{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T00:58:19Z","timestamp":1776214699055,"version":"3.50.1"},"reference-count":44,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,17]],"date-time":"2023-07-17T00:00:00Z","timestamp":1689552000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>In this paper, we develop a deterministic mathematical epidemic model for tuberculosis outbreaks in order to study the disease\u2019s impact in a given population. We develop a qualitative analysis of the model by showing that the solution of the model is positive and bounded. The global stability analysis of the model uses Lyapunov functions and the threshold quantity of the model, which is the basic reproduction number is estimated. The existence and uniqueness analysis for Caputo fractional tuberculosis outbreak model is presented by transforming the deterministic model to a Caputo sense model. The deterministic model is used to predict real data from Uganda and Rwanda to see how well our model captured the dynamics of the disease in the countries considered. Furthermore, the sensitivity analysis of the parameters according to R0 was considered in this study. The normalised forward sensitivity index is used to determine the most sensitive variables that are important for infection control. We simulate the Caputo fractional tuberculosis outbreak model using the Adams\u2013Bashforth\u2013Moulton approach to investigate the impact of treatment and vaccine rates, as well as the disease trajectory. Overall, our findings imply that increasing vaccination and especially treatment availability for infected people can reduce the prevalence and burden of tuberculosis on the human population.<\/jats:p>","DOI":"10.3390\/computation11070143","type":"journal-article","created":{"date-parts":[[2023,7,18]],"date-time":"2023-07-18T01:31:32Z","timestamp":1689643892000},"page":"143","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["Mathematical Modelling of Tuberculosis Outbreak in an East African Country Incorporating Vaccination and Treatment"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4598-8510","authenticated-orcid":false,"given":"Kayode","family":"Oshinubi","sequence":"first","affiliation":[{"name":"School of Informatics, Computing, and Cyber Systems, Northern Arizona University, Flagstaff, AZ 86011, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9448-1164","authenticated-orcid":false,"given":"Olumuyiwa James","family":"Peter","sequence":"additional","affiliation":[{"name":"Department of Mathematical and Computer Sciences, University of Medical Sciences, Ondo City PMB 536, Nigeria"},{"name":"Department of Epidemiology and Biostatistics, School of Public Health, University of Medical Sciences, Ondo City PMB 536, Nigeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2159-6299","authenticated-orcid":false,"given":"Emmanuel","family":"Addai","sequence":"additional","affiliation":[{"name":"College of Biomedical Engineering, Taiyuan University of Technology, Taiyuan 030024, China"},{"name":"Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7439-9064","authenticated-orcid":false,"given":"Enock","family":"Mwizerwa","sequence":"additional","affiliation":[{"name":"African Institute for Mathematical Science, Kigali KN3, Rwanda"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9909-0434","authenticated-orcid":false,"given":"Oluwatosin","family":"Babasola","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK"}]},{"given":"Ifeoma Veronica","family":"Nwabufo","sequence":"additional","affiliation":[{"name":"African Institute for Mathematical Sciences, Mbour BP 1418, Senegal"}]},{"given":"Ibrahima","family":"Sane","sequence":"additional","affiliation":[{"name":"Departement de Mathematiques, Laboratoire Maths Appliquees, Universite Assane Seck de Ziguinchor, Ziguinchor 27000, Senegal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4510-0369","authenticated-orcid":false,"given":"Umar Muhammad","family":"Adam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Federal University, Dutse F130, Nigeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9027-626X","authenticated-orcid":false,"given":"Adejimi","family":"Adeniji","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0083, South Africa"}]},{"given":"Janet O.","family":"Agbaje","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Montana Technological University, Butte, MT 59701, USA"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,17]]},"reference":[{"key":"ref_1","unstructured":"(2023, January 02). 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