MODELING THE CUMULATIVE EFFECT OF ECOLOGICAL FACTORS IN THE HABITAT ON THE SPREAD OF TUBERCULOSIS

Abstract

In this paper, the cumulative effect of ecological factors in the habitat on the spread of tuberculosis (TB) in human population is modeled and analyzed. The total human population is divided into two classes, susceptibles and infectives. It is assumed that TB is not only spread by direct contacts with infectives in the population but also indirectly by bacteria which are emitted by infectives in the habitat. It is assumed further that bacteria survive due to conducive ecological factors such as flower pots, plants, grasses, human clothes, etc. in the habitat. The cumulative density of ecological factors in the habitat is assumed to be governed by a population density dependent logistic model. The analysis of the model shows that as parameters governing the conducive ecological factors in the habitat increase, the spread of TB increases. The same result is also found with the increase in the parameter governing the survival and accumulation of bacteria in the habitat. It is further found that due to immigration of the population TB becomes more endemic. A numerical study of the model is also carried out to support the analytical results.