From regional pulse vaccination to global disease eradication: insights from a mathematical model of Poliomyelitis

Mass-vaccination campaigns are an important strategy in the global fight against poliomyelitis and measles. The large-scale logistics required for these mass immunisation campaigns magnifies the need for research into the effectiveness and optimal deployment of pulse vaccination. In order to better understand this control strategy, we propose a mathematical model accounting for the disease dynamics in connected regions, incorporating seasonality, environmental reservoirs and independent periodic pulse vaccination schedules in each region. The effective reproduction number, $R_e$, is defined and proved to be a global threshold for persistence of the disease. Analytical and numerical calculations show the importance of synchronising the pulse vaccinations in connected regions and the timing of the pulses with respect to the pathogen circulation seasonality. Our results indicate that it may be crucial for mass-vaccination programs, such as national immunisation days, to be synchronised across different regions. In addition, simulations show that a migration imbalance can increase $R_e$ and alter how pulse vaccination should be optimally distributed among the patches, similar to results found with constant-rate vaccination. Furthermore, contrary to the case of constant-rate vaccination, the fraction of environmental transmission affects the value of $R_e$ when pulse vaccination is present.Comment: Added section 6.1, made other revisions, changed titl

Rationalization of excited-state tuning through ultrafast transient absorption and vibrational coherence spectroscopy

Photophysical and-chemical processes make use of light as strongly quantized energy source, rendering mechanisms possible, which involve excited states that are thermally unavailable. This puts them at the heart of many exciting and promising technologies from photovoltaics to photocatalysis and photodynamic therapy. In this work, several strategies to tuning these excited states are rationalized by ultrafast transient absorption and impulsive vibrational spectroscopy, applied to two different classes of samples. Firstly, the excited-state dynamics of two iron(II) complexes are investigated for the tuning effect of solvent choice and ligand design. They toggle on and off the involvement of metal-centered (MC) excited states acting as loss channels for desired metal-to-ligand charge transfer (MLCT) states. Impulsive vibrational spectroscopy is established as suitable method for identifying MLCT-MC transitions in [Fe(bpy)(CN)4]2-, a well-known reference sample. The method is then applied to an iron(II)N-heterocyclic carbene complex and identifies an ultrafast MLCT-MC branching in this promising dye-sensitizer candidate. Secondly, the photophysics and -chemistry of triphenylamine is thoroughly investigated for the influences of solvent, the oxygen content therein and enforced planarity. In n-hexane, triphenylamine is converted to N-phenylcarbazole, with oxygen playing an intricate double role. The conversion is stopped completely by planarization due to the cancellation of p-orbital preorientation. In chloroform, ultrafast electron transfer to the solvent dominates the photochemistry, producing the radical cation leading to chromophore dimerization

