Transmission dynamic of Tuberculosis in two dissimilar groups through pathogens: A SIRS model

Chanda Purushwani; Hema Purushwani; Rajesh Kumar Deolia

doi:10.26637/MJM0803/0034

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

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Chanda Purushwani Department of Mathematics, ITM University, Gwalior- 474001, M. P., India.
Hema Purushwani Department of Mathematics, ITM University, Gwalior- 474001, M. P., India.
Rajesh Kumar Deolia Department of Mathematics, ITM University, Gwalior- 474001, M. P., India.

Pages: 930-938
Date Published: 01-07-2020
Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)

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