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

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.