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Approximately a quarter of the global population harbours the TB bacteria and another eight to nine million new cases of tuberculosis emerge every year [ 5 ]. To the best of our knowledge, this result has not been observed in previous TB modelling studies. The equilibria of the model are found by setting the rates of all variables in the left-hand side of Eq 1 to zero.

S5 Appendix Further discussion on parameters. Extended Abstracts, part II – page 70, Including the temporal change in PM2. Simulation tool with its expert interface for anslyse solar design. Raising the intensity of recurrent TB: Dynamical models of tuberculosis and their applications. Drebszok, Artur Wyrwa, Isabelle Blanc.

Backward bifurcation and hysteresis in models of recurrent tuberculosis

Hence, with relatively low immunity amongst recovered individuals [ 13 ] backward bifurcation can occur despite the fact that the Lipsitch and Murray [ 18 ] prediction would literally predict otherwise. New spatiotemporally resolved LCI applied to photovoltaic electricity. Causes of backward bifurcations in some epidemiological models.


Life cycle assessment of prospective energy scenarios for in an insular context: Reports 1 document Isabelle Blanc, Damien Friot. Following the methods in Garba et al. Contribution of life cycle assessment: Both Feng et al.

They showed that this implies. We now state the following Lemma This occurs when an asymptotically stable infection free equilibrium concurrently exists with a stable non-trivial equilibria even though the basic reproduction number R 0 is less than unity.

Exogenous reinfection in tuberculosis. Isabelle Blanc, Catherine Guermont. An epidemiological model is presented that provides a comprehensive description of the transmission pathways involved for recurrent tuberculosis TBwhereby cured individuals can become reinfected.

Backward bifurcation and hysteresis in models of recurrent tuberculosis

The Lancet infectious disease. Support Center Support Center. Illustrates backward bifurcation when recurrent TB parameters are included. A parameterized model for Denmark.

R 0 may be determined using the next generation operator method see [ smua ] as shown in S1 Appendixwhere it is sma that: No reinfection path Ai. Hence, this already suggests that R 0 alone is unable to completely quantify some key dynamical features of the TB epidemic, and is in fact the first sign that a backward bifurcation might be involved.

Computational and mathematical methods in medicine. A first application to photovoltaic systems. Chauffage, ventilation, conditionnement, 65 5pp.

Transmission of tuberculosis with exogenous re-infection and endogenous reactivation. National Center for Biotechnology InformationU. The solid blue line represent stable equilibrium while the dotted red line represent unstable equilibrium. The case of Tuberculosis. It can be seen from Eqs 11 and 12that when exogenous reinfection parameter p increases, R c decreases, and vice-versa.


In the absence of recurrent TB due to reinfection i. In the more recent literature, numerous studies have pointed out that initial infection may not confer protection against exogenous reinfection especially in high-risk populations [ 5051 ].

Pergamon Press, Oxford, p. Enhanced Structure Path Analysis: Model analysis Basic anapyse Following the methods in Garba et al.

Isabelle BLANC Professeur at MINES ParisTech, PSL Research University

Although, there are numerous TB models that have attempted to include the recurrent TB pathway for instance see [ 22 — 27 ]none have explored its role in the formation of backward bifurcation. The extra infectives from the latter compartment will tend to increase TB prevalence and thus widen the bifurcation curves. Conversely, when R 0 is above unity an epidemic may trigger and long-term disease persistence is feasible. Simplified life cycle approach: Simulation tool with its expert interface for the thermal design of multizone buildings.

This characteristic is indicative of forward bifurcation as seen in Fig 7.

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

Presses des Mines, 88 p. Thus, the following equality is satisfied.

Received Jun 27; Accepted Feb Ecological IndicatorsElsevier,11 5pp. Bruno Peuportier, Isabelle Blanc.