| Citation: |
Yifan Xing, Liang Zhang, Xinghao Wang. MODELLING AND STABILITY OF EPIDEMIC MODEL WITH FREE-LIVING PATHOGENS GROWING IN THE ENVIRONMENT[J]. Journal of Applied Analysis & Computation, 2020, 10(1): 55-70. doi: 10.11948/20180269
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MODELLING AND STABILITY OF EPIDEMIC MODEL WITH FREE-LIVING PATHOGENS GROWING IN THE ENVIRONMENT
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Abstract
To understand the impact of free-living pathogens (FLP) on the epidemics, an epidemic model with FLP is constructed. The global dynamics of our model are determined by the basic reproduction number $R_0$. If $R_0<1$, the disease free equilibrium is globally asymptotically stable, and if $R_0>1$, the endemic equilibrium is globally asymptotically stable. Some numerical simulations are also carried out to illustrate our analytical results.-
Keywords:
- Epidemics /
- free-living pathogen /
- basic reproduction number /
- global stability
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References
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Yifan Xing, Liang Zhang, Xinghao Wang. MODELLING AND STABILITY OF EPIDEMIC MODEL WITH FREE-LIVING PATHOGENS GROWING IN THE ENVIRONMENT[J]. Journal of Applied Analysis & Computation, 2020, 10(1): 55-70. doi: 10.11948/20180269
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- Figure 1. Transfer diagram for the dynamics of epidemic model with FLP.
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Figure 2. the graphs of functions
$ I = \psi(P) $ and$ P = \phi(I). $ -
Figure 6. When
$ \alpha\neq0 $ , the endemic equilibrium$ E^* $ is globally asymptotically stable. -
Figure 3. The disease free equilibrium
$ E_0 $ is globally asymptotically stable. -
Figure 4. When
$ \alpha = 0 $ , the endemic equilibrium$ E^* $ is globally asymptotically stable. - Figure 5. Local amplification of Figure 4
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Figure 7. The relationship among
$ R_0 $ and some parameter values -
Figure 8. The relationship among
$ R_0 $ ,$ r $ and$ \gamma $ -
Figure 9. The relationship among
$ R_0 $ ,$ \delta $ and$ \gamma $ -
Figure 10. The relationship among
$ R_0 $ ,$ \delta $ and$ r $ -
Figure 11. The relationship among
$ R_0 $ ,$ \beta $ and$ \delta $