A Mathematical Model of the Tuberculosis Epidemic. 2021

Ally Yeketi Ayinla, and Wan Ainun Mior Othman, and Musa Rabiu
University of Malaya, Institute of Mathematical Sciences, Kuala Lumpur, Malaysia.

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 I1, diagnosed infectious I2, 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 [Formula: see text] 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.

UI MeSH Term Description Entries
D008297 Male Males
D008962 Models, Theoretical Theoretical representations that simulate the behavior or activity of systems, processes, or phenomena. They include the use of mathematical equations, computers, and other electronic equipment. Experimental Model,Experimental Models,Mathematical Model,Model, Experimental,Models (Theoretical),Models, Experimental,Models, Theoretic,Theoretical Study,Mathematical Models,Model (Theoretical),Model, Mathematical,Model, Theoretical,Models, Mathematical,Studies, Theoretical,Study, Theoretical,Theoretical Model,Theoretical Models,Theoretical Studies
D003141 Communicable Diseases An illness caused by an infectious agent or its toxins that occurs through the direct or indirect transmission of the infectious agent or its products from an infected individual or via an animal, vector or the inanimate environment to a susceptible animal or human host. Infectious Diseases,Communicable Disease,Disease, Communicable,Disease, Infectious,Diseases, Communicable,Diseases, Infectious,Infectious Disease
D006801 Humans Members of the species Homo sapiens. Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D014376 Tuberculosis Any of the infectious diseases of man and other animals caused by species of MYCOBACTERIUM TUBERCULOSIS. Koch's Disease,Kochs Disease,Mycobacterium tuberculosis Infection,Infection, Mycobacterium tuberculosis,Infections, Mycobacterium tuberculosis,Koch Disease,Mycobacterium tuberculosis Infections,Tuberculoses
D050936 Basic Reproduction Number The expected number of new cases of an infection caused by an infected individual, amongst susceptible contacts only. Basic Reproductive Number,Basic Reproductive Ratio,Effective Reproduction Number,Effective Reproductive Number,R0 Basic Reproduction Number,RE Effective Reproduction Number,Re Effective Reproductive Number,Transmissibility Measures,Basic Reproduction Ratio,Basic Reproductive Rate,Basic Reproductive Numbers,Basic Reproductive Rates,Basic Reproductive Ratios,Effective Reproduction Numbers,Effective Reproductive Numbers,Rate, Basic Reproductive,Reproduction Number, Basic,Reproduction Number, Effective,Reproduction Ratio, Basic,Reproductive Number, Basic,Reproductive Number, Effective,Reproductive Rate, Basic,Reproductive Rates, Basic,Reproductive Ratio, Basic,Transmissibility Measure
D058872 Epidemics Sudden outbreaks of a disease in a country or region not previously recognized in that area, or a rapid increase in the number of new cases of a previous existing endemic disease. Epidemics can also refer to outbreaks of disease in animal or plant populations.

Related Publications

Ally Yeketi Ayinla, and Wan Ainun Mior Othman, and Musa Rabiu
January 1973, Ftiziologia,
Ally Yeketi Ayinla, and Wan Ainun Mior Othman, and Musa Rabiu
January 1997, Zhurnal mikrobiologii, epidemiologii i immunobiologii,
Ally Yeketi Ayinla, and Wan Ainun Mior Othman, and Musa Rabiu
April 2024, Computer methods in biomechanics and biomedical engineering,
Ally Yeketi Ayinla, and Wan Ainun Mior Othman, and Musa Rabiu
November 2001, AIDS alert,
Ally Yeketi Ayinla, and Wan Ainun Mior Othman, and Musa Rabiu
March 2022, Journal of computational biology : a journal of computational molecular cell biology,
Ally Yeketi Ayinla, and Wan Ainun Mior Othman, and Musa Rabiu
January 1972, Ftiziologia,
Ally Yeketi Ayinla, and Wan Ainun Mior Othman, and Musa Rabiu
October 2011, Mathematical biosciences and engineering : MBE,
Ally Yeketi Ayinla, and Wan Ainun Mior Othman, and Musa Rabiu
March 2020, Mathematical biosciences and engineering : MBE,
Ally Yeketi Ayinla, and Wan Ainun Mior Othman, and Musa Rabiu
December 1979, Journal of epidemiology and community health,
Ally Yeketi Ayinla, and Wan Ainun Mior Othman, and Musa Rabiu
January 2022, Mathematical biosciences and engineering : MBE,
Copied contents to your clipboard!