Jñānābha‎, Vol. 50 (2) (2020), (212-222)

MODELING THE EFFECT OF ECOLOGICAL CONDITIONS IN THE HABITAT ON THE SPREAD OF TUBERCULOSIS

 

By

Satya Narain Mishra

Department of Mathematics

Brahmanand College, Kanpur-208004, Uttar Pradesh, India

Email: snmishra2006@gmail.com

(Received : September 04, 2020; Revised: September 19, 2020)

 

 

In this paper, the cumulative effect of ecological conditions in the habitat on the spread of TB in human population is modeled and analyzed. The total human population is divided into two classes, susceptibles and infectives where the infective class is further subdivided into latent and actively infected subclasses. It is assumed that TB is spread by direct contact between members of the population as well as indirectly by bacteria which are emitted by infectives in the environment, survive and get accumulated due to favorable ecological conditions in the habitat. The cumulative density of ecological factors determining conditions in the habitat is assumed to follow a population density dependent logistic model. The analysis of the model shows that as parameters governing the ecological factors in the habitat increase, the spread of TB increases. The same result is also found with the increase in the parameter defining the 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 see the role of key parameters on the spread of tuberculosis and to support the analytical results.

 

2010 Mathematics Subject Classifications: 37C75, 92B05.

Keywords and phrases: Mycobacterium tuberculosis; Ecological status in the habitat; latently-infected; actively-infected.