This paper deals with the analysis of tuberculosis disease spread model with saturated infection rate and the treatment effect. We analyze the dynamical behavior of the model to observe the stability peroperty of the model’s equilibrium points. The Routh-Hurwitz Theorem is used to analyze the local stability peroperty of the free disease equilibrium point whereas Transcritical Bifurcation principle is used to analyze the local stability property of the endemic equilibrium pont. The result show that the local stability property of the equilibrium points is depending on the basic reproduction number value calculated by the next generation matrix (NGM). When the basic reproduction number is less than 1, the free disease equilibrium point is locally asymptotically stable, and when it is greater than 1, the endemic equilibrium point is locally asymptotically stable. Numeric simulation results were presented to describe the evolution of the dynamical behavior and to understand the treatment effectiveness for the tuberculosis disease of the population. From the simulation results, it was derived that the treatment in the infected subpopulation had a better result than the one in latent.
This study proposes a SVEIL model of tuberculosis disease spread with imperfect vaccination. Susceptible individuals can receive imperfect vaccination, but over the time the vaccine efficacy will decrease. Vaccinated individuals are in vulnerable class since they still have probability to get reinfected. The proposed model includes treatment for both high-risk latent and active TB patients. In fact, after getting appropriate treatment (get recovered) the individuals still have bacteria in their body and it is classified to low-risk laten class. Dynamical behaviour of the model is analyzed to understand the local stability equilibrium. The Routh-Hurwitz criterion is used to analyze the local stability equilibrium in disease free equilibrium (DFE) point and Center Manifold theorem is used to prove the local stability of the endemic equilibrium (EE) point. The local stability equilibrium state totally depends on the effective reproduction number R_v. If R_v<1 , then the DFE point is locally asymtotically stable, while if R_v>1 the EE point is locally asymptotically stable . The parameter used in this paper is based on the previous researches related to TB and the initial subpopulations are assumed. Numerical simulations show that the disease transmission rate affect the effective reproduction number, therefore it influences the stability of equilibrium points..
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.