{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T12:48:44Z","timestamp":1768481324012,"version":"3.49.0"},"reference-count":37,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"South African DST\/NRF SARChI Chair on Mathematical Models and Methods in Bioengineering and Biosciences"},{"name":"UP Doctoral Bursary Programme"},{"name":"Natural Science and Engineering Research Council"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational and Mathematical Methods in Medicine"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>A new model for the transmission dynamics of<jats:italic>Mycobacterium tuberculosis<\/jats:italic>and bovine tuberculosis in a community, consisting of humans and African buffalos, is presented. The buffalo-only component of the model exhibits the phenomenon of backward bifurcation, which arises due to the reinfection of exposed and recovered buffalos, when the associated reproduction number is less than unity. This model has a unique endemic equilibrium, which is globally asymptotically stable for a special case, when the reproduction number exceeds unity. Uncertainty and sensitivity analyses, using data relevant to the dynamics of the two diseases in the Kruger National Park, show that the distribution of the associated reproduction number is less than unity (hence, the diseases would not persist in the community). Crucial parameters that influence the dynamics of the two diseases are also identified. Both the buffalo-only and the buffalo-human model exhibit the same qualitative dynamics with respect to the local and global asymptotic stability of their respective disease-free equilibrium, as well as with respect to the backward bifurcation phenomenon. Numerical simulations of the buffalo-human model show that the cumulative number of<jats:italic>Mycobacterium tuberculosis<\/jats:italic>cases in humans (buffalos) decreases with increasing number of bovine tuberculosis infections in humans (buffalo).<\/jats:p>","DOI":"10.1155\/2014\/912306","type":"journal-article","created":{"date-parts":[[2014,9,2]],"date-time":"2014-09-02T21:02:07Z","timestamp":1409691727000},"page":"1-20","source":"Crossref","is-referenced-by-count":14,"title":["Dynamics of<i>Mycobacterium<\/i>and<i>bovine tuberculosis<\/i>in a Human-Buffalo Population"],"prefix":"10.1155","volume":"2014","author":[{"given":"A. S.","family":"Hassan","sequence":"first","affiliation":[{"name":"Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S. M.","family":"Garba","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. B.","family":"Gumel","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada R3T 2N2"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. 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