I have developed a number of colony-level mathematical models of within-host bacterial infections. These models are formulated as systems of ordinary differential equations (ODEs) and solved using both analytical methods (e.g. stability analysis) and numerical methods (e.g. the finite difference method). Models were carefully parameterised using data from an accompanying experimental programme and using parameter fitting methods such as the Markov Chain Monte Carlo (MCMC) method, genetic algorithms and nonlinear mixed-effects models.
 Roberts, P.A., Huebinger, R.M., Keen, E., Krachler, A.M., Jabbari, S., 2019. Mathematical Model Predicts Anti-adhesion–Antibiotic–Debridement Combination Therapies Can Clear an Antibiotic Resistant Infection. PLoS Comput. Biol., 15(7): e1007211 (39 pages). DOI
I developed the first mathematical models for anti-adhesion–antibiotic combination therapies. I demonstrated that these treatments are more than the sum of their parts, combining synergistically, rather than additively. I also determined optimal treatment regimens to eliminate bacteria while minimising antibiotic usage and avoiding the development of antimicrobial resistance.
 Roberts, P.A., Huebinger, R.M., Keen, E., Krachler, A.M., Jabbari, S., 2018. Predictive Modelling of a Novel Anti-adhesion Therapy to Combat Bacterial Colonisation of Burn Wounds. PLoS Comput. Biol., 14(5): e1006071 (28 pages). (selected by PLoS for press release) DOI (arXiv) (Code)
I developed the first mathematical model to consider the use of a novel anti-adhesion therapy for the treatment of bacterial infections. The model elucidated previously obscure mechanisms by which this treatment operates and predicted experimentally testable and clinically-relevant ways to improve therapeutic efficacy.