Extreme nonlinear optics in highly excited semiconductors

In dieser Arbeit werden extreme nichtlineare optische Phänomene in hoch angeregten ZnO Halbleiterproben untersucht. ZnO hat eine Bandlücke von 3,2 eV im nahen ultravioletten Spektralbereich und die optische Anregung erfolgt mit starken Lichtfeldern im nahen bis fernen nfrarot. Folglich ist die Energie der Photonen sehr viel kleiner als die Bandlücke des Materials. Bei den optischen Phönomenen, die untersucht wurden, ist die Reaktion des Materials durcheine nichtlineare Abhängigkeit des Ausgangs- von der Eingangssignalstärke gekennzeichnet. Insbesondere wurde die kohärente Umwandlung von Laserlicht in hohe Ordnungen der ursprünglichen Lichtfrequenz, auch bekannt als Erzeugung hoher Harmonischer (HHG), und optisch gepumptes Lasing untersucht. HHG in Festkörpern resultiert aus einer Kombination von Laserfeld getriebenen nichtlinearen Intraband-Strömen und Interband-Polarisationsfeldern, und Lasing ist das Ergebnis der Verstärkung von Licht durch stimulierte Emission. HHG von Laserpulsen im mittleren IR wurde in stark optisch angeregten kristallinem ZnO untersucht. Die gemessene HHG Emission zeigt ein Sättigungsverhalten und eine starke spektrale Blauverschiebung der harmonischen Ordnungen als Funktion der freien Ladungsträger. Darüber hinaus führen interatomare Kräfte aufgrund einer starken Modifikation der elektro-nischen Struktur zu einer Verschiebung der Gitterionen. Ein Pump-Probe-Experiment wurde durchgeführt, um die transiente Modulation des HHG-Prozesses als Funktion des Schwingungs-zustands der Gitterionen zu bestimmen. Die gemessenen Modulationsfrequenzen stimmen mit den charakteristischen optischen Phononenfrequenzen von ZnO überein. Folglich zeigte das Experiment die Wechselwirkung der Elektronen mit den Gitterionen auf einer Zeitskala kürzer als die halbe Schwingungsperiode des Laserfeldes. Laserpulse im mittleren IR-Spektralbereich mit wenigen Zyklen und kontrollierbarer absolutenphase (carrier envelope phase, CEP) wurden zur Erzeugung hoher Harmonischer in kristallinem ZnO benutzt, um eine einfache Methode zur Vermessung des relativen CEP des Laserpulses zudemonstrieren. Hierfür wurde die Interferenz spektral überlappender harmonischer Ordnungenausgewertet. Lasing setzt ein, wenn die Vestärkung aufgrund der stimulierten Emission die Verluste über-steigt. Um Verstärkung zu ermöglichen, muss die angeregte Ladungsträgerdichte einen Schwell-wert übersteigen (Inversion). Laseremission aufgrund optischer Anregung mit ultravioleten Licht in polykristallinen ZnO Dünnfilmen und ZnO-Nanodrähten (NW) wurde bereits demonstriert. In dieser Arbeit werden jedoch starke Lichtfelder im Spektralbereich vom nahen IR (0,8μm, 1,5 eV) bis zum fernen IR (10μm, 0,13 eV) benutzt, um optisch gepumptes Lasingin polykristallinen ZnO-Dünnfilmen und ZnO-NWs zu erreichen. Dabei ist das Verhältnis der Materialbandlücke zur Photonenenergie im Bereich zwischen 3 und 26.Die Laser- und spontanen Photolumineszenz (PL)-Emission von ZnO-Dünnfilmen wurde ge-messen, um die Auswirkung einer Materialdotierung und den Effekt der Pumplaserpolarisati-on (Elliptizität) auf die Laserschwelle bzw. die Lichtabsorption zu untersuchen. In Alumini-um dotierten ZnO-Dünnschichtproben ist die Pumpschwellenintensität im Vergleich zu einer intrinsischen Probe reduziert und Licht im nahen IR bei 0,8 μm wird effizienter über einen Drei-Photonen-Absorptionsprozess in ZnO absorbiert, wenn der Pumplaser linear anstelle von zirkular polarisiert ist. Die Messung der PL-Emission von Dünnschichtproben als Funktion der Pumplaserpolarisation stellt eine einfache Methode zur zerstörungsfreien Bestimmung des Absorptionskoeffizienten von zirkular polarisiertem Licht dar. Die Schwellwerte der Pumplaserintensität und des Verstärkungskoeffizienten um Lasing in ZnO-NW, angeordnet in vertikal ausgerichteten Arrays, zu erreichen, wurden experimentell verglichen. Die Ergebnisse ergaben, dass die Emissionseigenschaften von NW Arrays, durch die Einzeldrahtparameter definiert sind. Aufgrund der starken elektrischen Felder und der Licht-Materie-Wechselwirkung fern der Absorptionsresonanz erfolgt die Absorption von