Dengue Transmission Dynamics: A Fractional-Order Approach with Compartmental Modeling

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Abstract

This work presents a quantitative analysis of the transmission dynamics of dengue using the Caputo–Fabrizio fractional-order derivative. It presents an extensive framework for modeling a dengue epidemic, including the various stages of infection and encompassing a wide range of transmission pathways. The proposed model is subjected to a rigorous qualitative study, including the determination of a non-negative solution, the assessment of the basic reproduction number, and an evaluation of local stability. Numerical solutions are obtained using the Newton method. The fractional-order operator, developed using the Caputo–Fabrizio approach, provides a refined perspective on the transmission dynamics of dengue. This study contributes to a deeper understanding of the disease’s transmission mechanisms, considering both fractional-order dynamics and diverse transmission routes, thus offering insights for enhanced disease management and control.

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Most cited references 34

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The global distribution and burden of dengue

Samir Bhatt, Peter W. Gething, Oliver J Brady … (2013)

Dengue is a systemic viral infection transmitted between humans by Aedes mosquitoes 1 . For some patients dengue is a life-threatening illness 2 . There are currently no licensed vaccines or specific therapeutics, and substantial vector control efforts have not stopped its rapid emergence and global spread 3 . The contemporary worldwide distribution of the risk of dengue virus infection 4 and its public health burden are poorly known 2,5 . Here we undertake an exhaustive assembly of known records of dengue occurrence worldwide, and use a formal modelling framework to map the global distribution of dengue risk. We then pair the resulting risk map with detailed longitudinal information from dengue cohort studies and population surfaces to infer the public health burden of dengue in 2010. We predict dengue to be ubiquitous throughout the tropics, with local spatial variations in risk influenced strongly by rainfall, temperature and the degree of urbanisation. Using cartographic approaches, we estimate there to be 390 million (95 percent credible interval 284-528) dengue infections per year, of which 96 million (67-136) manifest apparently (any level of clinical or sub-clinical severity). This infection total is more than three times the dengue burden estimate of the World Health Organization 2 . Stratification of our estimates by country allows comparison with national dengue reporting, after taking into account the probability of an apparent infection being formally reported. The most notable differences are discussed. These new risk maps and infection estimates provide novel insights into the global, regional and national public health burden imposed by dengue. We anticipate that they will provide a starting point for a wider discussion about the global impact of this disease and will help guide improvements in disease control strategies using vaccine, drug and vector control methods and in their economic evaluation. [285]

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Jeffrey D Stanaway, Donald S. Shepard, Eduardo Undurraga … (2016)

Dengue is the most common arbovirus infection globally, but its burden is poorly quantified. We estimated dengue mortality, incidence, and burden for the Global Burden of Disease Study 2013.

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Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system

Abdon Atangana (2017)

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Author and article information

Contributors

Mutum Zico Meetei: (View ORCID Profile)

Abdullah A. Zaagan: (View ORCID Profile)

Ali M. Mahnashi: (View ORCID Profile)

Muhammad Idrees: (View ORCID Profile)

Journal

Journal ID (publisher-id): FFRRAO

Title: Fractal and Fractional

Abbreviated Title: Fractal Fract

Publisher: MDPI AG

ISSN (Electronic): 2504-3110

Publication date Created: April 2024

Publication date (Electronic): April 02 2024

Volume: 8

Issue: 4

Page: 207

Article

DOI: 10.3390/fractalfract8040207

SO-VID: 2a5ad565-4bd3-4811-8e7e-a84fad980929

License:

https://creativecommons.org/licenses/by/4.0/

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