Mean-field models in network inference and epidemic control

Systems that are comprised of agents and pairwise interactions between agents can be studied through the lenses of Network theory. As a general framework, Network Theory has applications in various disciplines, including Statistical Physics, Economics, and Biology. The interplay between the contact structure of a population and epidemic spreading is one of the most studied research areas in Epidemiology, where network based research has offered many breakthroughs in recent years. Since an individual based description is computationally intractable, as state spaces scale exponentially with the number of agents modelled, many mathematical approximations have been developed to describe the system in terms of low dimensional aggregate statistics, such as the average number of infected people. This thesis is focused on the application of such approximation techniques, in particular the well known mean-field models, to two key problems in Epidemiology: inference and epidemic control. In the first part of this work, the theme is the inference of network properties from the observation of outbreaks at a population-level. Typically, readily available information during an outbreak is (daily) case counts. With this in mind, a new mean-field like model is introduced to approximate epidemics on networks via Birthand-Death processes, whose rates are random variables which depend implicitly on the structure of the underlying network and disease dynamics. By using Bayesian model selection, it is possible to recover the most likely underlying network class from datasets that consist only of discrete-time observations from one single epidemic. Further, having a description in terms of Birth-and-Death processes allows to study the large N limit of the process as a one-dimensional Fokker-Planck equation, that implies an even greater reduction in dimensionality. In the second part of this thesis more standard mean-field models are adopted to perform epidemic control. The aim is to reduce the burden of an outbreak on a target population. Intervention policies may consist of one time interventions either to minimise the epidemic peak or the final size, or to maximise the average time to infection. Homogeneous mixing models are a nice tool to showcase how interventions that achieve such goals can be optimised. A network perspective is introduced to study the so-called disease-induced herd immunity: in principle, epidemics act like targeted vaccinations, preferentially immunising higher-risk individuals. This means that the herd-immunity threshold might be reached at lower levels compared to that derived from homogeneous mixing models, and this might be relevant for epidemic control. However, it is shown that the magnitude of this effect depends heavily on how both the topology of the contact network and the way non-pharmaceutical interventions are modelled. Finally, epidemic response can be thought of as a feedback process, that is, social distancing policies might be deployed depending on the observed epidemic curve, rather than being pre-determined from theoretical arguments.In this case, the goal is to maintain the epidemic at manageable levels throughout its course, by tailoring interventions that aim to be as less disruptive as possible. This possibility is investigated on a high dimensional network model, by deriving a feedback-loop control action that at its core is based on a mean-field approximation

Optimal timing of one-shot interventions for epidemic control

The interventions and outcomes in the ongoing COVID-19 pandemic are highly varied. The disease and the interventions both impose costs and harm on society. Some interventions with particularly high costs may only be implemented briefly. The design of optimal policy requires consideration of many intervention scenarios. In this paper we investigate the optimal timing of interventions that are not sustainable for a long period. Specifically, we look at at the impact of a single short-term non-repeated intervention (a “one-shot intervention”) on an epidemic and consider the impact of the intervention’s timing. To minimize the total number infected, the intervention should start close to the peak so that there is minimal rebound once the intervention is stopped. To minimise the peak prevalence, it should start earlier, leading to initial reduction and then having a rebound to the same prevalence as the pre-intervention peak rather than one very large peak. To delay infections as much as possible (as might be appropriate if we expect improved interventions or treatments to be developed), earlier interventions have clear benefit. In populations with distinct subgroups, synchronized interventions are less effective than targeting the interventions in each subcommunity separately

Il PON Reti e Mobilità e gli obiettivi di Sostenibilità: il ruolo del Piano di Monitoraggio Ambientale

The National Operative Program (PON) “Reti e mobilità” has been approved by European Commission on the 7th of December 2007. The strategic approach of the PON, exclusively devoted to the socalled “convergence regions” of Italy (Campania, Calabria, Sicilia, Puglia), aims to: 1. improve the modal balance by an economic, social and environmental perspective; 2. develop the inter-modality in order to move towards the integration of convergence area into the network of the European transport system; 3. improve the mobility and the accessibility, also to reduce the traffic congestion; 4. increase the efficiency related to security standards, to management techniques and to the quality of transportation services in the sector of freight; 5. guarantee the reduction of environmental impacts through a global improvement of the efficiency of the transport systems. In such a way it is clear that the PON “Reti e mobilità” takes greatly into account the Sustainability principles recognized at European scale as attested by the budget, namely over the 70% of the entire fund, associated with low-impacts infrastructures (railways and harbors). The PON has been submitted to the SEA procedure, following what the 2001/42/CE Directive establishes. The Environmental Report of PON devotes great attention to the monitoring activity as shown by the reported recommendation about the need for adequate measures for the environmental monitoring, also in order to apply corrective measures during the implementation of the program. By this point of view, a first and important step has been the elaboration of the “Environmental Monitoring Plan” (EMP) that represents the main methodological document for the following implementation of the monitoring activity. This paper, after a brief presentation of the program and of the objectives of Sustainability that the Programs aims to pursue through the realization of specific projects, is devoted to introduce the Environmental Monitoring Plan of the PON that has been approved by the Ministry of the Infrastructures and Transport -in charge as Management Authority of the PON- in February 2011. In detail, the PMA represents the tool through which, the Management Authority, that has specific responsibilities and functions in terms of monitoring and environmental assessment of the program, controls the significant impacts on the environment caused by the implementation of the PON and verify the level of achievement of the established objectives of environmental sustainability. The structure of EMP is based on three main aspects: 1) the adoption of the results of other interesting experiences carried out by experts institutions on the topic; 2) an approach favoring the creation of an “integrated” monitoring system with the others Operative Programs activated at regional scale; 3) the implementation of a cooperation and shared process with all the directly-involved actors

