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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

A Fractional Tuberculosis Host Population Model with Dynamical Analysis

Discontinuity, Nonlinearity, and Complexity 15(1) (2026) 87--98 | DOI:10.5890/DNC.2026.03.006

Suganya Dhandapani$^1$, Bhuvaneswari Venkatasubramaniam$^2$, Hariharan Soundararajan$^3$,\\ Shangerganesh Lingeshwaran$^4$

$^1$ Department of Mathematics, PSG College of Arts & Science, Coimbatore, 641 014, Tamilnadu, India

$^2$ Department of Mathematics with Computer Applications, PSG College of Arts & Science, Coimbatore, Tamilnadu, 641 014, India

$^3$ Department of Mathematics, School of Engineering, Dayananda Sagar University, Bangalore, Karnataka, 562112, India

$^4$ Department of Applied Sciences, National Institute of Technology Goa, Cuncolim, 403 703, Goa, India

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Abstract

In this paper, we extend ordinary differential equations to Caputo-type differential equations and apply optimal control theory to explore how control strategies can be implemented over a fractional order to reduce the number of active infected individuals while minimizing intervention costs. We demonstrate the criteria for the existence and uniqueness of the proposed model and examine the non-negativity and boundedness of the solutions. Additionally, we analyze the basic reproduction number and its sensitivity. We study the stability criteria for both the disease-free and endemic equilibrium to understand the qualitative behavior of the model. The proposed mathematical model incorporates three control terms, and using the Pontryagin Maximum Principle, we analytically derive the optimal control characteristics of the model. The analytical results are supported by numerical analysis and simulations, which demonstrate the most effective control of the intervention.

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