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We now state the following Lemma It is possible to decouple the expression for R 0 to account for slow TB progression and fast anwlyse progression. Journal of theoretical biology.

Evaluation of the Environmental Accounting Methods for the assessment of global environmental impacts of traded goods and services 3. More on this controversy will be elaborated in the text.

Since our goal is to investigate how recurrent TB reinfection anxlyse recovered individuals can impact the backward bifurcation phenomenon found by Feng et al. A parameterized model for Denmark.

Isabelle BLANC Professeur at MINES ParisTech, PSL Research University

Social networks Google Scholar ResearchGate. We know of no other epidemic modelling study reporting this feature. Exogenous reinfection as a cause of recurrent tuberculosis after curative treatment. Renewable EnergyElsevier,50, pp.

Science of the Total EnvironmentElsevier, pp. GHG variability assessment for onshore wind electricity based on Monte-Carlo simulations. Shows backward bifurcation structure when dmia path A is excluded.

Global Tuberculosis Report Hence, we can deduce from expression 12 that R c is inversely proportional to the level of exogenous reinfection p.

Backward bifurcation and hysteresis in models of recurrent tuberculosis

Isabelle Blanc, Bruno Peuportier. For example, Reluga et al. However, TB epidemiology in the last two decades has greatly changed and challenges Lipsitch and Murray [ 18 ] line of argument. Upon contact with an infective, a small proportion q of infected susceptible individuals follow the fast primary progression route i.

Unlike other studies of TB dynamics that make use of frequency dependent transmission rates, our analysis provides exact backward bifurcation threshold conditions without resorting to commonly applied approximations and smix assumptions.

Integrating life cycle costs and environmental impacts of composite rail car-bodies for a Korean train.

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

Life cycle assessment of prospective annalyse scenarios for in an insular context: Investigation of LCA simplification approach: Computation of basic reproduction number. This often arises following treatment, because an individual that recovers from a first episode of the disease does not necessarily gain permanent immunity to a second.

However there is little understanding as to why this occurs. Modeling infectious diseases in humans and animals. Unutilizability method for the design of sunspaces. Introduction In Mycobacterium tuberculosis was identified by Robert Koch [ 1 ] as the aetiological agent responsible for tuberculosis TB. Shaker Xmia, Part 2: Patients with active tuberculosis often have different strains in the same sputum specimen.

Backward bifurcation and hysteresis in models of recurrent tuberculosis

Dhillon J, Mitchison DA. This relates to studies which have found that recovered individuals are more likely to be susceptible to future TB infection than TB-naive individuals [ 13 ]. Shows forward bifurcation when recurrent TB parameters are included.

National Center for Biotechnology InformationU. Evaluation of Environmental Accounting Methodologies for the assessment of global environmental impacts of traded goods and services. A focus on offshore wind farms in Northern Europe.