Bindarit inhibits human coronary artery smooth muscle cell proliferation, migration and phenotypic switching

Bindarit, a selective inhibitor of monocyte chemotactic proteins (MCPs) synthesis, reduces neointimal formation in animal models of vascular injury and recently has been shown to inhibit in-stent late loss in a placebo-controlled phase II clinical trial. However, the mechanisms underlying the efficacy of bindarit in controlling neointimal formation/restenosis have not been fully elucidated. Therefore, we investigated the effect of bindarit on human coronary smooth muscle cells activation, drawing attention to the phenotypic modulation process, focusing on contractile proteins expression as well as proliferation and migration. The expression of contractile proteins was evaluated by western blot analysis on cultured human coronary smooth muscle cells stimulated with TNF-α (30 ng/mL) or fetal bovine serum (5%). Bindarit (100-300 µM) reduced the embryonic form of smooth muscle myosin heavy chain while increased smooth muscle α-actin and calponin in both TNF-α- and fetal bovine serum-stimulated cells. These effects were associated with the inhibition of human coronary smooth muscle cell proliferation/migration and both MCP-1 and MCP-3 production. The effect of bindarit on smooth muscle cells phenotypic switching was confirmed in vivo in the rat balloon angioplasty model. Bindarit (200 mg/Kg/day) significantly reduced the expression of the embryonic form of smooth muscle myosin heavy chain, and increased smooth muscle α-actin and calponin in the rat carodid arteries subjected to endothelial denudation. Our results demonstrate that bindarit induces the differentiated state of human coronary smooth muscle cells, suggesting a novel underlying mechanisms by which this drug inhibits neointimal formation

A NEW STRATEGIC WAVE MEASUREMENT STATION OFF NAPLES PORT MAIN BREAKWATER

The accuracy of directional wave spectra sensors is crucial for obtaining accurate forecasts of ocean and coastal wave conditions for scientific and engineering applications. In this paper, a newly designed, low-cost GPS-based wave buoy, called the Directional Wave Spectra Drifter (DWSD), is presented. A field test campaign was conducted at the Gulf of Naples, Italy with the goal of comparing the directional wave properties obtained with the DWSD and with a nearly co-located bottom-mounted Acoustic Doppler Current Profiler (ADCP) from Teledyne RD-Instruments. The comparison shows a very good agreement between the two methodologies. The reliability of this innovative instrument and its low costs allow a large variety of applications, including the implementation of a global, satellite-linked, real-time open-ocean network of drifting directional wave spectra sensors and monitoring the sea-state in harbors to aid ship transit and for planning coastal and offshore constructions. The DWSD is currently in use to better constrain the wave energy climatology with the goal of optimizing the design of a full-scale prototype Wave Energy Converter (WEC) in the port of Naples, Italy

Covid-19 and flattening the curve: a feedback control perspective

Many of the policies that were put into place during the Covid-19 pandemic had a common goal: to flatten the curve of the number of infected people so that its peak remains under a critical threshold. This letter considers the challenge of engineering a strategy that enforces such a goal using control theory. We introduce a simple formulation of the optimal flattening problem, and provide a closed form solution. This is augmented through nonlinear closed loop tracking of the nominal solution, with the aim of ensuring close-to-optimal performance under uncertain conditions. A key contribution of this letter is to provide validation of the method with extensive and realistic simulations in a Covid-19 scenario, with particular focus on the case of Codogno - a small city in Northern Italy that has been among the most harshly hit by the pandemic

Use of penile shear wave elastosonography for the diagnosis of Peyronie's Disease: a prospective case-control study

