Focus on bridging the gap between theoretical mathematics and biological phenomena to understand how biofilms grow, spread, and resist treatment, through mathematical modelling, analysis and simulation of biofilm interaction with interfaces and flows, specifically analyzing their resistance to antibiotics.
Pattern formation and morphogenesis
– Developed hybrid models combining discrete cellular rules with continuum fluid (Navier-Stokes) descriptions, to successfully simulate complex biofilm structures observed in experiments, such as ripples, mounds, streamers, and helical patterns, as well as the dynamics of bacterial aggregates in microflows.
pre12 srep16 springer17 springer18
– Developed hybrid models for biofilms on air/agar interfaces coupling discrete cellular rules with for bacterial growth and differentiation with von Karman plate equations to understand wrinkle formation as a response to the interaction with the substrate and its water content.
pre15 springer18
– Proposed poroelastic equations and multiphase porous media type approaches to account for internal liquid transport. These models account for the interaction between the solid biomass (cells and extracellular matrix) and fluid flow, specifically looking at how water intake from the environment leads to biofilm spreading and the formation of physical patterns like wrinkles.
jcp19 entropy20
– Established wellposedness of multiphase systems coupling conservation laws for porous biomass with reaction-diffusion systems for concentrations and fluid/elasticity equations for flows and tensions.
na24 amm23 cnsns26
Antibiotic resistance mechanisms
– Proposed Dynamic energy budget (DEB) theories to evaluate how antibiotics affect different bacterial types within a biofilm in hybrid cellular automata models. This helps explain why biofilms are so resistant to treatment, showing that certain bacterial populations can differentiate to produce more protective extracellular polymeric substances (EPS) or enter dormant states to survive.
cnsns18 amm23
– Introduced hybrid Immersed boundary – Dynamic energy budget models for the growth of bacterial aggregates taking into account bacterial shape and geometrical arrangements in antibiotic effects
ccp21
– Analysis of multiphase conservation laws for densities of alive and dead bacteria coupled to reaction-diffusion systems for concentrations, developing antibiotic cocktails that can drive biofilms to finite time extinction. This research provides a mathematical framework for optimizing dosage and timing to completely eliminate resistant bacterial communities.
cnsns26
Propagation of epidemics
Contributions to the mathematical analysis of infectious diseases, particularly regarding parameter identification with quantified uncertainty in epidemiological models of covid19 spread.
rip22 elsevier22
