{"title":"Mathematical insights into mumps transmission control with optimal strategies","authors":"Stephen Edward, Alberto Kimbuya Mathias","doi":"10.1016/j.idm.2025.06.007","DOIUrl":null,"url":null,"abstract":"<div><div>In this study, we develop an optimal control framework for managing mumps infections through a dynamic model that integrates public health interventions such as awareness programs, isolation protocols, and a two-dose immunization regimen. We begin by establishing the model's fundamental analytical properties, including the existence and stability of disease equilibria, the positivity and boundedness of solutions, and a threshold condition for disease transmission. Local stability analysis is conducted via the Routh-Hurwitz criteria, ensuring robust insights into the disease dynamics. The optimal control problem is formulated and analyzed using Pontryagin's Maximum Principle, which facilitates the derivation of optimal interventions. Numerical simulations are conducted to assess various control strategies and compare the effectiveness of single and combined interventions. Our results indicate that a balanced solution is key to effective disease mitigation. A comprehensive approach employing all four controls: awareness, isolation, primary and booster vaccination, is the most effective strategy. Moreover, strategies that incorporate vaccination consistently outperform those without. Interestingly, a three-control strategy closely approximates the effectiveness of the full four-control intervention, suggesting a cost-effective alternative for practical implementation. While the four-control strategy may incur higher implementation costs, the three-control strategy offers a balanced solution, achieving substantial disease reduction while optimizing resource allocation. Our findings underscore the crucial role of vaccination in mumps control. They offer valuable insights for policymakers, emphasizing the need to balance economic considerations with public health outcomes. Vaccination, as our study demonstrates, is a cornerstone of any effective mumps control strategy.</div></div>","PeriodicalId":36831,"journal":{"name":"Infectious Disease Modelling","volume":"10 4","pages":"Pages 1208-1228"},"PeriodicalIF":8.8000,"publicationDate":"2025-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Infectious Disease Modelling","FirstCategoryId":"3","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2468042725000570","RegionNum":3,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Medicine","Score":null,"Total":0}
引用次数: 0
Abstract
In this study, we develop an optimal control framework for managing mumps infections through a dynamic model that integrates public health interventions such as awareness programs, isolation protocols, and a two-dose immunization regimen. We begin by establishing the model's fundamental analytical properties, including the existence and stability of disease equilibria, the positivity and boundedness of solutions, and a threshold condition for disease transmission. Local stability analysis is conducted via the Routh-Hurwitz criteria, ensuring robust insights into the disease dynamics. The optimal control problem is formulated and analyzed using Pontryagin's Maximum Principle, which facilitates the derivation of optimal interventions. Numerical simulations are conducted to assess various control strategies and compare the effectiveness of single and combined interventions. Our results indicate that a balanced solution is key to effective disease mitigation. A comprehensive approach employing all four controls: awareness, isolation, primary and booster vaccination, is the most effective strategy. Moreover, strategies that incorporate vaccination consistently outperform those without. Interestingly, a three-control strategy closely approximates the effectiveness of the full four-control intervention, suggesting a cost-effective alternative for practical implementation. While the four-control strategy may incur higher implementation costs, the three-control strategy offers a balanced solution, achieving substantial disease reduction while optimizing resource allocation. Our findings underscore the crucial role of vaccination in mumps control. They offer valuable insights for policymakers, emphasizing the need to balance economic considerations with public health outcomes. Vaccination, as our study demonstrates, is a cornerstone of any effective mumps control strategy.
期刊介绍:
Infectious Disease Modelling is an open access journal that undergoes peer-review. Its main objective is to facilitate research that combines mathematical modelling, retrieval and analysis of infection disease data, and public health decision support. The journal actively encourages original research that improves this interface, as well as review articles that highlight innovative methodologies relevant to data collection, informatics, and policy making in the field of public health.