Journal of Multidisciplinary Applied Natural Science
Vol. 6 No. 3 (2026): Journal of Multidisciplinary Applied Natural Science

Mathematical Modeling and Cost-Effective Control of Tuberculosis through Vaccination and Treatment

Yudi Ari Adi (Department of Mathematics, Universitas Ahmad Dahlan, Yogyakarta-55191 (Indonesia))
Sugiyarto Sugiyarto (Department of Mathematics, Universitas Ahmad Dahlan, Yogyakarta-55191 (Indonesia))
Desi Nurfita (Department of Public Health Sciences, Universitas Ahmad Dahlan, Yogyakarta-55164 (Indonesia))
Ummu Atiqah Mohd Roslan (Special Interest Group Modelling and Data Analytics, Universiti Malaysia Terengganu, Terengganu-21030 (Malaysia))
Suparman Suparman (Department of Mathematics Education, Universitas Ahmad Dahlan, Yogyakarta-55191 (Indonesia))



Article Info

Publish Date
24 Jul 2026

Abstract

Tuberculosis (TB) remains a major global health concern, particularly in high-burden countries such as Indonesia. To better understand the transmission dynamics and evaluate intervention strategies, a compartmental SVEITR model is developed that incorporates vaccination, exposure, treatment adherence, and immunity loss. Using next-generation matrix methods, the basic reproduction number is derived and stability analysis demonstrated that the disease-free equilibrium is globally asymptotically stable when . Bifurcation analysis of the vaccine efficacy parameter revealed a forward bifurcation, indicating that TB can be eradicated once vaccine efficacy exceeds a critical threshold. Using Pontryagin's maximum principle, we developed an optimal control problem with time-dependent vaccination and treatment adherence control. Numerical simulations demonstrated that the combined implementation of vaccination and treatment adherence resulted in the greatest reduction in the exposed and infectious population. Further cost-effectiveness analysis showed that improving treatment adherence alone was the most economically efficient strategy (ACER ; ICER ), while vaccination alone was significantly less cost-effective (ACER ). Although combining vaccination with treatment adherence achieved additional health benefits, it incurs higher additional costs (ICER). These findings suggest that treatment adherence should be prioritized in resource-limited settings, with combined strategies considered when additional resources are available.

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Journal Info

Abbrev

jmans

Publisher

Subject

Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Energy Environmental Science Immunology & microbiology Materials Science & Nanotechnology Mathematics Physics

Description

Journal of Multidisciplinary Applied Natural Science (abbreviated as J. Multidiscip. Appl. Nat. Sci.) is a double-blind peer-reviewed journal for multidisciplinary research activity on natural sciences and their application on daily life. This journal aims to make significant contributions to ...