Licht über Interbandanregung aufgrund von Multiphotonenabsorption und Tunneln sowie Elektron-Elektron-Wechselwirkung (Stoßionisation)als Folge der Intraband-Elektronenbeschleunigung. Die Rolle der Interband- und Intraband-Absorptionsprozesse wurde durch Vergleichen der experimentellen Ergebnisse mit Berechnungen mittels eines Ratengleichenmodelles identifiziert.This thesis studies extreme nonlinear optical phenomena in highly excited ZnO semiconductor samples. ZnO with a band gap of 3.2 eV, in the near-ultraviolet spectral range, is irradiated with far-o resonance strong light fields in the near to the far-infrared. The response of the matter is characterized by a nonlinear dependence of the output on the input signal strength. Specifically, the coherent conversion of laser light into high orders of the original frequency, also known as high harmonic generation (HHG) and optically pumped lasing were investigated. HHG in solids results from a combination of laser field driven nonlinear intraband currents and interband polarization fields and lasing is the result of light amplification by stimulated emission. HHG from mid-IR laser pulses was investigated in crystalline bulk ZnO far out of its equilibrium state. As a result the saturation of the harmonic radiation and a strong spectral blueshift of the harmonic orders were measured as a function of the free carrier density. Furthermore, interatomic forces due to strong modification of the electronic structure lead to lattice ion displacement. Performing a pump-probe experiment, the transient modulation of the HHG process reveals the vibration state of the material. The modulation frequency overlaps with the characteristic optical phonon frequencies of ZnO. Consequently, the experiment revealed an interaction of the ionic- and electronic structure on a timescale below the oscillation period of the laser field. Using few-cycle and CEP controllable mid-IR laser pulses to generate high harmonics in crystalline ZnO, a simple method to measure the relative CEP of the laser pulse was demonstrated using the interference of spectrally overlapping harmonic orders. Lasing sets in when the material gain, due to stimulated emission, overcomes the material losses. For that, the excited electron density has to overcome a threshold value (inversion). Optical pump lasing was demonstrated upon UV pumping in polycrystalline ZnO thin films and ZnO nanowires (NW). However here, strong light fields in spectral range from the near-IR (0.8 m, 1.5 eV) to the far-IR (10 m, 0.13 eV) optically pump lasing in polycrystalline ZnO thin films and ZnO NWs. Thus, the ratios of the material band gap to the photon energy covered the range from 3 to 26. Studying the lasing and the spontaneous photoluminescence (PL) emission from ZnO thin films, the eect of Aluminium doping and the eect of the pump laser ellipticity on the lasing thresh-III old and light absorption, respectively, was determined. Aluminium doped ZnO thin film sample reduce the pump threshold intensity compared to an intrinsic sample and near-IR light at 0.8 m is more ecient absorbed via a three photon absorption process in ZnO when the laser is polarized linearly instead of circularly. Measuring the PL emission from thin film samples as a function of the pump laser polarization, depicts a simple method to determine the absorption coecient for circular polarized light in a non-destructive manner. Comparing the pump laser threshold intensity with the threshold gain value, which were determined by the averaged parameters of the ZnONWforming a vertically aligned array revealed that the emission properties of the NW array is defined by the single wire parameters. Due to the strong applied electric fields and the light-matter interaction far-o the resonance, the absorption of light via interband excitation occurs due to the multiphoton absorption and tunneling as well as electron-electron interaction (impact ionization) upon intraband free carrier absorption. The contribution of the interband and intraband absorption processes were identified by comparing the experimental results with calculations from a rate equation laser model

