Stability and Bifurcation Properties of Index-1 DAEs

Numerical Algorithms, 1998

Double singularity-induced bifurcation points and singular Hopf bifurcations

Dynamics and Stability of Systems, 2000

The singularity-induced bifurcation and its Kronecker normal form

SIAM J Matrix Analysis, 2001

An SIB theorem for infinite-dimensional implicit dynamical systems

Proc Royal Soc A, 2001 ... A much simpler proof of the main result of this paper.

this idea was awarded a SIAM student paper prize in 1999

The flow of a DAE near a singular equilibrium

SIAM J Matrix Analysis, 2002

The global structure of a spatial model of infectious disease

Proc Royal Soc A, 2003

Transversality and separation of zeros in second order differential equations

Proc American Math Society, 2003

Trajectories of a DAE near a pseudo-equilibrium

Nonlinearity, 2004

Finite-Time Extinction in Nonlinear Diffusion Equations

Applied Maths Letters, 2004

Sequential and continuum bifurcations in degenerate elliptic equations

Proc American Math Society, 2004

Bifurcations of periodic solutions satisfying the zero-Hamiltonian constraint in fourth-order differential equations

SIAM J Math Analysis, 2005

Classifying the Role of Trade-offs in the Evolutionary Diversity of Pathogens

Proc Royal Soc A, 2006

Algorithms for the Computation of Solutions and Bifurcations of the Ornstein-Zernike equation

Physical Review E, 2006

A Bifurcation Analysis of the Ornstein-Zernike Equation with Hypernetted Chain Closure

Mathematical Analysis and Applications, 2007

A Numerical Bifurcation Analysis of the Ornstein-Zernike equation with Hypernetted Chain Closure

SIAM J Scientific Computation, 2007

Constraints on microbial metabolism drives evolutionary diversification in homogeneous environments

  1. J.Evolutionary Biology, 2007

F1000 Biology recommendation

Hopf Bifurcations in Singular Differential-Algebraic Equations

Special Issue MATCOM: Structured Dynamical Systems, 2008

Normal Forms, Quasi-Invariant Manifolds and Bifurcations of Nonlinear Difference Algebraic Equations

SIAM J Math Analysis, 2008

Understanding the limits to generalizibility of experimental evolutionary models

Nature, 2008

+ a mathematical companion preprint

Antibiotic Cycling Versus Mixing: the Difficulty of Using Mathematical Models to Definitively Quantify their Relative Merits

Mathematical Biosciences and Engineering, 2010

Rotating Antibiotics Selects Optimally Against Antibiotic Resistance, in Theory

Mathematical Biosciences and Engineering, 2010

Modelling cognitive decline in the Hypertension in the Very Elderly Trial (HyVET) and proposed risk tables for population use

PLoS One, 2010

Metabolic Trade-offs and the Maintenance of the Flattest and the Fittest

Nature, 2011

reviewed in Nature Reviews Genetics

Selecting Against Antibiotic-Resistant Pathogens: Optimal Treatments in the Presence of Commensal Bacteria

Bulletin of Mathematical Biology, 2011

this paper will be announced the winner of the 2012 Lee Segel Prize

And many thanks to Philip Maini for his: Editor’s Choice, 2013

The optimal deployment of synergistic antibiotics: a control-theoretic approach

Royal Society Interface, 2012

F1000 Biology recommendation

When the Most Potent Combination of Antibiotics Selects for the Greatest Bacterial Load: the Smile-Frown Transition

PLoS Biology 2013


reviewed in a few places

Pharma Mag

The form of a trade-off determines the response to competition

Ecology Letters, 2013

Testing the Optimality Properties of a Dual Antibiotic Treatment in a 2-locus, 2-allele model

Royal Society Interface, 2014

Genomics of rapid adaptation to antibiotics: convergent evolution and scalable sequence amplification

Genome Biology and Evolution, 2014

Bistable expression of virulence genes in Salmonella leads to the formation of an antibiotic-tolerant subpopulation

PLoS Biology 2014

Biophysical mechanisms that maintain biodiversity through trade-offs

Nature Communications 2015

Using a Sequential Regimen to Eliminate Bacteria at Sub-Lethal Antibiotic Dosages

PLoS Biology 2015

Temporal variation in antibiotic environments slows down resistance evolution in pathogenic Pseudomonas aeruginosa

Evolutionary Applications 2015

Kinase Inhibition Leads to Hormesis in a Dual Phosphorylation-Dephosphorylation Cycle

PLoS Computational Biology 2016

Antibiotic Cycling and Antibiotic Mixing: which one best mitigates antibiotic resistance?

Molecular Biology and Evolution 2017 (Open Access)

F1000 Biology recommendation

The unconstrained evolution of fast efficient and antibiotic resistant bacterial genomes

Nature Ecology and Evolution 2017 - review in Nature E&E - behind the paper

The recent appearance of this article means our data must be accurate! :

Alternative Evolutionary Paths to Bacterial Antibiotic Resistance Cause Distinct Collateral Effects

Molecular Biology and Evolution 2017 (Open Access)

Antibiotic strategies in critical care: back to square one?

Lancet ID, 2018

Antibiotic combination efficacy (ACE) networks for a Pseudomonas aeruginosa model

PLoS Biology 2018

Drug-mediated, metabolic tipping: shifts to antimicrobial resistance in a mixed-species community

Nature Ecology & Evolution 2018

Predicting community dynamics of antibiotic-sensitive and -resistant species in fluctuating environments

Royal Society Interface 2020

Evolution of drug-resistant and virulent small colonies in phenotypically diverse populations of the human fungal pathogen Candida glabrata

Proceeding Royal Society B 2020

Antibiotic Dosages of Fastest Resistance Evolution: gene amplifications underpinning the inverted U

Molecular Biology and Evolution 2021

Predicting microbial growth dynamics in response to nutrient availability

PLoS Computational Biology 2021

Seeking patterns of antibiotic resistance in ATLAS, an open, raw MIC database with patient metadata

Nature Communications 2022 - Behind the paper community page


Amusing, perhaps not, that Creationists do not believe our paper shows any evidence of evolution (our E.coli did not turn into a man, apparently): this link.

It was (at least for a little while) one of PLoS Biology’s

top 5 viewed papers:

the proof....!

& a mini-tutorial:

reviewed in a few places