Modeling the impact of public health education on tungiasis dynamics with saturated treatment: Insight through the Caputo fractional derivative

Simphiwe M. Simelane; Phumlani G. Dlamini; Fadekemi J. Osaye; George Obaido; Blessing Ogbukiri; Kehinde Aruleba; Cadavious M. Jones; Chidozie W. Chukwu; Oluwaseun F. Egbelowo; Simphiwe M. Simelane; Phumlani G. Dlamini; Fadekemi J. Osaye; George Obaido; Blessing Ogbukiri; Kehinde Aruleba; Cadavious M. Jones; Chidozie W. Chukwu; Oluwaseun F. Egbelowo

doi:10.3934/mbe.2023332

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 5: 7696-7720. doi: 10.3934/mbe.2023332

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Modeling the impact of public health education on tungiasis dynamics with saturated treatment: Insight through the Caputo fractional derivative

1.
Department of Mathematics and Applied Mathematics, University of Johannesburg, Doornfontein, 2028, South Africa
2.
Department of Mathematics and Computer Science, Alabama State University, USA
3.
Center for Human Artificial Intelligence (CHAI), Berkeley Institute for Data Science (BIDS), University of California, Berkeley, CA 94720, USA
4.
Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada
5.
School of Computing and Mathematical Sciences, University of Leicester, Leicester LE1 7RH, UK
6.
Division of Science and Mathematics, Rust College, Holly Springs, Mississippi, USA
7.
Department of Mathematics, Wake Forest University, Winston-Salem, NC 27109, USA
8.
Department of Integrative Biology, University of Texas at Austin, USA

Received: 14 November 2022 Revised: 01 February 2023 Accepted: 07 February 2023 Published: 20 February 2023

Public health education is pivotal in the management and control of infectious and non-infectious diseases. This manuscript presents and analyses a nonlinear fractional model of tungiasis dynamics with the impact of public health education for the first time. The human population is split into five classes depending on their disease status. The infected population is split into two subgroups; infected but unaware and infected but aware. The model focuses on the impacts of public health education, contact and treatment contact on tungiasis transmission dynamics. Notably, public health education is important for containing as well as reducing disease outbreaks in communities. The Caputo fractional derivative is utilised in defining the model governing equations. Model equilibrium points existence and stability are investigated using simple matrix algebra. Model analysis shows that tungiasis is contained when the reproduction number is less than unity. Otherwise, if it is greater than unity, the disease persists and spread in the population. The generalised Adams-Bashforth-Moulton approach is utilised in solving the derived tungiasis model numerically. The impacts of public health education, treatment and contact rate on overall disease dynamics are discussed through numerical simulations. From the simulations, we see that for given fractional order, public health education and treatment increase the quality of life plus reduce equilibrium numbers of tungiasis-infected individuals. We observe that population classes converge quicker to their steady states when $ \alpha $ is increased. Thus, we can conclude that the derivative order $ \alpha $ captures the role of experience or knowledge that individuals have on the disease's history.
- Tungiasis,
- Caputo fractional derivative,
- public health education,
- treatment,
- Adams-Bashforth-Moulton method
Citation: Simphiwe M. Simelane, Phumlani G. Dlamini, Fadekemi J. Osaye, George Obaido, Blessing Ogbukiri, Kehinde Aruleba, Cadavious M. Jones, Chidozie W. Chukwu, Oluwaseun F. Egbelowo. Modeling the impact of public health education on tungiasis dynamics with saturated treatment: Insight through the Caputo fractional derivative[J]. Mathematical Biosciences and Engineering, 2023, 20(5): 7696-7720. doi: 10.3934/mbe.2023332

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Abstract

Public health education is pivotal in the management and control of infectious and non-infectious diseases. This manuscript presents and analyses a nonlinear fractional model of tungiasis dynamics with the impact of public health education for the first time. The human population is split into five classes depending on their disease status. The infected population is split into two subgroups; infected but unaware and infected but aware. The model focuses on the impacts of public health education, contact and treatment contact on tungiasis transmission dynamics. Notably, public health education is important for containing as well as reducing disease outbreaks in communities. The Caputo fractional derivative is utilised in defining the model governing equations. Model equilibrium points existence and stability are investigated using simple matrix algebra. Model analysis shows that tungiasis is contained when the reproduction number is less than unity. Otherwise, if it is greater than unity, the disease persists and spread in the population. The generalised Adams-Bashforth-Moulton approach is utilised in solving the derived tungiasis model numerically. The impacts of public health education, treatment and contact rate on overall disease dynamics are discussed through numerical simulations. From the simulations, we see that for given fractional order, public health education and treatment increase the quality of life plus reduce equilibrium numbers of tungiasis-infected individuals. We observe that population classes converge quicker to their steady states when $ \alpha $ is increased. Thus, we can conclude that the derivative order $ \alpha $ captures the role of experience or knowledge that individuals have on the disease's history.

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