964-8
DO - 10.1186/s13662-020-02964-8
M3 - Article
AN - SCOPUS:85091205080
SN - 1687-1839
VL - 2020
JO - Advances in Difference Equations
JF - Advances in Difference Equations
IS - 1
M1 - 502
ER -