Wave Curves Research Articles

Dispersion Curves of Love Waves in Elastic Waveguides Loaded with a Newtonian Liquid Layer of Finite Thickness

In this paper, the authors analyse the propagation of surface Love waves in an elastic layered waveguide (elastic guiding layer deposited on an elastic substrate) covered on its surface with a Newtonian liquid layer of finite thickness. By solving the equations of motion in the constituent regions (elastic substrate, elastic surface layer and Newtonian liquid) and imposing the appropriate boundary conditions, the authors established an analytical form of the complex dispersion equation for Love surface waves. Further, decomposition of the complex dispersion equation into its real and imaginary part, enabled for evaluation of the phase velocity and attenuation dispersion curves of the Love wave. Subsequently, the influence of the finite thickness of a Newtonian liquid on the dispersion curves was evaluated. Theoretical (numerical) analysis shows that when the thickness of the Newtonian liquid layer exceeds approximately four penetration depths 4δ of the wave in a Newtonian liquid, then this Newtonian liquid layer can be regarded as a semi-infinite half-space. The results obtained in this paper can be important in the design and optimization of ultrasonic Love wave sensors such as: biosensors, chemosensors and viscosity sensors. Love wave viscosity sensors can be used to assess the viscosity of various liquids, e.g. liquid polymers.

Study of Rheological-Mechanical Properties and Vibration Mechanics Bandgap of Row Pile Foundation

To analyze the rheological and mechanical properties as well as the vibration-mechanical forbidden zone effect of row pile foundations, this paper employs time-dependent modulus to examine the rheological mechanics of soil. Drawing from viscoelastic theory, we derive the expression of deformation modulus in the frequency domain to analyze the frequency dependence of the shear modulus of rheological soils. We construct a continuous medium dynamics model of the pile-soil periodic structure, taking into account soil rheology, and derive the dispersion equation of shear waves in the periodic structure using the multiple scattering method. The band gap characteristics and parameters that influence the law of shear waves in rheological soil-row pile foundations are studied through the analysis of arithmetic cases. The results show that under the loading condition, the zero-frequency shear modulus of soil is larger than the initial modulus value, and the real part of the shear modulus decreases monotonically with the increase of frequency and finally converges to the initial modulus value; under the unloading condition, the zero-frequency shear modulus of soil is smaller than the initial modulus value, and the real part of the shear modulus increases monotonically with the increase of frequency and finally converges to the initial modulus value; the larger the relaxation time of soil, the faster the convergence rate; the imaginary part of the shear modulus of soil The imaginary part of the soil shear modulus is positive under loading condition and negative under unloading condition, the value of the imaginary part increases and then decreases with increasing frequency and finally converges to 0. The imaginary part reaches the peak at the critical frequency, the larger the relaxation time the smaller the critical frequency, and the peak of the imaginary part is independent of the relaxation time. This study analyzed the dispersion curve of shear waves in a pile-soil periodic structure and found that increasing low-frequency shear wave velocity in rheological soil pile foundation shifts the band gap position to a higher frequency band, resulting in a smaller band gap width than in linear elastic soil. The relaxation time of soil affects the frequency position and width of the band gap, with larger relaxation times resulting in higher frequency positions and smaller widths. Additionally, soil rheology widens the forbidden vibration band gap of the pile periodic structure when the filling rate of the pile foundation is larger.

Bifurcation of solutions through a contact manifold in bidisperse models

This research focuses on a hyperbolic system that describes bidisperse suspensions, consisting of two types of small particles dispersed in a viscous fluid. The dependence of solutions on the relative position of contact manifolds in the phase space is examined. The wave curve method serves as the basis for the first and second analyses. The former involves the classification of elementary waves that emerge from the origin of the phase space. Analytical solutions to prototypical Riemann problems connecting the origin with any point in the state space are provided. The latter focuses on semi-analytical solutions for Riemann problems connecting any state in the phase space with the maximum packing concentration line, as observed in standard batch sedimentation tests. When the initial condition crosses the first contact manifold, a bifurcation occurs. As the initial condition approaches the second manifold, another structure appears to undergo bifurcation, although it does not represent an actual bifurcation according to the triple shock rule. The study reveals important insights into the behavior of solutions in relation to these contact manifolds. This research sheds light on the existence of emerging quasi-umbilic points within the system, which can potentially lead to new types of bifurcations as crucial elements of the elliptic/hyperbolic boundary in the system of partial differential equations. The implications of these findings and their significance are discussed.

Velocity Time Integral: A Novel Method for Assessing Fetal Anemia.

