https://doi.org/10.1140/epjp/s13360-025-06818-8
Regular Article
Modeling global asymptotic stability of malaria dynamics with structured infectious population
1
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan
2
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), 11432, Riyadh, Saudi Arabia
3
Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology, Ogbomoso, Nigeria
4
Mathematics Department, Faculty of Science, Taibah University, 41411, Al-Madinah Al-Munawarah, Saudi Arabia
a
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Received:
31
July
2025
Accepted:
30
August
2025
Published online:
11
September
2025
Abstract
Over the last few decades, malaria has become a serious risk to public health, particularly in tropical and sub-tropical areas where the climate is favorable for mosquito breeding. These insects are the primary carriers of the disease, transmitting it to humans through their bites. Here, we have formulated a mathematical framework that explores malaria transmission, incorporating a structured infectious population. Numerous dynamical system methodologies are instrumentalized in studying the malaria model in human-vector interacting populations. Firstly, we have proved that the model state variables has non-negative and bounded solutions throughout time. Then, we have obtained the threshold parameter 
by employing the next generation operator approach. We have proved that the proposed malaria model is stable locally and globally in an asymptotic manner by calculating the Jacobian matrix and Lyapunov function theory if 
. The malaria model is shown to have a unique endemic equilibrium point whenever the basic reproductive number 
. Consequently, the unique malaria-endemic steady point of the proposed malaria model is proven to be globally stable provided that . Sensitivity analysis is conducted to capture the most significant parameter causing malaria transmission and controlling in the human population. Furthermore, simulations are performed to support the qualitative results of the study, and the results are graphically presented.
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© 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.
