Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis
Abstract
:1. Introduction
2. Methodology
2.1. Mathematical Model
The Non-Negativeness of the Solutions
2.2. Stability Analysis
2.2.1. Steady States and Basic Reproduction Number
2.2.2. Local and Global Stabilities
2.2.3. Bifurcation Analysis
2.2.4. Sensitivity Analysis
3. Numerical Results
4. Discussion and Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Variable and Parameters | References |
---|---|
The number of the susceptible human populations | |
The number of the infected human populations | |
The number of the recovered human populations | |
The number of the susceptible human population with vaccines | |
The number of the infected human population with vaccines | |
The number of the susceptible vector populations | |
The number of the infected vector populations | |
Transmission rate of dengue virus from human to vector | |
Constant recruitment rate of vector populations | |
Birth rate of the human populations | |
Natural mortality rate of the human populations | |
Natural mortality rate of the vector populations | |
Mortality rate from the infected of the human populations | |
Mortality rate from the infected of the vector populations | |
Total human populations | |
Total vector populations |
Parameters | Sensitivity Indices |
---|---|
0.50000 | |
0.50000 | |
0.50000 | |
0.00010 | |
0.18643 | |
−0.01736 | |
−0.03510 | |
−0.00660 | |
0.17551 | |
0.11116 | |
0.21333 | |
0.26206 | |
0.34021 | |
0.21120 |
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Chamnan, A.; Pongsumpun, P.; Tang, I.-M.; Wongvanich, N. Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis. Mathematics 2022, 10, 904. https://doi.org/10.3390/math10060904
Chamnan A, Pongsumpun P, Tang I-M, Wongvanich N. Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis. Mathematics. 2022; 10(6):904. https://doi.org/10.3390/math10060904
Chicago/Turabian StyleChamnan, Anusit, Puntani Pongsumpun, I-Ming Tang, and Napasool Wongvanich. 2022. "Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis" Mathematics 10, no. 6: 904. https://doi.org/10.3390/math10060904
APA StyleChamnan, A., Pongsumpun, P., Tang, I.-M., & Wongvanich, N. (2022). Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis. Mathematics, 10(6), 904. https://doi.org/10.3390/math10060904