Mathematics and Applied Data Science

A special issue of Mathematical and Computational Applications (ISSN 2297-8747).

Deadline for manuscript submissions: 31 December 2025 | Viewed by 588

Special Issue Editors


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Guest Editor
1. Department of Mathematics and Computer Sciences, Faculty of Science, Necmettin Erbakan University, 42090 Meram, Konya, Turkey
2. Centre for Environmental Mathematics, Faculty of Environment, Science and Economy, University of Exeter, Penryn TR10 9FE, Cornwall, UK
3. Department of Applied Mathematics and Informatics, Kyrgyz-Turkish Manas University, Bishkek, Kyrgyzstan
Interests: applied mathematics; fractional calculus and applications; mathematical biology; mathematical modelling; optimal control and applications
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
Faculty of Electronics Sciences, Autonomous University of Puebla, Puebla 72410, Mexico
Interests: chaos theory; chaotic dynamics and applications; nonlinear circuits and systems; mathematical modeling; electronics; fractional-order chaotic systems; fractional-order calculus
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue will mainly consist of selected papers presented at The First International Conference on Mathematics and Applied Data Science (ICMADS‘25; see https://icmads.org/ for detailed information). However, other works that fit within the scope of ICMADS’25 are also welcome.

Topics of interest include (but are not limited to) the following:

  • Mathematics:
    • Computational mathematics;
    • Control theory and applications;
    • Mathematical biology and ecology;
    • Fractional calculus with applications;
    • Nonlinear dynamical systems and chaos theory;
    • Mathematics of communication and cryptography;
    • Analysis;
    • Algebra;
    • Geometry;
    • Topology.
  • Data Science Applications in Mathematics:
    • Computational and mathematical neuroscience and medicine;
    • AI and machine learning applications;
    • Optimization and operations research;
    • Mathematical finance, marketing, and risk analysis;
    • Data science in engineering;
    • Data science in energy management;
    • Computational statistics and probability;
    • Data science for cybersecurity;
    • Data science in education and natural sciences.

Prof. Dr. Mehmet Yavuz
Prof. Dr. Jesus M. Munoz-Pacheco
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematical and Computational Applications is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • computational mathematics
  • control theory
  • mathematical biology
  • fractional calculus

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Published Papers (1 paper)

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Research

30 pages, 877 KB  
Article
Fractional Optimal Control of Anthroponotic Cutaneous Leishmaniasis with Behavioral and Epidemiological Extensions
by Asiyeh Ebrahimzadeh, Amin Jajarmi and Mehmet Yavuz
Math. Comput. Appl. 2025, 30(6), 122; https://doi.org/10.3390/mca30060122 - 6 Nov 2025
Viewed by 225
Abstract
Sandflies spread the neglected vector-borne disease anthroponotic cutaneous leishmaniasis (ACL), which only affects humans. Despite decades of control, asymptomatic carriers, vector pesticide resistance, and low public awareness prevent eradication. This study proposes a fractional-order optimal control model that integrates biological and behavioral aspects [...] Read more.
Sandflies spread the neglected vector-borne disease anthroponotic cutaneous leishmaniasis (ACL), which only affects humans. Despite decades of control, asymptomatic carriers, vector pesticide resistance, and low public awareness prevent eradication. This study proposes a fractional-order optimal control model that integrates biological and behavioral aspects of ACL transmission to better understand its complex dynamics and intervention responses. We model asymptomatic human illnesses, insecticide-resistant sandflies, and a dynamic awareness function under public health campaigns and collective behavioral memory. Four time-dependent control variables—symptomatic treatment, pesticide spraying, bed net use, and awareness promotion—are introduced under a shared budget constraint to reflect public health resource constraints. In addition, Caputo fractional derivatives incorporate memory-dependent processes and hereditary effects, allowing for epidemic and behavioral states to depend on prior infections and interventions; on the other hand, standard integer-order frameworks miss temporal smoothness, delayed responses, and persistence effects from this memory feature, which affect optimal control trajectories. Next, we determine the optimality conditions for fractional-order systems using a generalized Pontryagin’s maximum principle, then solve the state–adjoint equations numerically with an efficient forward–backward sweep approach. Simulations show that fractional (memory-based) dynamics capture behavioral inertia and cumulative public response, improving awareness and treatment efforts. Furthermore, sensitivity tests indicate that integer-order models do not predict the optimal allocation of limited resources, highlighting memory effects in epidemiological decision-making. Consequently, the proposed method provides a realistic and flexible mathematical basis for cost-effective and sustainable ACL control plans in endemic settings, revealing how memory-dependent dynamics may affect disease development and intervention efficiency. Full article
(This article belongs to the Special Issue Mathematics and Applied Data Science)
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