Evaluating vaccination and quarantine for measles intervention strategy in Jakarta, Indonesia through mathematical modeling
This article introduces a system of seven-dimensional nonlinear differential equations to analyze the influence of vaccination strategies on the spread of measles in Jakarta, using weekly incidence data for parameter estimation. Our dynamical analysis begins by determining the existence and stabilit...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-06-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818125001184 |
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| author | Dipo Aldila Abdullah Hasan Hassan Chidozie Williams Chukwu Stephane Yanick Tchoumi Muhamad Hifzhudin Noor Aziz |
| author_facet | Dipo Aldila Abdullah Hasan Hassan Chidozie Williams Chukwu Stephane Yanick Tchoumi Muhamad Hifzhudin Noor Aziz |
| author_sort | Dipo Aldila |
| collection | DOAJ |
| description | This article introduces a system of seven-dimensional nonlinear differential equations to analyze the influence of vaccination strategies on the spread of measles in Jakarta, using weekly incidence data for parameter estimation. Our dynamical analysis begins by determining the existence and stability of equilibrium states and calculating the basic reproduction number, denoted by R0. The analysis indicates that the disease-free equilibrium is globally asymptotically stable if R0<1. Conversely, the endemic equilibrium always persists and remains stable if R0>1. Next, we conduct a global sensitivity analysis using the Partial Rank Correlation Coefficient (PRCC) method integrated with Latin Hypercube Sampling (LHS). The results indicate that the initial-dose vaccination intervention plays the most critical role in reducing the reproduction number, highlighting its significant potential as a measles control strategy. Additionally, we extend the model into an optimal control problem framework to identify the most effective strategy for preventing measles spread while minimizing intervention costs. This control optimization is formulated using Pontryagin’s Maximum Principle and solved numerically through the forward–backward sweep method. The cost-effectiveness analysis indicates that a combination of vaccination and quarantine is the most effective strategy compared to other possible control measures. |
| format | Article |
| id | doaj-art-80d6bf70e6ee4b44a5a6ea0317686e24 |
| institution | OA Journals |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-80d6bf70e6ee4b44a5a6ea0317686e242025-08-20T02:29:43ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-06-011410119110.1016/j.padiff.2025.101191Evaluating vaccination and quarantine for measles intervention strategy in Jakarta, Indonesia through mathematical modelingDipo Aldila0Abdullah Hasan Hassan1Chidozie Williams Chukwu2Stephane Yanick Tchoumi3Muhamad Hifzhudin Noor Aziz4Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok 16424, Indonesia; Corresponding author.Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok 16424, IndonesiaDepartment of Mathematical Sciences, DePaul University, Chicago, IL 60614, USADepartment of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa; Department of Mathematics and Computer Sciences ENSAI, University of Ngaoundere, Ngaoundere, CameroonInstitute of Mathematical Sciences, Faculty of Science, Universiti Malaya, 50603 Kuala Lumpur, MalaysiaThis article introduces a system of seven-dimensional nonlinear differential equations to analyze the influence of vaccination strategies on the spread of measles in Jakarta, using weekly incidence data for parameter estimation. Our dynamical analysis begins by determining the existence and stability of equilibrium states and calculating the basic reproduction number, denoted by R0. The analysis indicates that the disease-free equilibrium is globally asymptotically stable if R0<1. Conversely, the endemic equilibrium always persists and remains stable if R0>1. Next, we conduct a global sensitivity analysis using the Partial Rank Correlation Coefficient (PRCC) method integrated with Latin Hypercube Sampling (LHS). The results indicate that the initial-dose vaccination intervention plays the most critical role in reducing the reproduction number, highlighting its significant potential as a measles control strategy. Additionally, we extend the model into an optimal control problem framework to identify the most effective strategy for preventing measles spread while minimizing intervention costs. This control optimization is formulated using Pontryagin’s Maximum Principle and solved numerically through the forward–backward sweep method. The cost-effectiveness analysis indicates that a combination of vaccination and quarantine is the most effective strategy compared to other possible control measures.http://www.sciencedirect.com/science/article/pii/S2666818125001184MeaslesBasic reproduction numberVaccinationQuarantineJakartaOptimal control |
| spellingShingle | Dipo Aldila Abdullah Hasan Hassan Chidozie Williams Chukwu Stephane Yanick Tchoumi Muhamad Hifzhudin Noor Aziz Evaluating vaccination and quarantine for measles intervention strategy in Jakarta, Indonesia through mathematical modeling Partial Differential Equations in Applied Mathematics Measles Basic reproduction number Vaccination Quarantine Jakarta Optimal control |
| title | Evaluating vaccination and quarantine for measles intervention strategy in Jakarta, Indonesia through mathematical modeling |
| title_full | Evaluating vaccination and quarantine for measles intervention strategy in Jakarta, Indonesia through mathematical modeling |
| title_fullStr | Evaluating vaccination and quarantine for measles intervention strategy in Jakarta, Indonesia through mathematical modeling |
| title_full_unstemmed | Evaluating vaccination and quarantine for measles intervention strategy in Jakarta, Indonesia through mathematical modeling |
| title_short | Evaluating vaccination and quarantine for measles intervention strategy in Jakarta, Indonesia through mathematical modeling |
| title_sort | evaluating vaccination and quarantine for measles intervention strategy in jakarta indonesia through mathematical modeling |
| topic | Measles Basic reproduction number Vaccination Quarantine Jakarta Optimal control |
| url | http://www.sciencedirect.com/science/article/pii/S2666818125001184 |
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