The velocity time integral (VTI) is a clinical Doppler ultrasound measurement of blood flow, measured by the area under the wave curve and equivalent to the distance traveled by the blood. This retrospective study assessed the middle cerebral artery (MCA) VTI of fetuses in pregnancies complicated by maternal alloimmunization. Doppler indices of the MCA were retrieved from electronic medical records. Systolic deceleration-diastolic time, systolic acceleration time, VTI, and peak systolic velocity (PSV) were measured at 16-40 weeks gestation. Cases with PSV indicating fetal anemia (cutoff 1.5 MoM) and normal PSV were compared. The study included 255 Doppler ultrasound examinations. Of these, 41 were at 16-24 weeks (group A), 100 were at 25-32 weeks (group B), and 114 were at 33-40 weeks (group C). VTI increased throughout gestation (5.5 cm, 8.6 cm, and 12.1 cm in groups A, B, and C, respectively, p = 0.003). VTI was higher in waveforms calculated to have MCA-PSV ≥ 1.5 MoM compared to those with MCA-PSV < 1.5 MoM (9.1 cm vs. 14.1 cm, respectively, p < 0.001), as was VTI/s (22.04 cm/s vs. 33.75 cm/s, respectively; p < 0.001). The results indicate that the MCA VTI increases significantly among fetuses with suspected anemia, indicating higher perfusion of hemodiluted blood to the brain. This feasible measurement might provide a novel additional marker for the development of fetal anemia.

Lunar active seismic profiler for investigating shallow substrates of the Moon and other extraterrestrial environments

To investigate the structures and properties of shallow material in extraterrestrial environments, we have developed a lunar active seismic profiler (LASP), which integrates active seismic sources and receivers in a short (~1 m) array that can be deployed on a rover. The small active source generates a chirp waveform that sweeps over a wide frequency range (20–250 Hz). The receivers are coupled to the ground by their own weight, but nevertheless deliver acceptable performance. We improve the signal-to-noise ratio of the seismic signal by stacking waveforms, enabling a minimal source to support the exploration of geological substrates. By processing shot gather of the LASP data, we calculated a dispersion curve of surface waves and obtained an accurate S-wave velocity profile from surface to 1 m depth. The results suggest that regions with even small amounts of subsurface ice (~0.5 wt%) can be identified in LASP results by their anomalously high S-wave velocity. Field experiments demonstrate that the LASP can support estimates of 3D S-wave velocity distributions and the identification of a buried geological boundary. The LASP also detected different degrees of compaction at the experimental site. If two rovers carry these profilers, or if a single rover combines one with a separately deployed receiver or active seismic source, seismic refraction and seismic reflection analyses can be conducted simultaneously in addition to surface wave analyses. These seismic surveys for longer-offset data achieve the exploration of deeper substrates in extraterrestrial settings such as the Moon, Mars, and other solid bodies.

The transition of Riemann solutions with composite waves for the improved Aw–Rascle–Zhang model in dusty gas

We study the cavitation and concentration of the Riemann solutions for the improved Aw–Rascle–Zhang (IARZ) model in dusty gas with a non-genuinely nonlinear field. The Riemann solutions containing composite waves are constructed by Liu-entropy condition first. Second, we investigate the limits of the inflection point and tangent point along the 1-family wave curve and find that the composite waves tend to elementary waves as pressure vanishes. Third, we obtain the limiting behavior of the Riemann solutions and observe the formation of δ-shock wave and vacuum as pressure vanishes. We conclude that the limit of Riemann solutions of the IARZ model is not the Riemann solutions of the limit of the IARZ model. The phenomenon is consistent with the work of C. Shen and M. Sun [“Formation of delta-shocks and vacuum states in the vanishing pressure limit of solutions to the Aw–Rascle model,” J. Differ. Equations 249, 3024–3051 (2010)]. Finally, we perform some numerical simulations to verify our theoretical analysis.

Endovascular aortic repair impact on myocardial contractility: A prospective study.

This study aimed to estimate if the altered sphygmic wave transmission may affect the left ventricular (LV) contractile function in patients undergoing endovascular aortic repair (EVAR). A prospective single-centre study was carried out on consecutive patients undergoing EVAR for abdominal aortic aneurysm. A preoperative and 6-month single photon emission computed tomography (SPECT) with arterial stiffness measurement were performed to evaluate variations in pressure wave curve and myocardial perfusion parameters. From 2018 to 2020 a total of 16 patients were included in the study. Among the parameters evaluated, we found a measurable reduction of the reflected wave transit time from pre- to postoperative period, for both stress (115.13 ± 7.2 ms-111.1 ± 7.0 ms, p = .08) and rest SPECT acquisitions (115.3 ± 6.2 ms-112.2 ± 5.6 ms, p = .1). Unidirectional increase of both LV end-systolic volume (34 ± 9 mL-39 ± 8 mL, p = .02) and end-diastolic volume (85 ± 34 mL-89 ± 29 mL, p = .6) was also observed. Lastly, the ratio between the end-systolic pressure and the end-systolic volume (maximal systolic myocardial stiffness) decreased from 3.6 ± 1.5 mmHg/mL to 2.66 ± .74 mmHg/mL (p = .03). Our data showed that EVAR induced an altered transmission of the sphygmic wave associated with an early LV contractile impairment.

