A fractional order model for the transmission dynamics of shigellosis

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dc.contributor.authorEdward, Stephen
dc.date.accessioned2024-08-19T12:00:33Z
dc.date.available2024-08-19T12:00:33Z
dc.date.issued2024
dc.descriptionFull text. Available at DOI:https://doi.org/10.1016/j.heliyon.2024.e31242
dc.description.abstractShigellosis, a highly contagious bacterial infection causing diarrhea, fever, and abdominal pain, necessitates a deep understanding of its transmission dynamics to devise effective control measures. Our study takes a novel approach, employing a fractional order framework to explore the influence of memory and control measures on Shigellosis transmission dynamics, thereby making a unique contribution to the field. The model is presented as a system of Caputo fractional differential equations capturing time constant controls. The Caputo derivatives are chosen for their inherent benefits. The qualitative features of the model, such as the solutions' existence and uniqueness, positivity, and boundedness, are thoroughly investigated. Moreover, the equilibria of the model are derived and analyzed for their stability using suitable theorems. In particular, local stability was proved through Routh's criteria, while global stability results were established in the Ulam-Hyers sense. The model is then solved numerically with the help of the predict-evaluate-correct-evaluate method of Adams-Bashforth-Moulton. The numerical results underscore the significant impact of memory on disease evolution, highlighting the novelty of integrating memory-related aspects into the meticulous planning of effective disease control strategies. Using fractional-order derivatives is more beneficial for understanding the dynamics of Shigellosis transmission than integral-order models. The advantage of fractional derivatives is their ability to provide numerous degrees of freedom, allowing for a broader range of analysis of the system's dynamic behaviour, including nonlocal solutions. Also, an investigation on the impacts of control measures via parameter variation is done; the findings show that applying treatment and sanitation minimizes disease eruption.
dc.identifier.citationEdward, S. (2024). A fractional order model for the transmission dynamics of shigellosis. Heliyon, 10(10).
dc.identifier.doi10.1016/j.heliyon.2024.e31242
dc.identifier.otherDOI: 10.1016/j.heliyon.2024.e31242
dc.identifier.urihttps://repository.udom.ac.tz/handle/20.500.12661/4829
dc.language.isoen
dc.publisherElsevier BV
dc.relation.ispartofHeliyon
dc.subjectMemory
dc.subjectPredictor-corrector method
dc.subjectCaputo fractional derivative
dc.subjectControl strategies
dc.subjectUlam-Hyers stability
dc.titleA fractional order model for the transmission dynamics of shigellosis
dc.typeArticle
oaire.citation.issue10
oaire.citation.volume10
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