Uncertainty quantification in mechanistic epidemic models via cross-entropy approximate Bayesian computation.

This paper proposes a data-driven approximate Bayesian computation framework for parameter estimation and uncertainty quantification of epidemic models, which incorporates two novelties: (i) the identification of the initial conditions by using plausible dynamic states that are compatible with observational data; (ii) learning of an informative prior distribution for the model parameters via the cross-entropy method. The new methodology's effectiveness is illustrated with the aid of actual data from the COVID-19 epidemic in Rio de Janeiro city in Brazil, employing an ordinary differential equation-based model with a generalized SEIR mechanistic structure that includes time-dependent transmission rate, asymptomatics, and hospitalizations. A minimization problem with two cost terms (number of hospitalizations and deaths) is formulated, and twelve parameters are identified.

Data-driven modelling of social forces and collective behaviour in zebrafish.

Zebrafish are rapidly emerging as a powerful model organism in hypothesis-driven studies targeting a number of functional and dysfunctional processes. Mathematical models of zebrafish behaviour can inform the design of experiments, through the unprecedented ability to perform pilot trials on a computer. At the same time, in-silico experiments could help refining the analysis of real data, by enabling the systematic investigation of key neurobehavioural factors.

Data-driven stochastic modelling of zebrafish locomotion.

In this work, we develop a data-driven modelling framework to reproduce the locomotion of fish in a confined environment. Specifically, we highlight the primary characteristics of the motion of individual zebrafish (Danio rerio), and study how these can be suitably encapsulated within a mathematical framework utilising a limited number of calibrated model parameters. Using data captured from individual zebrafish via automated visual tracking, we develop a model using stochastic differential equations and describe fish as a self propelled particle moving in a plane.

Analytical modelling of the spread of disease in confined and crowded spaces.

Since 1927 and until recently, most models describing the spread of disease have been of compartmental type, based on the assumption that populations are homogeneous and well-mixed. Recent models have utilised agent-based models and complex networks to explicitly study heterogeneous interaction patterns, but this leads to an increasing computational complexity. Compartmental models are appealing because of their simplicity, but their parameters, especially the transmission rate, are complex and depend on a number of factors, which makes it hard to predict how a change of a single environmental, demographic, or epidemiological factor will affect the population.

How to turn a genetic circuit into a synthetic tunable oscillator, or a bistable switch.

Systems and Synthetic Biology use computational models of biological pathways in order to study in silico the behaviour of biological pathways. Mathematical models allow to verify biological hypotheses and to predict new possible dynamical behaviours. Here we use the tools of non-linear analysis to understand how to change the dynamics of the genes composing a novel synthetic network recently constructed in the yeast Saccharomyces cerevisiae for In-vivo Reverse-engineering and Modelling Assessment (IRMA).