Modelling the critical characteristic area for the control of tuberculosis in densely populated communities

J. Y.T. Mugishay, A. Ssematimba, L. S. Luboobi, H. Ddumba

Research output: Contribution to journalArticlepeer-review


A density-dependent mathematical model for the dynamics of tuberculosis is analyzed. We use the data from internally-displaced peoples’ camps to illustrate the role of overcrowding in the propagation of a contagious epidemic that would otherwise have been localized. The critical characteristic area per individual required for eradication of tuberculosis is obtained as 0.25 square kilometers. The effect of R0 on the different epidemiological classes shows an increase in number of infecteds for higher values of R0. This study also shows that a reduction in the contact rate and/or progression rate results into a decrease in size of the required critical characteristic area thereby easing the task of eradicating tuberculosis. Stability analysis of the endemic and disease-free equilibria has been carried out, and a forward bifurcation exists at the bifurcation point R0 = 1. Results from the study also show that much as we can try to reduce overcrowding, in un-avoidable circumstances such as lack of vast tracts of land for resettling internally displaced people, measures to reduce on the contact and progression rates should be applied.

Original languageEnglish (US)
Pages (from-to)57-69
Number of pages13
JournalJournal of Mathematical Control Science and Applications
Issue number2
StatePublished - Jul 1 2019
Externally publishedYes

Bibliographical note

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  • Basic Reproductive Number
  • Critical characteristic area
  • Forward bifurcation
  • Progression and contact rates


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