Browsing by Author "Nyabadza, Farai"

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A fractional order model for transmission dynamics of TB with funding-driven vaccination and social processes
(Elsevier, 2025-12) Ruoja, Chiganga; Nyerere, Nkuba; Mayengo, Maranya; Nyabadza, Farai
This study highlights the role of human preventive behavior, positive attitudes towards hospital-based treatment, and funding of vaccination programs in understanding the transmission dynamics of tuberculosis. To effectively account for human experiences, a Caputo-based fractional-order mathematical model is formulated. The well-posedness of the proposed model is examined using the Generalized Mean Value Theorem, Mittag-Leffler functions, and the Banach contraction mapping principle. To examine the robustness of the solutions, the Ulam–Hyers approach is employed. The next-generation matrix technique is adopted to derive the socioeconomic reproduction number, denoted as . Estimation of parameter values is done by fitting the model to real tuberculosis data reported by the World Health Organization for Tanzania, covering the years 2000 to 2023. The system of equations is solved using the Predict-Evaluate-Correct-Evaluate Adams–Bashforth–Moulton scheme. Both analytical and numerical results indicate that increasing funding for vaccination programs, raising the level of disease-induced fear, and higher proportion of patients with positive attitudes towards hospital-based treatment can potentially reduce the disease burden in the community. Furthermore, incorporating human behavioral responses and experiences improves the accuracy of future disease dynamics predictions rather than ignoring them.
Exploring the role of funding-driven vaccination in infection dynamics of TB: A mathematical modeling approach
(Elsevier B.V., 2025-08-26) Ruojaa, Chiganga; Mayengoa, Maranya; Nyerere, Nkuba; Nyabadza, Farai
This study explores the impact of funding-driven vaccination on the transmission and spread of tuberculosis within the human population. To accurately capture the human behavior, a deterministic mathematical model is formulated, incorporating attitudes of patients towards hospital treatment. The well-posedness of the model is examined using the Lipschitz condition. An effective funding reproduction number is derived via the next-generation matrix method. Model parameters for simulation reasons are estimated by fitting to real-world data. Both theoretical and numerical findings show that decreases with increased vaccination funding and a higher proportion of patients exhibiting positive attitudes towards hospital treatment. These findings underscore the importance for policymakers to prioritize health by ensuring sufficient funding for vaccination programs, which is crucial for reducing disease burden in the community.
Modeling the influence of fear and patients’ attitudes on the transmission dynamics of tuberculosis
(Springer Nature, 2025-01-08) Ruoja, Chiganga; Mayengo, Maranya; Nyerere, Nkuba; Nyabadza, Farai
In this study we discussed the ongoing global health challenge of tuberculosis (TB), which is caused by the Mycobacterium tuberculosis bacteria. While in several studies, the transmission dynamics of TB were examined, it is noted in this work that the impacts of social processes like disease-induced fear and patient attitudes toward hospital treatment have been receiving a poor discussion on understanding the disease transmission and its control. In this paper we present and discuss a deterministic mathematical model to investigate how these social processes influence the transmission dynamics of TB. The basic reproduction number is calculated and used to examine the stability of steady states. Additionally, we conducted a sensitivity analysis which tells what are the parameters that most significantly affect . The key findings from the analytical and numerical simulations indicate that high levels of disease-induced fear in the population, coupled with positive attitudes toward hospital treatment, can significantly reduce TB prevalence. Based on these results, the study recommends implementing control programs that address these social processes as part of the ongoing efforts to combat the TB burden.