RESUMEN

The Hodgkin-Huxley (H-H) landmark model is described by a system of four nonlinear differential equations that describes how action potentials in neurons are initiated and propagated. However, obtaining some of the parameters of the model requires a tedious combination of experiments and data tuning. In this letter, we propose the use of a minimal error iteration method to estimate some of the parameters in the H-H model, given the measurements of membrane potential. We provide numerical results showing that the approach approximates well some of the model's parameters, using the measured voltage as data, even in the presence of noise.

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RESUMEN

We use an age-dependent SIR system of equations to model the evolution of the COVID-19. Parameters that measure the amount of interaction in different locations (home, work, school, other) are approximated from in-sample data using a random optimization scheme, and indicate changes in social distancing along the course of the pandemic. That allows the estimation of the time evolution of classical and age-dependent reproduction numbers. With those parameters we predict the disease dynamics, and compare our results with out-of-sample data from the City of Rio de Janeiro. Finally, we provide a numerical investigation regarding age-based vaccination policies, shedding some light on whether is preferable to vaccinate those at most risk (the elderly) or those who spread the disease the most (the youngest). There is no clear upshot, as the results depend on the age of those immunized, contagious parameters, vaccination schedules and efficiency.

RESUMEN

The derivation by Alan Hodgkin and Andrew Huxley of their famous neuronal conductance model relied on experimental data gathered using the squid giant axon. However, the experimental determination of conductances of neurons is difficult, in particular under the presence of spatial and temporal heterogeneities, and it is also reasonable to expect variations between species or even between different types of neurons of the same species.We tackle the inverse problem of determining, given voltage data, conductances with non-uniform distribution in the simpler setting of a passive cable equation, both in a single or branched neurons. To do so, we consider the minimal error iteration, a computational technique used to solve inverse problems. We provide several numerical results showing that the method is able to provide reasonable approximations for the conductances, given enough information on the voltages, even for noisy data.

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