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In the more recent literature, numerous studies have pointed out that initial infection may analys confer protection against exogenous reinfection especially in high-risk populations [ 5051 ]. Increasing recurrent TB analsye TB prevalence. Extraordinarily, TB is a treatable disease and can be prevented and cured through the use of prophylaxis and therapeutics for individuals with latent and clinically active TB respectively.

International Journal of Vehicle DesignInderscience,20pp.

CV HAL : Isabelle BLANC Professeur at MINES ParisTech, PSL Research University

This characteristic is indicative of forward bifurcation as seen in Fig 7. We are particularly interested in recurrent TB, which is defined as the emergence of a second episode of TB after the first anayse has been successfully cured [ 9 ]. Dhillon J, Mitchison DA. Exogenous reinfection in tuberculosis. Bulletin of mathematical biology.


Conversely, when R 0 is above unity an epidemic may trigger and long-term disease persistence is feasible. Loss of Life Expectancy related to temporal evolution of PM2. Computational and mathematical methods in medicine.

Global sensitivity analysis as a support for the generation of simplified building stock energy models. This article has been cited by other articles in PMC.

Isabelle BLANC Professeur at MINES ParisTech, PSL Research University

The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Isabelle Blanc, Eric Labouze. Furthermore, recurrent TB can independently induce backward bifurcation phenomena if it exceeds a certain threshold. Proceedings World Geothermal Congresspp. Fate and exposure to organic compounds emitted indoors. Development of an object oriented model for the assessment of the environment quality of buildings.

Estimating particulate matter health impact related to smiz combustion of different fossil fuels.

In their controversial paper, Lipsitch and Murray [ 18 ] argued that in the real world recovered individuals gain immunity to reinfection, and thus reinfection amongst exposed individuals must be less than the probability of progressing to the infectious stage of TB.

Estimating the loss of life expectancy attributable to PM2. Mathematical Biosciences and Engineering. Upon contact with an infective, a small proportion q of infected susceptible individuals follow the fast primary progression route i.

Endogenous designates situations where the individual is already harbouring the causing agent, which is under some healthy control by the immune system, but which destabilizes and leads to disease. Indeed, Feng et al. S2 Appendix Detailed derivation of p c in Lemma 3. Including the temporal change in PM2.


Understanding LCA results variability: In the region denoted by NBB, the level of exogenous reinfection is too low to induce backward bifurcation while in region denoted by BB the level of exogenous reinfection is sufficient to cause multiple equilibria.

Characteristically, when R 0 is below unity, the introduction of a few infected individuals in a susceptible population will only lead to disease die-out, as the disease is unable to reproduce itself or transmit through the population effectively.

Although recurrent TB is recognized as a serious problem it receives little attention [ 10 ]. Applying LCA to design alternatives.

In [ 13 ] it was found that persons who had TB have a greatly increased risk of smka TB when reinfected. Presses des Mines, 88 p. Towards a global criteria based framework for the sustainability assessment of bioethanol supply chains: Fig 2 provides a typical bifurcation diagram that shows the key features of a backward bifurcation.