Singularity and Symmetry Analyses for Tuberculosis Epidemics

Singularity and symmetry analyses of mathematical models of epidemics

Application of Symmetry and Symmetry Analyses to Systems of First-Order Equations Arising from Mathematical Modelling in Epidemiology

We examine the integrability, in terms of the Painlevé singularity analysis and of the Lie symmetry analysis, of systems of nonlinear first-order ordinary differential equations that arise in the particular area of Mathematical Modelling known as Rational Epidemiology. These analyses are presented as being complementary to the standard analysis using the methods of Dynamical Systems. The import...

Analytic Behaviour of Competition among Three Species

We analyse the classical model of competition between three species studied by May and Leonard (SIAM J Appl Math 29 (1975) 243-256) with the approaches of singularity analysis and symmetry analysis to identify values of the parameters for which the system is integrable. We observe some striking relations between critical values arising from the approach of dynamical systems and the singularity ...

Quantifying the intrinsic transmission dynamics of tuberculosis.

Previously we have formulated transmission models of untreated tuberculosis epidemics (Blower et al., Nature, Medicine 1 (1995), 815-821); in this paper, we present time-dependent uncertainty and sensitivity analyses in order to quantitatively understand the transmission dynamics of tuberculosis epidemics in the absence of treatment. The time-dependent uncertainty analysis enabled us to evaluat...

Identification of Mycobacterium tuberculosis adherence-mediating components: a review of key methods to confirm adhesin function

Anti-adhesion therapy represents a potentially promising avenue for the treatment and prevention of tuberculosis in a post-antibiotic era. Adhesins are surface-exposed microbial structures or molecules that enable pathogenic organisms to adhere to host surfaces, a fundamental step towards host infection. Although several Mycobacterium tuberculosis adhesins have been identified, it is predicted ...