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Van den Driessche P, Watmough J. Thus, the following equality is satisfied.

Qnalyse For the usual forward bifurcation eg. Backward bifurcation is likely to occur in this scenario, since reinfection will be greater than endogenous reactivation i. Isabelle Blanc, Camille Marini.

Hence, we can deduce from expression 12 that R c is inversely proportional to the level of exogenous reinfection p. Our main goal is to determine conditions that lead to the appearance of a backward bifurcation. The natural history of tuberculosis: Exogenous reinfection as a cause of recurrent tuberculosis after curative treatment.

Rate of reinfection tuberculosis snia successful treatment is higher than rate of new tuberculosis. In addition, recurrent TB can induce forward bifurcation with hysteresis, rather than just the usual forward bifurcation.


Backward bifurcation and hysteresis in models of recurrent tuberculosis

Geothermal Energy, 2, pp. Quantifying the intrinsic transmission dynamics of tuberculosis. Isabelle Blanc, Catherine Guermont. On the role of variable latent periods in mathematical models for tuberculosis.

Isabelle BLANC Professeur at MINES ParisTech, PSL Research University

New spatiotemporally resolved LCI applied to photovoltaic electricity. The threshold implies that TB can be eliminated from the community if the basic reproduction number is maintained below R c i.

John Wiley and Sons; Estimating the loss of life expectancy attributable to PM2. The model is represented graphically in Fig 3 and is ana,yse on the following processes.

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

The stability of the DFE is controlled by the basic reproduction number R 0 which represents the average number of new infections generated by an anqlyse individual when introduced into an entirely susceptible population. Our extended model has some interesting insights with regard to these studies.

Furthermore, recurrent TB can independently induce backward bifurcation phenomena if it exceeds a certain threshold. Number of documents As such, Lipsitch and Murray [ 18 ] argued that backward bifurcations should not be expected in the real world.

Backward bifurcation and hysteresis in models of recurrent tuberculosis

TB is unusual smiw that it can arise via both exogenous and endogenous infection. Thus, the exposure to tubercle bacilli does not necessarily result in the manifestation of clinical forms of TB. Development of an object oriented model for the assessment of the environment quality of buildings.


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.

Shaker Verlag, Part 2: 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. Applying LCA to design alternatives.

Swiss bioethanol supply inWhat are the sustainability stakes of two scenarios for Switzerland?. A key goal of this paper is to investigate the effect of recurrent TB on the formation of backward bifurcations through detailed mathematical modelling. Presses des Mines, 88 p.