Transmission dynamic of Tuberculosis in two dissimilar groups through pathogens: A SIRS model
Authors :
Chanda Purushwani 1 *, Hema Purushwani 2 and Rajesh Kumar Deolia 3
Author Address :
1,2,3 Department of Mathematics, ITM University, Gwalior- 474001, M. P., India.
*Corresponding author.
Abstract :
Tuberculosis is a communicable disease which spreads in the human population through pathogens. Coughing by the infective individual generate large number of droplets. In this paper, a SIRS mathematical model is proposed to study the transmission of Tuberculosis by droplet infection in two dissimilar groups, considering the economic status of the individuals. The basic reproduction number $R_{0}$ from the model has been derived for the study of disease dynamics. It has been shown that the disease free equilibrium point is stable if $R_{0}<1$ and unstable if $R_{0}>1$. It has been also shown that the unique endemic equilibrium point exists when $R_{0}>1.$ It may be concluded that if $R_{0}<1$ then the disease will not spread and if $R_{0}>1$ then the disease will be endemic in the population. We have also concluded from the analysis of the model that Tuberculosis can be controlled by reducing the rate at which an infective individual produces pathogens. The analytical results are supported by the relevant graphs.
Keywords :
SIRS model, Equilibrium points, Basic Reproduction Number, Stability Analysis.
DOI :
Article Info :
Received : January 04, 2020; Accepted : April 19, 2020.