Global stability of disease-free equilibria in a two-group SI model with feedback control

In this letter, a two-group SI epidemic model is tackled with an eye to population mobility. Using the method of Lyapunov functions, global stability of the disease-free equilibria with respect to one group as well as both groups is investigated. We find that the disease outbreak can be effectively controlled through adjusting the feedback control variables. Examples are worked out to illustrate the theoretical results

Coherent lattice and molecular dynamics in ultrafast single-shot spectroscopy

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 2005.Includes bibliographical references.This thesis focuses on the development, refinement, and application of dual- echelon single-shot ultrafast spectroscopy to the study of coherent nuclear motion in condensed phase systems. The general principles of the single-shot method are described, and particular emphasis is given to the general applicability and shortcomings of this technique and the extraction of data from raw laboratory images. Coupled to the single-shot system is a synchronously pumped dual-beam noncollinear optical parametric amplifier which was developed to provide independently tunable pump and probe beams in the visible and UV regions of the electromagnetic spectrum. The second part of the thesis concerns the application of this technique to the study of atomic motions in liquids and solids. Single-shot nonresonant impulsive stimulated Raman scattering (ISRS) measurements in m-iodoanisole and bismuth germanate reveal the existence of transient coherent behavior. High-field resonant excitation of the semimetals bismuth, antimony and tellurium, as well as the semiconductor germanium telluride, reveals dramatic lattice anharmoniticity as a function of pump fluence. Finally, ultrafast photodissociation of the triiodide ion both in solution and in the solid state gives considerable insight regarding the role of the local environment in mediating chemical reaction dynamics.by Peter Roland Poulin.Ph.D

Determination and evaluation of clinically efficient stopping criteria for the multiple auditory steady-state response technique

Background: Although the auditory steady-state response (ASSR) technique utilizes objective statistical detection algorithms to estimate behavioural hearing thresholds, the audiologist still has to decide when to terminate ASSR recordings introducing once more a certain degree of subjectivity. Aims: The present study aimed at establishing clinically efficient stopping criteria for a multiple 80-Hz ASSR system. Methods: In Experiment 1, data of 31 normal hearing subjects were analyzed off-line to propose stopping rules. Consequently, ASSR recordings will be stopped when (1) all 8 responses reach significance and significance can be maintained for 8 consecutive sweeps; (2) the mean noise levels were ≤ 4 nV (if at this “≤ 4-nV” criterion, p-values were between 0.05 and 0.1, measurements were extended only once by 8 sweeps); and (3) a maximum amount of 48 sweeps was attained. In Experiment 2, these stopping criteria were applied on 10 normal hearing and 10 hearing-impaired adults to asses the efficiency. Results: The application of these stopping rules resulted in ASSR threshold values that were comparable to other multiple-ASSR research with normal hearing and hearing-impaired adults. Furthermore, in 80% of the cases, ASSR thresholds could be obtained within a time-frame of 1 hour. Investigating the significant response-amplitudes of the hearing-impaired adults through cumulative curves indicated that probably a higher noise-stop criterion than “≤ 4 nV” can be used. Conclusions: The proposed stopping rules can be used in adults to determine accurate ASSR thresholds within an acceptable time-frame of about 1 hour. However, additional research with infants and adults with varying degrees and configurations of hearing loss is needed to optimize these criteria

Ultrafast Laser Control of Molecular Quantum Dynamics from a Core-Electron Perspective

This work introduces two experimental approaches to control quantum dynamics in molecules, employing core electrons as messengers. A laser source providing ultrashort pulses has been developed to access the timescale of electronic and structural dynamics inside molecules. Pulses of few-cycle durations in the 1 µm to 2 µm short-wavelength infrared (SWIR) spectral region provide intensities up to 1015 W/cm2 . In combination with a vacuum beamline, this experimental setup allows for ultrafast laser control of molecular dynamics probed by core-electron transitions via x-ray absorption spectroscopy (XAS). The first experiment investigates the manipulation of molecular electronic structure. Here, a soft x-ray (SXR) pulse probes simultaneously to an SWIR pulse of variable intensity. The measured intensityvii dependent absorbance changes in SF6 reveal an increased effective electronic-exchange energy. This demonstrates the alteration of this purely quantum-mechanical component of the electron-electron interaction for the first time. In a second experiment, an SWIR pulse induces coherent molecular vibrations with amplitudes of ten times the diameter of the nucleus. Subsequently, a time-delayed SXR pulse probes the bond-length changes via core-level transitions. This enables an unprecedented 14 femtometer precision which paves the way for site-specific vibrational metrology in gas-phase molecules. Overall, these results enable ultrafast chemical control on a quantum level

