https://doi.org/10.1140/epjp/s13360-025-06206-2
Regular Article
Impact of local and global awareness campaigns on malaria transmission: A mathematical model with protected human class and optimal control approach
1
Department of Mathematics, Asansol Girls’ College, 713304, Asansol, India
2
CITMAga, Departamento de Estatística, Análise Matemática e Optimización, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain
3
Department of Mathematics, Faculty of Science, King Khalid University, 62529, Abha, Saudi Arabia
4
Department of Mathematics, Aksum University, 1010, Aksum, Ethiopia
Received:
17
December
2024
Accepted:
9
March
2025
Published online:
31
March
2025
This article presents a mathematical model to study malaria transmission dynamics influenced by awareness campaigns and optimal control strategies. Protected human class is included as a model variable that can be increased by social media awareness and treatment, as a result, infected cases are reduced. The nonnegativity and boundedness of the solutions of the model are analyzed. The proposed model possesses two equilibria, namely the disease-free equilibrium and the endemic equilibrium point. The disease-free equilibrium point is stable when the basic reproduction number, 
and endemic equilibrium exists when 
. Consequently, forward bifurcation occurs at 
. Sensitivity analysis is provided which identifies the more important parameters of the model system related to the disease transmission. Finally, optimal control theory has been applied to maximize the number of protected human and minimize the cost of malaria management. The optimal problem comprises of three control parameters, and it is solved using the ‘maximum principle.’ This study concluded that public awareness is important for malaria control, and a combination of awareness-based interventions such as use of bed nets, spraying insecticides, and treatment can optimally increase the protected human as well as minimize the malaria cases cost-effectively.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
