arXiv subjects

J. M. McCaw

Publications and source records attributed to J. M. McCaw.

3 recordsLinked to original sources

arXiv2016

A biological model of scabies infection dynamics and treatment explains why mass drug administration does not lead to elimination

Despite a low global prevalence, infections with Sarcoptes scabiei, or scabies, are still common in remote communities such as in northern Australia and the Solomon Islands. Mass drug administration (MDA) has been utilised in these communities, and although prevalence drops substantially initially, these reductions have not been sustained. We develop a compartmental model of scabies infection dynamics and incorporate both ovicidal and non-ovicidal treatment regimes. By including the dynamics of mass drug administration, we are able to reproduce the phenomena of an initial reduction in prevalence, followed by the recrudescence of infection levels in the population. We show that even under a `perfect' two-round MDA, eradication of scabies under a non-ovicidal treatment scheme is almost impossible. We then go on to consider how the probability of elimination varies with the number of treatment rounds delivered in an MDA. We find that even with infeasibly large numbers of treatment rounds, elimination remains challenging.

q-bio.PE↗

arXiv2005

On the continuous spectral component of the Floquet operator for a periodically kicked quantum system

By a straightforward generalisation, we extend the work of Combescure from rank-1 to rank-N perturbations. The requirement for the Floquet operator to be pure point is established and compared to that in Combescure. The result matches that in McCaw. The method here is an alternative to that work. We show that if the condition for the Floquet operator to be pure point is relaxed, then in the case of the delta-kicked Harmonic oscillator, a singularly continuous component of the Floquet operator spectrum exists. We also provide an in depth discussion of the conjecture presented in Combescure of the case where the unperturbed Hamiltonian is more general. We link the physics conjecture directly to a number-theoretic conjecture of Vinogradov and show that a solution of Vinogradov's conjecture solves the physics conjecture. The result is extended to the rank-N case. The relationship between our work and the work of Bourget on the physics conjecture is discussed.

math-ph↗

arXiv2005

Pure point spectrum for the time evolution of a periodically rank-N kicked Hamiltonian

We find the conditions under which the spectrum of the unitary time evolution operator for a periodically rank-N kicked system remains pure point. This stability result allows one to analyse the onset of, or lack of chaos in this class of quantum mechanical systems, extending the results for rank-1 systems produced by Combescure and others. This work includes a number of unitary theorems equivalent to those well known and used in the self-adjoint theory.

math-ph↗