| Citation: |
Chong-Yang Yin, Xin-You Meng, Jia-Ming Zuo. MODELING THE EFFECTS OF VACCINATING STRATEGIES AND PERIODIC OUTBREAKS ON DENGUE IN SINGAPORE[J]. Journal of Applied Analysis & Computation, 2025, 15(3): 1284-1309. doi: 10.11948/20240205
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MODELING THE EFFECTS OF VACCINATING STRATEGIES AND PERIODIC OUTBREAKS ON DENGUE IN SINGAPORE
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Abstract
Effective vaccination strategies can significantly reduce virus transmission, while periodic outbreaks require model prediction and early intervention to mitigate their impact. A novel dengue epidemic model with periodicity and vaccination is introduced in this paper. First, the positivity of solutions and the invariant set are given, and the basic reproduction number is obtained. Then, the disease-free periodic solution is globally asymptotically stable when the basic reproduction number is less than one, and periodic solution is consistent persistence when the basic reproduction number is more than one. Actual data are used to develop more scientific and reasonable prevention and control measures, reducing the transmission risk of dengue fever. Next, based on the dengue fever data in Singapore from 2014 to 2017, the best fitting parameters of such model are determined by using the Markov Chain Monte Carlo algorithm. Finally, some numerical simulations are carried out. These indicate that vaccination is of great significance to control the spread of disease.
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Keywords:
- Dengue /
- disease extinction /
- vaccination /
- periodicity /
- consistent persistence
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References
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Chong-Yang Yin, Xin-You Meng, Jia-Ming Zuo. MODELING THE EFFECTS OF VACCINATING STRATEGIES AND PERIODIC OUTBREAKS ON DENGUE IN SINGAPORE[J]. Journal of Applied Analysis & Computation, 2025, 15(3): 1284-1309. doi: 10.11948/20240205
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Figure 1.
Flowchart of the dengue epidemic model.
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Figure 2.
The global stability of the disease-free periodic solution. (a)
$ S(t) $ $ V(t) $ $ E(t) $ $ A(t) $ $ I(t) $ $ R(t) $ -
Figure 3.
The global stability of the disease-free periodic solution. (a)
$ S(t) $ $ V(t) $ $ E(t) $ $ A(t) $ $ I(t) $ $ R(t) $ -
Figure 4.
The fitting results from January 2014 to April 2017. (a) The number of new cases reported, (b) The number of cumulative reported.
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Figure 5.
The basic reproduction number of
$ R_{0} $ $ R_{0} $ $ R_{0} $ $ R_{0} $ $ R_{0} $ -
Figure 6.
Plot of the output (1000 runs) of model (4.1). The ordinate represents variable I(t), and the abscissa represents time (weeks).
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Figure 7.
The sensitivity of the parameters changes as the dynamics of model (4.1) progress.
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Figure 8.
P values of each parameter on the 80th days. (a)
$ \Lambda $ $ \Pi $ $ \gamma_{a} $ $ \theta $ $ \delta $ -
Figure 9.
The impact of infection rates
$ \beta(t) $ $ \rho(t) $ $ \beta(t) $ $ \rho(t) $ -
Figure 10.
The number of the reported infected individuals with different vaccination. (a) 50%, (b) 80%.