Using mobility data in the design of optimal lockdown strategies for the COVID-19 pandemic.

A mathematical model for the COVID-19 pandemic spread, which integrates age-structured Susceptible-Exposed-Infected-Recovered-Deceased dynamics with real mobile phone data accounting for the population mobility, is presented. The dynamical model adjustment is performed via Approximate Bayesian Computation. Optimal lockdown and exit strategies are determined based on nonlinear model predictive control, constrained to public-health and socio-economic factors. Through an extensive computational validation of the methodology, it is shown that it is possible to compute robust exit strategies with realistic reduced mobility values to inform public policy making, and we exemplify the applicability of the methodology using datasets from England and France.

General requirement for harvesting antennae at ca and h channels and transporters.

The production and dissipation of energy in cells is intimately linked to the movement of small molecules in and out of enzymes, channels, and transporters. An analytical model of diffusion was described previously, which was used to estimate local effects of these proteins acting as molecular sources. The present article describes a simple but more general model, which can be used to estimate the local impact of proteins acting as molecular sinks. The results show that the enzymes, transporters, and channels, whose substrates are present at relatively high concentrations like ATP, Na(+), glucose, lactate, and pyruvate, do not operate fast enough to deplete their vicinity to a meaningful extent, supporting the notion that for these molecules the cytosol is a well-mixed compartment. One specific consequence of this analysis is that the well-documented cross-talk existing between the Na(+)/K(+) ATPase and the glycolytic machinery should not be explained by putative changes in local ATP concentration. In contrast, Ca2(+) and H(+) transporters like the Na(+)/Ca2(+) exchanger NCX and the Na(+)/H(+) exchanger NHE, show experimental rates of transport that are two to three orders of magnitude faster than the rates at which the aqueous phase may possibly feed their binding sites. This paradoxical result implies that Ca2(+) and H(+) transporters do not extract their substrates directly from the bulk cytosol, but from an intermediate "harvesting" compartment located between the aqueous phase and the transport site.