Enhancing public health strategies for tungiasis: A mathematical approach with fractional derivative

Norliyana Nor Hisham Shah; Rashid Jan; Hassan Ahmad; Normy Norfiza Abdul Razak; Imtiaz Ahmad; Hijaz Ahmad; Norliyana Nor Hisham Shah; Rashid Jan; Hassan Ahmad; Normy Norfiza Abdul Razak; Imtiaz Ahmad; Hijaz Ahmad

doi:10.3934/bioeng.2023023

AIMS Bioengineering

2023, Volume 10, Issue 4: 384-405. doi: 10.3934/bioeng.2023023

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Research article Special Issues

Enhancing public health strategies for tungiasis: A mathematical approach with fractional derivative

1.
Institute of Energy Infrastructure (IEI), Department of Civil Engineering, College of Engineering, Universiti Tenaga Nasional (UNITEN), Putrajaya Campus, Jalan IKRAM-UNITEN, 43000 Kajang, Selangor, Malaysia
2.
Department of Mathematics, University of Swabi, Swabi 23561, KPK, Pakistan
3.
Institute of Informatics and Computing in Energy (IICE), Universiti Tenaga Nasional, Kajang, Selangor, Malaysia
4.
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39,00186 Roma, Italy

Received: 12 August 2023 Revised: 30 September 2023 Accepted: 10 October 2023 Published: 25 October 2023

In this study, we formulate a mathematical model in the framework of the Atangana-Baleanu fractional derivative in Caputo sense to study the transmission of tungiasis. In this formulation, interactions between the human host and the sand fleas are taken into consideration, including factors like infestation rate, incubation duration, and recovery rate. We calculate the basic reproduction parameter for the system, symbolized by $\mathcal{R}_0$ with the help of the next-generation matrix technique. A novel numerical scheme for encapsulating the non-local and memory-dependent aspects of the system is conceptualized via the Atangana-Baleanu fractional derivative. We prove the existence and uniqueness of the solution of the model of the infection and establish stability of the steady-states of the model. In addition to this, numerical simulations are carried out to evaluate the efficiency of interventions like campaigns for better sanitation and treatment, and to investigate the influence of various management techniques on the prevalence of tungiasis. The outcomes of the numerical simulations give us information about the possible efficacy of different control strategies in lowering the incidence of tungiasis. This research gives quantitative tools to enhance decision-making processes in public health treatments and advances our understanding of the dynamics of the tungiasis.
- tungiasis,
- mathematical model,
- endemic indicator,
- Atangan-Baleanu derivative,
- fixed point theory,
- time series analysis
Citation: Norliyana Nor Hisham Shah, Rashid Jan, Hassan Ahmad, Normy Norfiza Abdul Razak, Imtiaz Ahmad, Hijaz Ahmad. Enhancing public health strategies for tungiasis: A mathematical approach with fractional derivative[J]. AIMS Bioengineering, 2023, 10(4): 384-405. doi: 10.3934/bioeng.2023023

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Abstract

In this study, we formulate a mathematical model in the framework of the Atangana-Baleanu fractional derivative in Caputo sense to study the transmission of tungiasis. In this formulation, interactions between the human host and the sand fleas are taken into consideration, including factors like infestation rate, incubation duration, and recovery rate. We calculate the basic reproduction parameter for the system, symbolized by $\mathcal{R}_0$ with the help of the next-generation matrix technique. A novel numerical scheme for encapsulating the non-local and memory-dependent aspects of the system is conceptualized via the Atangana-Baleanu fractional derivative. We prove the existence and uniqueness of the solution of the model of the infection and establish stability of the steady-states of the model. In addition to this, numerical simulations are carried out to evaluate the efficiency of interventions like campaigns for better sanitation and treatment, and to investigate the influence of various management techniques on the prevalence of tungiasis. The outcomes of the numerical simulations give us information about the possible efficacy of different control strategies in lowering the incidence of tungiasis. This research gives quantitative tools to enhance decision-making processes in public health treatments and advances our understanding of the dynamics of the tungiasis.

Acknowledgments

No external funding is used regarding this research.

Conflict of interest

Hijaz Ahmad is on a special issue editorial board for AIMS Bioengineering and was not involved in the editorial review or the decision to publish this article. All authors declare that there are no competing interests. The authors declare that there is no conflict of interests regarding the publication of this paper.

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