article · Journal of Taibah University for Science
Tuberculosis transmission has been modelled using a system of four fractional differential equations based on the Caputo operator. The mathematical formulation captures essential epidemiological characteristics of the disease, with established existence, positivity, uniqueness, and boundedness of solutions. Disease-free and endemic equilibrium states were identified, followed by local stability and bifurcation analyses. The basic reproduction number was calculated alongside a sensitivity analysis to pinpoint primary epidemiological parameters affecting transmission. An optimal control framework applying Pontryagin's maximum principle was implemented to evaluate prevention measures, specifically isolation and protective strategies. Numerical simulations demonstrated that individual interventions reduce disease spread to varying degrees. However, the findings reveal that the most effective outcome is achieved by combining all proposed control efforts simultaneously.
Tuberculosis remains a major public health challenge globally. Mathematical modelling of disease spread allows analysts to evaluate the potential impact of different interventions before deploying them in the field. By demonstrating that combining protective measures with patient isolation yields the best outcome, this theoretical work supports more effective, evidence-based planning for public health disease containment.
This work is early-stage theoretical research that could inform public health policy, epidemiological software tools, or decision-support platforms used by health authorities and disease control planners. While it demonstrates the optimal integration of isolation and prevention strategies through numerical simulations, the abstract does not indicate any direct software development, clinical trial, or clear pathway to commercial deployment.
AI-generated from the published abstract. Always read the original work before citing.
In this research paper, we develop a fractional mathematical model consisting of a system of four fractional differential equations (FDEs) utilizing the Caputo operator. This model aims to capture the key epidemiological characteristics of Tuberculosis infection and its transmission dynamics. To assess the well-posedness of the model, we examine the existence, positivity, uniqueness, and boundedness of solutions. We also identify the disease-free and endemic equilibrium points (EPs) and analyze their local stability, alongside conducting a bifurcation analysis. To determine whether the infection is spreading within the population, we calculate the basic reproduction number ([Formula: see text]) and perform a sensitivity analysis to identify the primary epidemiological parameters that influence the proposed model. Furthermore, we implement a fractional optimal control problem (FOCP) for the proposed model utilizing the maximum principle of Pontryagin (PMP). This includes control variables that represent prevention measures against Tuberculosis transmission, such as isolation and protective strategies. We establish the necessary optimality conditions (NOCs) for this FOCP. Numerical simulations are conducted and presented graphically to illustrate the effects of various optimal control strategies on the transmission dynamics of Tuberculosis. The results indicate that all proposed control measures contribute to limiting the spread of the disease to some degree, with the most effective approach being the combination of all control efforts.
This page summarises published work. The authoritative version sits with the publisher.
DOI: 10.1080/16583655.2025.2475579
Is something wrong with this record? Report it or request removal.
Discussion
Have you built on this work, tried to replicate it, or seen it applied in practice? Share what you know. Verified researchers and MARATTO™ domain experts can open a discussion, and any member can reply. Contributions are reviewed before they appear.
No discussion yet. Open the first thread.
New to MARATTO™? Create a free account.
