| Citation: |
Rong Liu, Guirong Liu. ANALYSIS OF A STOCHASTIC SIS EPIDEMIC MODEL WITH TRANSPORT-RELATED INFECTION[J]. Journal of Applied Analysis & Computation, 2021, 11(3): 1296-1321. doi: 10.11948/20200157
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ANALYSIS OF A STOCHASTIC SIS EPIDEMIC MODEL WITH TRANSPORT-RELATED INFECTION
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Abstract
In this paper, we consider a stochastic SIS epidemic model with transport-related infection, which is proposed to investigate the dynamics of disease propagation between two regions. Firstly, we show that the model has a unique global positive solution. Next, the properties of the solution are studied. Especially, by constructing a suitable positive-definite decrescent radially unbounded function and stopping times, we show that the differences between susceptible populations or infected populations in two regions will disappear with probability one. Then we show that the diseases in each region is extinct and the susceptible in each region is stable in the mean. Moreover, we prove that the model has a stationary distribution and the solution has the ergodic property. At last, some numerical simulations are introduced to justify the analytical results.
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References
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Rong Liu, Guirong Liu. ANALYSIS OF A STOCHASTIC SIS EPIDEMIC MODEL WITH TRANSPORT-RELATED INFECTION[J]. Journal of Applied Analysis & Computation, 2021, 11(3): 1296-1321. doi: 10.11948/20200157
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Figure 1. The differences between susceptible populations or infected populations in two cities of model (1.2) with
$ \sigma_{1}^{2} = 0.1 $ and$ \sigma_{2}^{2} = 0.1 $ . - Figure 2. Numerical simulation of deterministic model (1.1).
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Figure 3. Numerical simulation of model (1.2) with
$ \sigma_{1}^{2} = 0.1 $ and$ \sigma_{2}^{2} = 0.4 $ . -
Figure 4. Numerical simulation of model (1.2) with
$ \sigma_{1}^{2} = 0.02 $ and$ \sigma_{2}^{2} = 0.03 $ . -
Figure 5. The density functions of
$ S(t) $ and$ I(t) $ in (4.2) at$ t = 30000 $ with$ (S_{0}, I_{0}) = (2.4, 0.2) $ and$ (S_{0}, I_{0}) = (2, 0.5) $ . (a) the density of$ S(t) $ ; (b) the density of$ I(t) $ . -
Figure 6. The density functions of
$ S_{1}(t) $ ,$ S_{2}(t) $ ,$ I_{1}(t) $ and$ I_{2}(t) $ in model (1.2) at$ t = 30000 $ with$ (S_{10}, I_{10}, S_{20}, I_{20}) = (2.4, 0.2, 2, 0.5) $ . (a) the density functions of$ S_{1}(t) $ and$ S_{2}(t) $ ; (b) the density functions of$ I_{1}(t) $ and$ I_{2}(t) $ .