A mathematical model of the tuberculosis epidemic
Document Type
Article
Publication Date
9-1-2021
Abstract
Tuberculosis has continued to retain its title as ``the captain among these men of death''. This is evident as it is the leading cause of death globally from a single infectious agent. TB as it is fondly called has become a major threat to the achievement of the sustainable development goals (SDG) and hence require inputs from different research disciplines. This work presents a mathematical model of tuberculosis. A compartmental model of seven classes was used in the model formulation comprising of the susceptible S, vaccinated V, exposed E, undiagnosed infectious I-1, diagnosed infectious I-2, treated T and recovered R. The stability analysis of the model was established as well as the condition for the model to undergo backward bifurcation. With the existence of backward bifurcation, keeping the basic reproduction number less than unity (R0<1) is no more sufficient to keep TB out of the community. Hence, it is shown by the analysis that vaccination program, diagnosis and treatment helps to control the TB dynamics. In furtherance to that, it is shown that preference should be given to diagnosis over treatment as diagnosis precedes treatment. It is as well shown that at lower vaccination rate (0-20%), TB would still be endemic in the population. As such, high vaccination rate is required to send TB out of the community.
Keywords
Tuberculosis, Vaccine, Diagnosis, Bifurcation, Contact rate
Divisions
MathematicalSciences
Publication Title
Acta Biotheoretica
Volume
69
Issue
3
Publisher
Springer
Publisher Location
VAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, NETHERLANDS