• Gurpreet Singh Tuteja

In this paper, we have modified the SIR model based on compartment theory [5] to study the mathematical and stability analysis of the transmission dynamics of Tuberculosis by including latent infection. This modified model consists of four compartments SLIR, defined as Susceptible, Latent (infection), Infection and Recover. The susceptible become infected if they are infected by airborne infection mycobacterium and then they move from susceptible compartment to the latent (infected) compartment (L) which carries the infection but not infectious. If not treated, becomes infected and infectious, moves to the compartment infection (I). The treatment is a long procedure, many a time the infected feels better and doesn’t complete the treatment. Thus, patient instead of recovering completely moves back to the latent (infection) compartment, wherein the bacteria remain inactive for a while. As soon as bacteria become active, latently infected returns to the infection compartment. The governing differential equations are defined. The reproduction number 𝑅0 of the model is calculated using the Jacobian matrix method [6]. A brief of stability and numerical analysis is also done.

Modified SIR Model for Tuberculosis with Latent disease

"Modified SIR Model for Tuberculosis with Latent disease", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.5, Issue 10, page no.822-828, October-2018, Available :http://www.jetir.org/papers/JETIR1810A25.pdf

"Modified SIR Model for Tuberculosis with Latent disease", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.5, Issue 10, page no. pp822-828, October-2018, Available at : http://www.jetir.org/papers/JETIR1810A25.pdf