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Co-dynamics of measles and hand-foot-mouth disease
Article ID: 3359
Vol 3, Issue 2, 2025
DOI: https://doi.org/10.54517/mss3359
Vol 3, Issue 2, 2025
Received: 28 February 2025; Accepted: 3 April 2025; Available online: 14 April 2025; Issue release: 30 June 2025
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Abstract
This study develops two compartmental models to analyze the co-dynamics between measles and hand, foot, and mouth disease (HFMD): a four-compartment model and a seven-compartment HFMD-Measles co-infection model. For the four-compartment model, we systematically analyzed the co-dynamics of measles and hand, foot, and mouth disease (HFMD), and employed the next-generation matrix method to calculate the basic reproduction number of measles and that of HFMD. Through the analytical study of these two types of basic reproduction numbers, we rigorously determined the existence of the disease equilibrium points, with their quantitative relationship were clearly illustrated through graphical representations. The global asymptotic stability of these equilibria is established by applying LaSalle invariance principle, with stability regions of the four equilibrium points precisely defined. The analysis reveals that within the stability region of the disease-free equilibrium, both diseases will eventually die out, preventing any outbreaks. In the stability region corresponding to the measles equilibrium, HFMD is eliminated while measles remains endemic. Conversely, in the stability region of the HFMD-only equilibrium, measles dies out whereas HFMD persists. Finally, within the stability region of the coexistence equilibrium, both diseases persist and become endemic. Numerical simulations further validate the consistency and reliability of these theoretical results. For the seven-compartment infectious disease model, we calculated the basic reproduction number and verified the threshold theorem. We derived the conditions for both local and global asymptotic stability of the disease-free equilibrium. In particular, the disease-free equilibrium is locally stable when the basic reproduction number is less than one, and we also provided conditions for its global stability. Model validation is performed by fitting empirical data from China on HFMD and measles cases.
Keywords
co-infection; basic reproduction number; LaSalle invariance principle; global asymptotic stability
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License URL: https://creativecommons.org/licenses/by/4.0/
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Prof. Youssri Hassan Youssri
Cairo University, Egypt
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2025-05-08
Prof. Rami Ahmad El-Nabulsi is highly deserving of a Lifetime Achievement Award
Prof. Rami Ahmad El-Nabulsi, Researcher at Czech Academy of Science, Czech Republic, received the Lifetime Achievement Award!
2025-03-01
Publication Frequency of MSS changes to be quarterly!
We are pleased to announce that, effective from 2025, the publication frequency of this journal will be adjusted to a quarterly schedule, with four issues released annually in March, June, September, and December....
2024-09-20
Highly Read Article Recommendation
Since the journal launched in 2023, we have been proud to publish a plethora of insightful findings in the realms of mathematics and systems science....
2024-07-10
Meeting our Editor-in-Chief and Associate Editor
It is with great pride that we introduce Prof. Youssri Hassan Youssri and Prof. Ali Akgül, who are the Editor-in-Chief and Associate Editor of our esteemed journal.
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