Analysis of effect of overcrowding on the spread of tuberculosis using deterministic modelling approach: A case study of internally displaced riverside settlements by hydro electric generating power stations of Nigeria

Abstract

In this study, the effects of population density on the dynamics of  tuberculosis were discussed using deterministic modeling approach . A mathematical model was formulated that incorporated the size of the area occupied by the population being studied. The results suggested that the observed trend in tuberculosis incidence was partly as a result of explosive population growth due to urbanization and resettlements. In the  qualitative analysis of the model, the disease free steady state was analyzed for stability using Rowth Hurwitz theorem. The analysis showed that there exists a globally stable disease-free equilibrium point. The disease-free equilibrium point will be globally asymptotically stable provided the characteristic area per individual is greater than the product of the probability of survival from latent stage into the infectious stage and the number of latent infections produced by a typical infectious individual during the mean infectious period. The results of numerical simulation were remarkably in line with those of the qualitative analysis of the model.

Key words: Tuberculosis, Population density, Equilibrium State and Stability Analysis.