Background: To evaluate the stiffness of the tunica albuginea (TA), we used a new noninvasive diagnostic technique called shear wave elastography (SWE). We determined whether SWE values are correlated with the degree of penile curvature, the time of disease onset, and pain severity experienced by patients during erection. This study analyzed the elasticity of the TA of patients with Peyronie's disease compared to that of the control group. We also analyzed any correlations between the stiffness of the cavernous bodies and the degree of curvature, time from diagnosis to curvature onset, and erectile pain severity. This was a prospective case-control study involving 100 men enrolled from September 2020 to August 2021. Participants were divided into group A (case group, n = 50), which included men with PD, with or without pain, and with penile curvature, or group B (control group, n = 50), which included healthy patients older than 18 years who visited the urology clinic for reasons other than PD. The medical history was collected for all patients who also underwent objective examination, B-mode ultrasound evaluation, and SWE. The International Index of Erectile Function (IIEF-15) visual analog scale (VAS) questionnaire was administered to all participants. Results: There were no significant between-group differences regarding age, weight, and height (p > 0.05); however, there was a significant difference in the stiffness values (p < 0.05). An inverse correlation was observed between stiffness and the VAS score (p < 0.0001). A positive correlation was observed between the degree of curvature (p < 0.0001) and the time of curvature onset (p < 0.0001). The IIEF-15 scores were poorer in group A than in group B (p < 0.0001). Conclusion: SWE is an inexpensive, noninvasive method that can be used to measure the stiffness of PD patients

The impact of contact structure and mixing on control measures and disease-induced herd immunity in epidemic models: a mean-field model perspective

The contact structure of a population plays an important role in transmission of infection. Many ‘structured models’ capture aspects of the contact pattern through an underlying network or a mixing matrix. An important observation in unstructured models of a disease that confers immunity is that once a fraction 1−1/R0 has been infected, the residual susceptible population can no longer sustain an epidemic. A recent observation of some structured models is that this threshold can be crossed with a smaller fraction of infected individuals, because the disease acts like a targeted vaccine, preferentially immunising higher-risk individuals who play a greater role in transmission. Therefore, a limited ‘first wave’ may leave behind a residual population that cannot support a second wave once interventions are lifted. In this paper, we set out to investigate this more systematically. While networks offer a flexible framework to model contact patterns explicitly, they suffer from several shortcomings: (i) high-fidelity network models require a large amount of data which can be difficult to harvest, and (ii) very few, if any, theoretical contact network models offer the flexibility to tune different contact network properties within the same framework. Therefore, we opt to systematically analyse a number of well-known mean-field models. These are computationally efficient and provide good flexibility in varying contact network properties such as heterogeneity in the number contacts, clustering and household structure or differentiating between local and global contacts. In particular, we consider the question of herd immunity under several scenarios. When modelling interventions as changes in transmission rates, we confirm that in networks with significant degree heterogeneity, the first wave of the epidemic confers herd immunity with significantly fewer infections than equivalent models with less or no degree heterogeneity. However, if modelling the intervention as a change in the contact network, then this effect may become much more subtle. Indeed, modifying the structure disproportionately can shield highly connected nodes from becoming infected during the first wave and therefore make the second wave more substantial. We strengthen this finding by using an age-structured compartmental model parameterised with real data and comparing lockdown periods implemented either as a global scaling of the mixing matrix or age-specific structural changes. Overall, we find that results regarding (disease-induced) herd immunity levels are strongly dependent on the model, the duration of the lockdown and how the lockdown is implemented in the model

Digital measurement of SARS-CoV-2 transmission risk from 7 million contacts

How likely is it to become infected by SARS-CoV-2 after being exposed? Almost everyone wondered about this question during the COVID-19 pandemic. Contact-tracing apps1,2 recorded measurements of proximity3 and duration between nearby smartphones. Contacts—individuals exposed to confirmed cases—were notified according to public health policies such as the 2 m, 15 min guideline4,5, despite limited evidence supporting this threshold. Here we analysed 7 million contacts notified by the National Health Service COVID-19 app6,7 in England and Wales to infer how app measurements translated to actual transmissions. Empirical metrics and statistical modelling showed a strong relation between app-computed risk scores and actual transmission probability. Longer exposures at greater distances had risk similar to that of shorter exposures at closer distances. The probability of transmission confirmed by a reported positive test increased initially linearly with duration of exposure (1.1% per hour) and continued increasing over several days. Whereas most exposures were short (median 0.7 h, interquartile range 0.4–1.6), transmissions typically resulted from exposures lasting between 1 h and several days (median 6 h, interquartile range 1.4–28). Households accounted for about 6% of contacts but 40% of transmissions. With sufficient preparation, privacy-preserving yet precise analyses of risk that would inform public health measures, based on digital contact tracing, could be performed within weeks of the emergence of a new pathogen