https://doi.org/10.1140/epjp/s13360-026-07471-5
Regular Article
Mathematical modeling and optimal control of HIV/AIDS–COVID-19 syndemic dynamics in India
Department of Mathematics, Institute of Science, Banaras Hindu University, 221005, Varanasi, Uttar Pradesh, India
a
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Received:
12
January
2026
Accepted:
18
February
2026
Published online:
12
March
2026
Abstract
The COVID-19 pandemic has posed significant challenges to healthcare systems worldwide, particularly for populations living with chronic infectious diseases such as HIV. In this study, a deterministic compartmental model is formulated to investigate the transmission dynamics of HIV–COVID-19 co-infection. A key feature of the model is the inclusion of an exposed HIV compartment, representing recently exposed but non-infectious individuals, thereby allowing the incorporation of preventive interventions such as post-exposure prophylaxis. The model is shown to be mathematically well posed, with solutions that remain positive and bounded within an invariant region. Threshold dynamics are characterized through the derivation of basic reproduction numbers, and the local and global stability properties of the disease-free and endemic equilibria are analyzed. Model parameters are estimated using reported epidemiological data from India via nonlinear least-squares fitting. Numerical simulations support the theoretical results and demonstrate that HIV-induced immunosuppression substantially increases COVID-19 transmission and disease burden, leading to higher hospitalization levels among co-infected individuals. An optimal control framework is further developed to evaluate time-dependent intervention strategies for HIV and COVID-19. The results indicate that combined control measures are more effective than single-disease interventions in reducing overall infection levels. These findings highlight the importance of integrated public health strategies for managing co-circulating infectious diseases.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
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.
