Vaccination and combined optimal control measures for malaria prevention and spread mitigation

Khadiza Akter Eme; Md Kamrujjaman; Muntasir Alam; Md Afsar Ali; Khadiza Akter Eme; Md Kamrujjaman; Muntasir Alam; Md Afsar Ali

doi:10.3934/mbe.2025075

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 8: 2039-2071. doi: 10.3934/mbe.2025075

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Vaccination and combined optimal control measures for malaria prevention and spread mitigation

1.
Department of Physical Sciences, Independent University, Bangladesh, Dhaka 1229, Bangladesh
2.
Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh
3.
Department of Mathematics, Asian University for Women, Chittagong 4000, Bangladesh
4.
Department of Applied Mathematics, University of Dhaka, Dhaka 1000, Bangladesh
5.
Department of Mathematics, Tuskegee University, Tuskegee, AL 36088, USA

Received: 16 January 2025 Revised: 25 May 2025 Accepted: 11 June 2025 Published: 27 June 2025

Malaria is a life-threatening mosquito-borne infectious disease prevalent in tropical regions, primarily transmitted to humans by the bites of infected Anopheles mosquitoes. This study presents a mathematical model analysis aimed at understanding the dynamics of malaria transmission and the effectiveness of various prevention strategies. Despite being preventable and curable, malaria continues to pose significant public health challenges, notably due to the risk of recurrent infections if improperly treated. The proposed deterministic model establishes the positivity and boundedness of solutions alongside the local stability of equilibria. A sensitivity analysis is conducted to identify key parameters impacting the basic reproduction number ($ R_0 $), which is crucial for evaluating intervention strategies. The findings indicate that although the current vaccines are not $ 100\% $ effective, vaccination could significantly contribute to malaria control alongside existing preventive measures, such as mosquito nets and insecticide spraying. The study underscores the need for a comprehensive approach combining multiple strategies to effectively reduce malaria transmission and improve health outcomes in endemic regions. Overall, this research highlights the importance of mathematical modeling in formulating effective disease control policies.
- epidemiology,
- vector–host model,
- malaria,
- vaccination,
- optimal control
Citation: Khadiza Akter Eme, Md Kamrujjaman, Muntasir Alam, Md Afsar Ali. Vaccination and combined optimal control measures for malaria prevention and spread mitigation[J]. Mathematical Biosciences and Engineering, 2025, 22(8): 2039-2071. doi: 10.3934/mbe.2025075

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Abstract

Malaria is a life-threatening mosquito-borne infectious disease prevalent in tropical regions, primarily transmitted to humans by the bites of infected Anopheles mosquitoes. This study presents a mathematical model analysis aimed at understanding the dynamics of malaria transmission and the effectiveness of various prevention strategies. Despite being preventable and curable, malaria continues to pose significant public health challenges, notably due to the risk of recurrent infections if improperly treated. The proposed deterministic model establishes the positivity and boundedness of solutions alongside the local stability of equilibria. A sensitivity analysis is conducted to identify key parameters impacting the basic reproduction number ($ R_0 $), which is crucial for evaluating intervention strategies. The findings indicate that although the current vaccines are not $ 100\% $ effective, vaccination could significantly contribute to malaria control alongside existing preventive measures, such as mosquito nets and insecticide spraying. The study underscores the need for a comprehensive approach combining multiple strategies to effectively reduce malaria transmission and improve health outcomes in endemic regions. Overall, this research highlights the importance of mathematical modeling in formulating effective disease control policies.

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