Photoinduced phase transitions studied by femtosecond single-shot spectroscopy

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 2010.Vita. Cataloged from PDF version of thesis.Includes bibliographical references (p. 221-228).Single-shot femtosecond spectroscopy has been developed and employed for the study of phase transitions of solid-state materials. Using two crossed echelons, a two dimensional spatial delay gradient was generated across a single probe pulse profile. This novel scheme enables us to monitor irreversible change in solids by acquiring many time-resolved data points with a single laser pulse. With the integration with a non-collinear optical parametric amplifier (NOPA) and a conventional pump-probe instrument, ultrafast dynamics of coherent lattice vibrations and photo-induced phase transitions were examined in two different systems. Ultrafast dynamics such as coherent lattice vibrations and bond softening were investigated for Bi thin films and bulk single crystals. Depending on the thickness, transient reflectivity was changed significantly. The variations are ascribed to different electronic structures possibly originating from quantum confinement. Bond softening exhibits a strong thickness dependence due to hot carrier dynamics as well as to the different electronic structures. At high pump fluences, no phonon oscillations were observed suggesting a phase transition to liquid or to a higher symmetry crystalline phase (reverse Peierls distortion). Together with thermal modeling, double pump measurements reveal nonthermal melting occurring in bulk and thin Bi films. A higher threshold fluence for nonthermal melting is observed in bulk bismuth as compared to thin films, suggesting ultrafast carrier dynamics such as ballistic transport. In addition to nonthermal effects, thermal effects such as inelastic electron-phonon scattering and nonradiative recombination play a crucial role in melting and cooling at later times after nonthermal melting takes place. A quasi one-dimensional platinum iodide complex showed strong oscillations in reflectivity which are attributed to oscillatory motions of wave packets on a selftrapped exciton (STE) potential surface., As optical excitation increased, electron transfer from Pt 2+ to an adjacent Pt4+ occurred over a wider range of lattice sites and weakened the oscillations. Above a certain pump fluence, oscillations disappeared completely indicating that the mixed valence, charge density wave state changed to monovalent, Mott-Hubbard phase. The reverse phase transition, i.e., from the MottHubbard phase to the charge density wave state began within 3 ps of the optical pump.by Taeho Shin.Ph.D

Quantum dynamics in weak and strong fields measured by XUV nonlinear spectroscopy

In this work fundamental nonlinear dynamics inside the neon atom are studied in two respects: At first, correlations between electronic inner-shell excitations in the extreme-ultraviolet (XUV) spectral range are probed on their natural sub-femtosecond time scale. To this end, the concept of attosecond transient absorption with a highharmonic generated (HHG) attosecond and a single time-delayed moderately strong nearinfrared (NIR) pulse was extended by a third, perturbative NIR pulse to perform timeresolved four-wave-mixing spectroscopy. This allowed to retrieve coupling dynamics between states of odd and even parity in a two-dimensional spectral representation. While the first part of this work explores the sequential interaction of several weak and moderately strong, fully coherent laser pulses with the target neon, the second part addresses the impact of strong, partially-coherent fields delivered by the XUV free-electron laser in Hamburg (FLASH). For this purpose, a novel beamline setup was developed and assembled at FLASH which allowed to perform first XUV-pump—XUV-probe transient absorption measurements. The measurements revealed the time-delay and intensity-dependent control of sequential ionization processes, coherence-enhancement effects, and strongcoupling signatures of bound—bound transitions in doubly-ionized neon. For the interpretation of the experimental results numerical simulations based on quantum mechanical few-level models were employed. Future applications of this method involve the two-dimensional spectroscopy both with HHG and FLASH pulses to probe site-specific information of electronic processes in molecules