Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis
The effect of vaccination on the dengue fever epidemic described by an age structured modified SIR (Susceptible-Infected-Retired) model is studied using standard stability analysis. The chimeric yellow fever dengue tetravalent dengue vaccine (CYD-TDV™) is a vaccine recently developed to control this...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-03-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/6/904 |
| _version_ | 1797445396600979456 |
|---|---|
| author | Anusit Chamnan Puntani Pongsumpun I-Ming Tang Napasool Wongvanich |
| author_facet | Anusit Chamnan Puntani Pongsumpun I-Ming Tang Napasool Wongvanich |
| author_sort | Anusit Chamnan |
| collection | DOAJ |
| description | The effect of vaccination on the dengue fever epidemic described by an age structured modified SIR (Susceptible-Infected-Retired) model is studied using standard stability analysis. The chimeric yellow fever dengue tetravalent dengue vaccine (CYD-TDV™) is a vaccine recently developed to control this epidemic in several Southeast Asian countries. The dengue vaccination program requires a total of three injections, 6 months apart at 0, 6, and 12 months. The ages of the recipients are nine years and above. In this paper, we analyze the mathematical dynamics SIR transmission model of the epidemic. The stability of the model is established using Routh–Hurwitz criteria to see if a Hopf Bifurcation occurs and see when the equilibrium states are local asymptotically stable or global asymptotically stable. We have determined the efficiency of CYD-TDV by simulating the optimal numerical solution for each age range for this model. The numerical results showed the optimal age for vaccination and significantly reduced the severity and severity of the disease. |
| first_indexed | 2024-03-09T13:26:12Z |
| format | Article |
| id | doaj.art-564464ea64744a65ac72e31a6276afff |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T13:26:12Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-564464ea64744a65ac72e31a6276afff2023-11-30T21:23:49ZengMDPI AGMathematics2227-73902022-03-0110690410.3390/math10060904Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability AnalysisAnusit Chamnan0Puntani Pongsumpun1I-Ming Tang2Napasool Wongvanich3Department of Mathematics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, ThailandDepartment of Mathematics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, ThailandDepartment of Physics, Faculty of Science, Mahidol University, Bangkok 10400, ThailandDepartment of Instrumentation and Control Engineering, School of Engineering, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, ThailandThe effect of vaccination on the dengue fever epidemic described by an age structured modified SIR (Susceptible-Infected-Retired) model is studied using standard stability analysis. The chimeric yellow fever dengue tetravalent dengue vaccine (CYD-TDV™) is a vaccine recently developed to control this epidemic in several Southeast Asian countries. The dengue vaccination program requires a total of three injections, 6 months apart at 0, 6, and 12 months. The ages of the recipients are nine years and above. In this paper, we analyze the mathematical dynamics SIR transmission model of the epidemic. The stability of the model is established using Routh–Hurwitz criteria to see if a Hopf Bifurcation occurs and see when the equilibrium states are local asymptotically stable or global asymptotically stable. We have determined the efficiency of CYD-TDV by simulating the optimal numerical solution for each age range for this model. The numerical results showed the optimal age for vaccination and significantly reduced the severity and severity of the disease.https://www.mdpi.com/2227-7390/10/6/904dengue feverlocal stabilityglobal stabilityvaccination |
| spellingShingle | Anusit Chamnan Puntani Pongsumpun I-Ming Tang Napasool Wongvanich 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 dengue fever local stability global stability vaccination |
| title | Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis |
| title_full | Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis |
| title_fullStr | Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis |
| title_full_unstemmed | Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis |
| title_short | Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis |
| title_sort | effect of a vaccination against the dengue fever epidemic in an age structure population from the perspective of the local and global stability analysis |
| topic | dengue fever local stability global stability vaccination |
| url | https://www.mdpi.com/2227-7390/10/6/904 |
| work_keys_str_mv | AT anusitchamnan effectofavaccinationagainstthedenguefeverepidemicinanagestructurepopulationfromtheperspectiveofthelocalandglobalstabilityanalysis AT puntanipongsumpun effectofavaccinationagainstthedenguefeverepidemicinanagestructurepopulationfromtheperspectiveofthelocalandglobalstabilityanalysis AT imingtang effectofavaccinationagainstthedenguefeverepidemicinanagestructurepopulationfromtheperspectiveofthelocalandglobalstabilityanalysis AT napasoolwongvanich effectofavaccinationagainstthedenguefeverepidemicinanagestructurepopulationfromtheperspectiveofthelocalandglobalstabilityanalysis |