Open AccessA Mathematical Model of a Tuberculosis Transmission Dynamics Incorporating First and Second Line Treatment
Author(s) -
J. Andrawus,
Felix Yakubu Eguda,
I.G. Usman,
S.I. Maiwa,
I.M. Dibal,
T. G. Urum,
G.H. Anka
Publication year - 2020
Publication title -
journal of applied science and environmental management
Language(s) - English
Resource type - Journals
eISSN - 2659-1499
pISSN - 2659-1502
DOI - 10.4314/jasem.v24i5.29
Subject(s) - equilibrium point , stability theory , basic reproduction number , reproduction , mathematics , stability (learning theory) , transmission (telecommunications) , point (geometry) , control theory (sociology) , computer science , control (management) , physics , biology , mathematical analysis , ecology , demography , differential equation , population , telecommunications , geometry , quantum mechanics , nonlinear system , machine learning , artificial intelligence , sociology
This paper presents a new mathematical model of a tuberculosis transmission dynamics incorporating first and second line treatment. We calculated a control reproduction number which plays a vital role in biomathematics. The model consists of two equilibrium points namely disease free equilibrium and endemic equilibrium point, it has been shown that the disease free equilibrium point was locally asymptotically stable if thecontrol reproduction number is less than one and also the endemic equilibrium point was locally asymptotically stable if the control reproduction number is greater than one. Numerical simulation was carried out which supported the analytical results.
Keywords: Mathematical Model, Biomathematics, Reproduction Number, Disease Free Equilibrium, Endemic Equilibrium Point