Edward Stephen, Mathias Alberto Kimbuya
Department of Mathematics and Statistics, University of Dodoma, Box 338, Dodoma, Tanzania.
Infect Dis Model. 2025 Jun 30;10(4):1208-1228. doi: 10.1016/j.idm.2025.06.007. eCollection 2025 Dec.
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.
在本研究中，我们通过一个动态模型开发了一个用于管理腮腺炎感染的最优控制框架，该模型整合了诸如宣传项目、隔离方案和两剂免疫接种方案等公共卫生干预措施。我们首先建立模型的基本分析性质，包括疾病平衡点的存在性和稳定性、解的正性和有界性以及疾病传播的阈值条件。通过劳斯 - 赫尔维茨准则进行局部稳定性分析，确保对疾病动态有稳健的见解。使用庞特里亚金极大值原理来制定和分析最优控制问题，这有助于推导最优干预措施。进行数值模拟以评估各种控制策略，并比较单一干预和联合干预的有效性。我们的结果表明，平衡的解决方案是有效减轻疾病的关键。采用所有四种控制措施：宣传、隔离、初次和加强疫苗接种的综合方法是最有效的策略。此外，纳入疫苗接种的策略始终优于未纳入的策略。有趣的是，一种三控制策略与完整的四控制干预的有效性非常接近，这表明了一种在实际实施中具有成本效益的替代方案。虽然四控制策略可能会产生更高的实施成本，但三控制策略提供了一个平衡的解决方案，在优化资源分配的同时实现了疾病的大幅减少。我们的研究结果强调了疫苗接种在腮腺炎控制中的关键作用。它们为政策制定者提供了有价值的见解，强调了在经济考虑与公共卫生结果之间取得平衡的必要性。正如我们的研究所表明的，疫苗接种是任何有效的腮腺炎控制策略的基石。
