Mathematical modeling and optimal control approaches for dengue

Articles in Press

Document Type : Research Article

Authors

• mohamed baroudi ¹
• hicham gourram ¹
• mohamed alia ²
• abderrahim labzai ¹
• mohamed belam ¹

¹ Laboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University of Casablanca, Morocco.

² Laboratory of Mathematics and Population Dynamics (LMPD), Faculty of Sciences Semlalia-Marrakech (FSSM), Cadi Ayyad University, Morocco.

10.22067/ijnao.2024.90023.1529

Abstract

This research explores a continuous-time mathematical model that outlines the transmission dynamics of the dengue virus across different regions, involving both human and mosquito hosts. We propose an optimal strategy that includes awareness campaigns, safety measures, and health interventions in dengue-endemic areas, with the goal of reducing transmission between individuals and mosquitoes, thus lowering human infections and eliminating the virus in mosquito populations. Utilizing the discrete-time Pontryagin's maximum principle, we identify optimal control measures and employ an iterative approach to solve the optimal system. Numerical simulations are carried out using Matlab, and a cost-effectiveness ratio is computed. Through an in-depth cost-effectiveness analysis, we highlight the effectiveness of strategies focused on protecting at-risk populations, preventing contact between infected humans and mosquitoes, and promoting the use of quarantine facilities as the most powerful methods for controlling the spread of the dengue virus.

Keywords

• Optimal Control
• Dengue virus
• Spread of dengue

Main Subjects

• Control and Optimization

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