Infectious Disease Spreading Fought by Multiple Vaccines Having a Prescribed Time Effect.

We propose a framework for the description of the effects of vaccinations on the spreading of an epidemic disease. Different vaccines can be dosed, each providing different immunization times and immunization levels. Differences due to individuals' ages are accounted for through the introduction of either a continuous age structure or a discrete set of age classes. Extensions to gender differences or to distinguish fragile individuals can also be considered. Within this setting, vaccination strategies can be simulated, tested and compared, as is explicitly described through numerical integrations.

An age and space structured SIR model describing the Covid-19 pandemic.

We present an epidemic model capable of describing key features of the Covid-19 pandemic. While capturing several qualitative properties of the virus spreading, it allows to compute the basic reproduction number, the number of deaths due to the virus and various other statistics. Numerical integrations are used to illustrate the adherence of the evolutions described by the model to specific well known real features of the present pandemic. In particular, this model is consistent with the well known relevance of quarantine, shows the dramatic role of care houses and accounts for the increase in the death toll when spatial movements are not constrained. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (10.1186/s13362-020-00090-4) contains supplementary material.

Special issue: Mathematical Modeling with Measures.

The special issue is available from: http://www.aimspress.com/newsinfo/1132.html.

Optimizing vaccination strategies in an age structured SIR model.

We present a modeling framework based on a structured SIR model where different vaccination strategies can be tested and compared. Vaccinations can be dosed at prescribed ages or at prescribed times to prescribed portions of the susceptible population. Different choices of these prescriptions lead to entirely different evolutions of the disease. Once suitable "costs" are introduced, it is natural to seek, correspondingly, the "best" vaccination strategies. Rigorous results ensure the Lipschitz continuous dependence of various reasonable costs on the control parameters, thus ensuring the existence of optimal controls and suggesting their search, for instance, by means of the steepest descent method.

A modeling framework for biological pest control.

We present an analytic framework where biological pest control can be simulated. Control is enforced through the choice of a time and space dependent function representing the deployment of a species of predators that feed on pests. A sample of different strategies aimed at reducing the presence of pests is considered, evaluated and compared. The strategies explicitly taken into account range, for instance, from the uniform deployment of predators on all the available area over a short/long time interval, to the alternated insertion of predators in different specific regions, to the release of predators in suitably selected regions. The effect of each strategy is measured through a suitably defined cost, essentially representing the total amount of prey present over a given time interval over all the considered region, but the variation in time of the total amount of pests is also evaluated. The analytic framework is provided by an integro-differential hyperbolic-parabolic system of partial differential equations. While prey diffuse according to the usual Laplace operator, predators hunt for prey, moving at finite speed towards regions of higher prey density.

Implementation of Portable Emissions Measurement Systems (PEMS) for the Real-driving Emissions (RDE) Regulation in Europe.

Vehicles are tested in controlled and relatively narrow laboratory conditions to determine their official emission values and reference fuel consumption. However, on the road, ambient and driving conditions can vary over a wide range, sometimes causing emissions to be higher than those measured in the laboratory. For this reason, the European Commission has developed a complementary Real-Driving Emissions (RDE) test procedure using the Portable Emissions Measurement Systems (PEMS) to verify gaseous pollutant and particle number emissions during a wide range of normal operating conditions on the road. This paper presents the newly-adopted RDE test procedure, differentiating six steps: 1) vehicle selection, 2) vehicle preparation, 3) trip design, 4) trip execution, 5) trip verification, and 6) calculation of emissions. Of these steps, vehicle preparation and trip execution are described in greater detail. Examples of trip verification and the calculations of emissions are given.

Preface to '' Modeling with measures ''.

Different communities met in the research workshop ``Modeling with Measures" that took place at the Lorentz Center (Leiden, The Netherlands) during 26th--30th of August 2013. They were groups of researchers active in the following fields.

Stability and optimization in structured population models on graphs.

We prove existence and uniqueness of solutions, continuous dependence from the initial datum and stability with respect to the boundary condition in a class of initial--boundary value problems for systems of balance laws. The particular choice of the boundary condition allows to comprehend models with very different structures. In particular, we consider a juvenile-adult model, the problem of the optimal mating ratio and a model for the optimal management of biological resources. The stability result obtained allows to tackle various optimal management/control problems, providing sufficient conditions for the existence of optimal choices/controls.

The THRombolysis and STatins (THRaST) study.

OBJECTIVE: To assess the impact on stroke outcome of statin use in the acute phase after IV thrombolysis. METHODS: Multicenter study on prospectively collected data of 2,072 stroke patients treated with IV thrombolysis. Outcome measures of efficacy were neurologic improvement (NIH Stroke Scale [NIHSS] ≤ 4 points from baseline or NIHSS = 0) and major neurologic improvement (NIHSS ≤ 8 points from baseline or NIHSS = 0) at 7 days and favorable (modified Rankin Scale [mRS] ≤ 2) and excellent functional outcome (mRS ≤ 1) at 3 months. Outcome measures of safety were 7-day neurologic deterioration (NIHSS ≥ 4 points from baseline or death), symptomatic intracerebral hemorrhage type 2 with NIHSS ≥ 4 points from baseline or death within 36 hours, and 3-month death. RESULTS: Adjusted multivariate analysis showed that statin use in the acute phase was associated with neurologic improvement (odds ratio [OR] 1.68, 95% confidence interval [CI] 1.26-2.25; p < 0.001), major neurologic improvement (OR 1.43, 95% CI 1.11-1.85; p = 0.006), favorable functional outcome (OR 1.63, 95% CI 1.18-2.26; p = 0.003), and a reduced risk of neurologic deterioration (OR: 0.31, 95% CI 0.19-0.53; p < 0.001) and death (OR 0.48, 95% CI 0.28-0.82; p = 0.007). CONCLUSION: Statin use in the acute phase of stroke after IV thrombolysis may positively influence short- and long-term outcome.