Optimal control for an SIR model with limited hospitalised patients.

This paper analyses the optimal control of infectious disease propagation using a classic susceptible-infected-recovered (SIR) model characterised by permanent immunity and the absence of available vaccines. The control is performed over a time-dependent mean reproduction number, in order to minimise the cumulative number of ever-infected individuals (recovered), under different constraints. We consider constraints on non-pharmaceutical interventions ranging from partial lockdown to non-intervention, as well as the social and economic costs associated with such interventions, and the capacity limitations of intensive care units that limits the number of infected individuals to a maximum allowed value. We rigorously derive an optimal quarantine strategy based on necessary optimality conditions. The obtained optimal strategy is of a boundary-bang type, comprising three phases: an initial phase with no intervention, a second phase maintaining the infected population at its maximum possible value, and a final phase of partial lockdown applied over a single interval. The optimal policy is further refined by optimising the transition times between these phases. We show that these results are in excellent agreement with the numerical solution of the problem.

Transient frequency preference responses in cell signaling systems.

Ligand-receptor systems, covalent modification cycles, and transcriptional networks are the fundamental components of cell signaling and gene expression systems. While their behavior in reaching a steady-state regime under step-like stimulation is well understood, their response under repetitive stimulation, particularly at early time stages is poorly characterized. Yet, early-stage responses to external inputs are arguably as informative as late-stage ones. In simple systems, a periodic stimulation elicits an initial transient response, followed by periodic behavior. Transient responses are relevant when the stimulation has a limited time span, or when the stimulated component's timescale is slow as compared to the timescales of the downstream processes, in which case the latter processes may be capturing only those transients. In this study, we analyze the frequency response of simple motifs at different time stages. We use dose-conserved pulsatile input signals and consider different metrics versus frequency curves. We show that in ligand-receptor systems, there is a frequency preference response in some specific metrics during the transient stages, which is not present in the periodic regime. We suggest this is a general system-level mechanism that cells may use to filter input signals that have consequences for higher order circuits. In addition, we evaluate how the described behavior in isolated motifs is reflected in similar types of responses in cascades and pathways of which they are a part. Our studies suggest that transient frequency preferences are important dynamic features of cell signaling and gene expression systems, which have been overlooked.

Effects of the fungicide azoxystrobin in two habitats representative of mediterranean coastal wetlands: A mesocosm experiment.

This paper investigates the effects of the fungicide azoxystrobin, a compound widely used in rice farming, on aquatic communities representative of two habitats characteristic of Mediterranean wetland ecosystems: water springs and eutrophic lake waters. The long-term effects of azoxystrobin were evaluated on several structural (phytoplankton, zooplankton, macroinvertebrate populations and communities) and functional (microbial decomposition, macrophyte and periphyton growth) parameters making use of freshwater mesocosms. Azoxystrobin was applied in two pulses of 2, 20, 200 µg/L separated by 14 d using the commercial product ORTIVA (23 % azoxystrobin w/w). The results show that these two habitats responded differently to the fungicide application due to their distinct physico-chemical, functional, and structural characteristics. Although overall sensitivity was found to be similar between the two (lowest NOEC < 2 µg/L), the taxa and processes that were affected differed substantially. In general, the most sensitive species to the fungicide were found in the water spring mesocosms, with some species of phytoplankton (Nitzschia sp.) or macrocrustaceans (Echinogammarus sp. and Dugastella valentina) being significantly affected at 2 µg/L. In the eutrophic lake mesocosms, effects were found on phytoplankton taxa (Desmodesmus sp. and Coelastrum sp.), on numerous zooplankton taxa, on chironomids and on the beetle Colymbetes fuscus, although at higher concentrations. The hemipteran Micronecta scholtzi was affected in both treatments. In addition, functional parameters such as organic matter decomposition or macrophyte growth were also affected at relatively low concentrations (NOEC 2 µg/L). Structural Equation Modelling was used to shed light on the indirect effects caused by azoxystrobin on the ecosystem. These results show that azoxystrobin is likely to pose structural and functional effects on Mediterranean wetland ecosystems at environmentally relevant concentrations. Moreover, it highlights the need to consider habitat-specific features when conducting ecotoxicological research at the population and community levels.

Optimal control for a SIR epidemic model with limited quarantine.

Social distance, quarantines and total lock-downs are non-pharmaceutical interventions that policymakers have used to mitigate the spread of the COVID-19 virus. However, these measures could be harmful to societies in terms of social and economic costs, and they can be maintained only for a short period of time. Here we investigate the optimal strategies that minimize the impact of an epidemic, by studying the conditions for an optimal control of a Susceptible-Infected-Recovered model with a limitation on the total duration of the quarantine. The control is done by means of the reproduction number [Formula: see text], i.e., the number of secondary infections produced by a primary infection, which can be arbitrarily varied in time over a quarantine period T to account for external interventions. We also assume that the most strict quarantine (lower bound of [Formula: see text]) cannot last for a period longer than a value [Formula: see text]. The aim is to minimize the cumulative number of ever-infected individuals (recovered) and the socioeconomic cost of interventions in the long term, by finding the optimal way to vary [Formula: see text]. We show that the optimal solution is a single bang-bang, i.e., the strict quarantine is turned on only once, and is turned off after the maximum allowed time [Formula: see text]. Besides, we calculate the optimal time to begin and end the strict quarantine, which depends on T, [Formula: see text] and the initial conditions. We provide rigorous proofs of these results and check that are in perfect agreement with numerical computations.