Plateaus, rebounds and the effects of individual behaviours in epidemics

Plateaus and rebounds of various epidemiological indicators are widely reported in Covid-19 pandemics studies but have not been explained so far. Here, we address this problem and explain the appearance of these patterns. We start with an empirical study of an original dataset obtained from highly precise measurements of SARS-CoV-2 concentration in wastewater over nine months in several treatment plants around the Thau lagoon in France. Among various features, we observe that the concentration displays plateaus at different dates in various locations but at the same level. In order to understand these facts, we introduce a new mathematical model that takes into account the heterogeneity and the natural variability of individual behaviours. Our model shows that the distribution of risky behaviours appears as the key ingredient for understanding the observed temporal patterns of epidemics.

The effects of heterogeneity and stochastic variability of behaviours on the intrinsic dynamics of epidemics

We report here on a campaign of weekly measurements of concentration of SARS-Cov-2 in wastewater in several treatment plants around the Thau lagoon in the Southwest of France over a nine month period of time. The use of Digital PCR yielded very precise measurements. The observations thus generated exhibit a rough stabilization on plateaus of the epidemic and other remarkable features. Such plateaus are widely reported in the setting of the Covid-19 pandemics. In this paper we raise the question of why such plateaus and other features of epidemics dynamics arise. Indeed, the classical SIR model and its extensions hardly provide an explanation for such behavior. To address this question we introduce here a new model, which takes into account heterogeneity and natural variability of behaviors in populations. Owing to this model, we show that features such as plateaus, rebounds, and shoulders are part of the intrinsic dynamics of an epidemic. In particular, in the context of the Thau lagoon, we argue that they are not generated by public health policy measures or psychological reactions of the population. We then show that this model fits very well the measures obtained around the Thau lagoon.

Effects of experimental warming on small phytoplankton, bacteria and viruses in autumn in the Mediterranean coastal Thau Lagoon

To investigate the responses of a natural microbial plankton community of coastal Mediterranean waters to warming, which are still poorly known, an in situ mesocosm experiment was carried out in Thau Lagoon during autumn 2018. Several microorganisms, including virio-, bacterio-, and phytoplankton < 10 µm in size, were monitored daily and analysed using flow cytometry for 19 consecutive days in six mesocosms. Three mesocosms (control) had the same natural water temperature as the lagoon, and the other three were warmed by + 3 °C in relation to the control temperature. The cytometric analyses revealed an unexpected community dominated by picophytoplanktonic cells, including Prochlorococcus-like and Picochlorum-like cells, which had not previously been found in Thau Lagoon. The experimental warming treatment increased the abundances of nanophytoplankton, cyanobacteria, bacteria and viruses during the experiment and triggered earlier blooms of cyanobacteria and picoeukaryotes. Only the abundance of Picochlorum-like cells was significantly reduced under warmer conditions. The growth and grazing rates of phytoplankton and bacterioplankton estimated on days 2 and 8 showed that warming enhanced the growth rates of most phytoplankton groups, while it reduced those of bacteria. Surprisingly, warming decreased grazing on phytoplankton and bacteria at the beginning of the experiment, while during the middle of the experiment it decreased the grazing on prokaryote only but increased it for eukaryotes. These results reveal that warming affected the Thau Lagoon plankton community from viruses to nanophytoplankton in fall, inducing changes in both dynamics and metabolic rates.

Hydraulic and geochemical impact of occasional saltwater intrusions through a submarine spring in a karst and thermal aquifer (Balaruc peninsula near Montpellier, France)

Submarine springs are a common discharge feature of the karst aquifers along the Mediterranean coast. In some instances, occasional and localized saltwater intrusions can occur through the submarine spring and negatively impact the quality of the groundwater resource. The hydraulic and geochemical behaviour of a submarine spring discharging into the Thau Lagoon just offshore of the Balaruc peninsula near Montpellier, France, has been characterized to determine the impacts of such phenomena to better understand the dynamics of a regional karst aquifer and improve its groundwater management. This work is based on both historical and new hydrogeological and geochemical data, illustrating six occasional saltwater intrusion events (from 1967 to 2014) in the Thau Lagoon area (southern France). Hydraulic perturbation of the aquifer is propagated instantly within the Balaruc-les-Bains peninsula and reaches a distance of about 5 km upgradient within 9 d. Comparison of hydraulic heads during seawater intrusion events in 2010 and 2014 indicates an aggravation of the phenomenon with an increase in hydraulic head variations. In contrast, isotopic tracers (87Sr∕86Sr, D/H, 18O∕16O) and rare earth elements (REEs) demonstrate that the geochemical impact of these inversac events is only observed at the local scale but is still perceptible several years after the event. For example, some of the thermal wells had not recovered their initial geochemical state 20 and 40 months after the last two inversac events (2010 and 2014, respectively), suggesting a geochemical legacy of this phenomenon within the complex karst system. By contrast, an adjacent deep karst compartment located south of the study area is not affected by the saltwater intrusion and is characterized by distinctly different hydrodynamic behaviour. Overall, this work on occasional and localized saltwater intrusions constitutes a key step in understanding the dynamics of this complex karstic and thermal aquifer and will support the management of the groundwater resource.

