A Mathematical Model for Increasing Incidence ofTuberculosis in Poverty Driven Confined Areas and Measures for Control

Abstract

Tuberculosis is observed to be most prevalent airborne infectious diseases killing hundreds and thousands of people every year. Mostly, the disease spreads in poverty driven poor countries and also to some extent in developing nations. The disease transmits in situations where infected persons are in close contact with others in confined spaces and also living in poor and unhygienic conditions. It is well recognized that overcrowding increases the risk of transmission. A detailed analysis is presented in this paper with respect to the various participating parameters. Interestingly, the results presented in this paper illustrate the occurrence and propagation of the disease as a mathematical model. The results are in agreement with the real life situations and the number of new infections is observed to be linear. It is seen that for fixed time (t), as the room volume (V) increases, the new infections(C) decreases gradually. In general it is seen that as the ventilation rate (N) increases, the new infections decreases quite rapidly. Further, it is observed that as time increases for a constant ventilation rate, an increase in the new infections is noted. Also, for a constant room volume as time increases, the number of new infections is found to be increasing. An interesting feature is that as the ventilation is progressive, a steep fall in the new infections is noted in the initial stages and subsequently, the drop is not that significant. The influence of time gradually seems to be diminishing as the ventilation rate increases. As the room volume increases, the new infections decrease at a faster rate. However, in each of these observations, it is seen that as ventilation rate increases, the number of new infections are found to be inversely proportional. Such a decrease is more predominant in the initial stages but decreases subsequently