| Citation: |
Qigui Yang, Jiabing Huang. A STOCHASTIC MULTI-SCALE COVID-19 MODEL WITH INTERVAL PARAMETERS[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 515-542. doi: 10.11948/20230298
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A STOCHASTIC MULTI-SCALE COVID-19 MODEL WITH INTERVAL PARAMETERS
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Abstract
A stochastic multi-scale COVID-19 model that coupling within-host and between-host dynamics with interval parameters is established. The model is composed of a within-host fast model and a between-host slow stochastic model. The dynamics of fast model can be governed by basic reproduction number $ R_{0w} $. The uninfected equilibrium $ E_{0w} $ is globally asymptotically stable (g.a.s) when $ R_{0w}<1 $, but infected equilibrium $ E_{fast}^{*} $ is g.a.s when $ R_{0w}>1 $. The dynamics of the coupling slow stochastic model can be governed by stochastic threshold $ R_{s} $. The disease will die out when $ R_{s}<1 $ and will persistent in mean when $ R_{s}>1 $. One finds that $ R_{s} $ is an increasing function of $ R_{0w} $. Further, some numerical simulations are presented to demonstrate the results and reveal that the dynamics of the slow stochastic model are approximate to the stochastic multi-scale model. It provides us a method to investigate the stochastic multi-scale model. Furthermore, some effective measures are given to control the COVID-19. Moreover, our work contributes basic understandings of coupling within-host and between-host models with interval parameters and environmental noises.
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Keywords:
- COVID-19 /
- stochastic multi-scale /
- interval parameter /
- stochastic threshold /
- persistence in mean
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References
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Qigui Yang, Jiabing Huang. A STOCHASTIC MULTI-SCALE COVID-19 MODEL WITH INTERVAL PARAMETERS[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 515-542. doi: 10.11948/20230298
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Figure 1.
(a) Fitting the deterministic model (1.2) to the real data in Hongkong: the number of COVID-19 infected person; (b) Variation of
$ R_{0b} $ $ R_{s} $ $ k $ $ [\sigma_{i}^{l}, \sigma_{i}^{u}]=[0.2, 0.3], \, ( i=1, 2, 3) $ -
Figure 2.
(a) Times series of
$ I(t) $ $ Q(t) $ $ S(t) $ $ [\sigma_{i}^{l}, \sigma_{i}^{u}]=[0.003, 0.01], \, (i=1, 2, 3) $ $ (S(0), I(0), Q(0))=(7413070, 200, 145) $ -
Figure 3.
(a) Times series of
$ I(t) $ $ Q(t) $ $ S(t) $ $ [\delta ^{l}, \delta ^{u}]=[0.3, 0.4] $ $ [\sigma_{i}^{l}, \sigma_{i}^{u}]=[0.003, 0.01], \, (i=1, 2, 3) $ $ (S(0), I(0), Q(0))=(7413070, 200, 145) $ -
Figure 4.
(a) Times series of
$ I(t) $ $ Q(t) $ $ S(t) $ $ [\beta_{w}^{l}, \beta_{w}^{u}]=[0.01, 0.05] $ $ (S(0), I(0), Q(0))=(7413070, 200, 145) $ -
Figure 5.
(a) Times series of
$ I(t) $ $ Q(t) $ $ S(t) $ $ [\pi_{\nu}^{l}, \pi_{\nu}^{u}]=[0.0192, 0.0288] $ $ (S(0), I(0), Q(0))=(7413070, 200, 145) $ -
Figure 6.
(a) Variation of
$ R_{0b} $ $ R_{s} $ $ R_{0w} $ $ [\sigma_{i}^{l}, \sigma_{i}^{u}]=[0.2, 0.3], \, ( i=1, 2, 3) $