Modeling Syphilis and HIV Coinfection: A Case Study in the USA

Syphilis and HIV infections form a dangerous combination. In this paper, we propose an epidemic model of HIV-syphilis coinfection. The model always has a unique disease-free equilibrium, which is stable when both reproduction numbers of syphilis and HIV are less than 1. If the reproduction number of...

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Bibliographic Details
Published inBulletin of mathematical biology Vol. 85; no. 3; p. 20
Main Authors Wang, Cheng-Long, Gao, Shasha, Li, Xue-Zhi, Martcheva, Maia
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2023
Springer Nature B.V
Subjects
Cell Biology
Coexistence
Coinfection - epidemiology
Epidemic models
Equilibrium
HIV
HIV Infections - complications
HIV Infections - epidemiology
Human immunodeficiency virus
Humans
Life Sciences
Mathematical and Computational Biology
Mathematical Concepts
Mathematics
Mathematics and Statistics
Models, Biological
Original
Original Article
Reproduction
Syphilis
Syphilis - complications
Syphilis - epidemiology
United States > US
Coinfection
Epidemic model
HIV transmission
Invasion numbers
Reproduction numbers
Syphilis infection
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Summary:Syphilis and HIV infections form a dangerous combination. In this paper, we propose an epidemic model of HIV-syphilis coinfection. The model always has a unique disease-free equilibrium, which is stable when both reproduction numbers of syphilis and HIV are less than 1. If the reproduction number of syphilis (HIV) is greater than 1, there exists a unique boundary equilibrium of syphilis (HIV), which is locally stable if the invasion number of HIV (syphilis) is less than 1. Coexistence equilibrium exists and is stable when all reproduction numbers and invasion numbers are greater than 1. Using data of syphilis cases and HIV cases from the US, we estimated that both reproduction numbers for syphilis and HIV are slightly greater than 1, and the boundary equilibrium of syphilis is stable. In addition, we observed competition between the two diseases. Treatment for primary syphilis is more important in mitigating the transmission of syphilis. However, it might lead to increase of HIV cases. The results derived here could be adapted to other multi-disease scenarios in other regions.
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ISSN:0092-8240
1522-9602
DOI:10.1007/s11538-023-01123-w