Hydraulic and geochemical impact of occasional saltwater intrusions through a submarine spring in a karst and thermal aquifer (Balaruc peninsula near Montpellier, France)

Submarine springs are a common discharge feature of the karst aquifers along the Mediterranean coast. In some instances, occasional and localized saltwater intrusions can occur through the submarine spring and negatively impact the quality of the groundwater resource. The hydraulic and geochemical behavior of a submarine spring discharging into the Thau lagoon just offshore of the Balaruc peninsula near Montpellier, France has been characterized to determine the impacts of such phenomena to better understand the dynamics of a regional karst aquifer and improve its groundwater management. This work is based on both historical and new hydrogeological and geochemical data, illustrating 6 occasional saltwater intrusion events (from 1967 to 2014) in the Thau lagoon area (southern France). Hydraulic perturbation of the aquifer is propagated instantly within the Balaruc-les-Bains peninsula and reaches a distance of about 5 km upgradient within 9 days. Comparison of hydraulic heads during seawater intrusion events in 2010 and 2014 indicates an aggravation of the phenomenon with an increase in hydraulic head variations. In contrast, isotopic tracers (87Sr/86Sr, D/H, 18O/16O,) and Rare Earth Elements (REE) demonstrate that the geochemical impact of these inversac events is only observed at the local scale, but is still perceptible several years after the event. For example, some of the thermal wells had not recovered their initial geochemical state 20 and 40 months after the last two inversac events (2010 and 2014, respectively), suggesting a geochemical legacy of this phenomenon within the complex karst system. By contrast, an adjacent deep karst compartment located south of the study area is not affected by the saltwater intrusion and is characterized by distinctly different hydrodynamic behavior. Overall, this work on occasional and localized saltwater intrusions constitutes a key step in understanding the dynamics of this complex karstic and thermal aquifer and will support the management of the groundwater resource.

Groundwater circulation and mixing inferred from age dating with dissolved gas tracers in a complex Mediterranean karstic and thermal aquifer (Thau lagoon area, Montpellier, France).

&lt;p&gt;Groundwater in coastal area is a strategic but fragile resource since it undergoes high anthropogenic pressure that can lead to saltwater intrusion. Therefore the use of coastal groundwater needs a thorough understanding of the groundwater flow and mixing to assure a suitable management of the resource.&lt;/p&gt;&lt;p&gt;The coastal and thermal karstic hydrosystem of the Thau basin (South of France) shows a good example of the pressure that can undergoes coastal groundwater as it is a strategic resource for drinking water, spa activities as well as shellfish aquaculture. In this aquifer, groundwater originates from 3 different naturally sources with contrasted mean residence time (MRT): 1) cold and young karstic water, 2) warm and mineralized thermal waters with long MRT, and 3) marine waters (Thau lagoon and/or seawater). In this context, age dating tracers can be valuable tools for the characterization of the groundwater flow circulations, the estimation of their residence time but also of the mixing which can affect the thermal system.&lt;/p&gt;&lt;p&gt;We used dissolved gases (CFCs and SF6) and &lt;sup&gt;3&lt;/sup&gt;H age dating tracers to characterize the young end-member, as these tracers are particularly suitable for identifying and quantifying water mixing of different ages (Newman et al., 2010). Strategic locations representative of each component of the system (surficial and deep karst, springs and thermal boreholes) were sampled during different hydrogeological contexts (high flow/base flow).&lt;/p&gt;&lt;p&gt;The first results show that as expected, in general, the thermal component has a very low level of dissolved gas indicating long MRT and few mixing whereas karstic springs show high contents of dissolved gas. However, some thermal wells show important and variable gas content indicating mixing with the karstic component and rapid circulation in some parts of the system. These data will contribute to determine the groundwater transfer model(s) in the Thau system and to estimate the contribution of the current karst water to the Balaruc thermal system. These results will in turn, be used within the framework of the &amp;#8220;Dem&amp;#8217;Eaux Thau project&amp;#8221; to develop tools for groundwater resources management allowing decision-makers to take on the challenges of this region.&lt;/p&gt;