Comparison of the EndoPAT device with a unique vascular assessment of reactive hyperemia

The EndoPAT device (Itamar Medical) is used to determine endothelial function by using peripheral arterial tonometry during reactive hyperemia. It has been shown to be related to the gold standard non-invasive technique of flow-mediated dilation ultrasound assessment. These methodologies have technical requirements and/or ongoing operational costs that could be prohibitive to under-resourced clinics or researchers. We hypothesized that using a re-usable and cost-effective procedure of determining the reactive hyperemic response using piezo-electric pulse transducers (ADInstruments) would give similar results to the EndoPAT. Reactive hyperemia was induced by occluding blood flow to the forearm for 5 minutes using a blood pressure cuff inflated to +50mmHg above systolic blood pressure. The vascular response to the release of the occlusion was assessed using EndoPAT on the index fingers and using piezo-electric transducers on the middle fingers, concurrently. Twenty-five healthy participants (15 female; 31±12years) participated in the study. Participants refrained from caffeine, alcohol, fatty foods, smoking and strenuous exercise for at least 12 hours prior to testing. The EndoPAT reactive hyperemia index (RHI) was determined using proprietary software. The area under the curve (AUC) of the finger pulse waves from the piezoelectric pulse transducers was also determined. The ratio of the AUC of the peak hyperemic response (10s average) compared to the baseline period (3.5min) in the occluded arm was compared to the equivalent ratio in the control arm to determine the pulse-wave reactive hyperemia index (PWRHI). Univariate linear regression and correlation analysis was conducted between RHI and PWRHI. When comparing the two methods, Spearman’s r was 0.67 (p=0.0002) with a coefficient of determination of 0.58. We have found that the two methods correlate well to each other and the PWRHI technique has the potential to make microvascular assessments more accessible to clinicians and researchers. Our PWRHI method still needs to be validated in larger populations with vascular dysfunction and over a wider age-range. Funding provided by the Natural Sciences and Engineering Research Council of Canada. This is the full abstract presented at the American Physiology Summit 2023 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

Multi-Mode Imaging of Ambient Background Noise for Karst Detection in the Limestone Area Based on Frequency-Bessel Transform

In response to the challenges of karst geophysical exploration in an environment with strong external interference, this paper proposes a new method, namely the frequency-Bessel transform method, for extracting multi-order dispersion curves of surface waves from background noise to characterize karst. The observation noise data of the Wuhan karst development area are used as an example, where the dolomitic limestone and limestone mixed with dolomite of the Jialing River Formation of the middle lower Triassic are widely developed in the observation area. The frequency-Bessel transform method involves performing a Bessel integral transformation on the cross-correlation coefficient of background noise in the frequency domain. Firstly, by synthesizing theoretical noise data and comparing it with the spatial autocorrelation method—which is currently the main method for extracting the fundamental dispersion curve of surface waves—it is verified that the frequency-Bessel transform method can extract the higher-mode dispersion curve. Then, by taking the actual measured single-point noise data as an example, the effect of applying the frequency-Bessel transform to the actual noise data is tested, and the inversion of the fine structure of the strata by the addition of higher-mode dispersion, the use of the damped least squares inversion method, and the joint inversion of fundamental and higher-mode dispersion curves are analyzed. The higher-mode dispersion curve of Rayleigh surface wave extracted by the frequency-Bessel transform is much clearer, and the 2D shear wave velocity structure profile obtained from inversion explains the karst development area, karst strip area, and thickness of the Quaternary overburden. The inferred results match with the actual borehole data. Multi-mode imaging of background noise based on the frequency-Bessel method can be applied to depict karst in complex backgrounds, and has significant potentiality in the field of ambient seismic noise tomography, providing a new idea and method for karst detection in near-surface engineering.

Characteristics of inverse dispersion curve of Rayleigh wave in pavement shallow structure with engineering application

The inverse dispersion curve depicts the dispersion characteristics of inverse layered models, in the layer velocity decreases with depth. To reveal the inverse dispersion characteristics of Rayleigh-wave propagation in pavement, we established a method to determine the dispersion curve of Rayleigh-wave multimodal coupling superposition in pavement structure by decomposing the contribution of multi-mode phase velocity to the vertical displacement of road surface, which was verified by the velocity-stress finite difference scheme. On this basis, further comparative calculations found that the generalized reflection and transmission coefficient method for solving the Rayleigh wave fundamental dispersion curve can fully demonstrate the dispersion characteristics of the coupling superposition of multi-mode dispersion curves of Rayleigh wave in pavement structure, which is suitable for the calculation of Rayleigh-wave inverse dispersion characteristics. Meanwhile, the analysis of dispersion characteristics shows that when the frequency is higher than 5000 Hz, the phase velocities are determined by surface materials. In the low frequency band with frequency <10 Hz, the phase velocities are determined by soil-based deepest materials. And with the increase of the thickness of the intermediate layer, the phase velocity range of dispersion curve moves to the low frequency. In this regard, through sensitivity calculation, an optimization method for Rayleigh wave testing and inversion of elastic modulus of pavement structural layers was established by combining Levenberg-Marquardt and adaptive genetic algorithm. Through the comparative test on the scale model of three-layer pavement structure in laboratory, the results show that the elastic modulus of each layer of pavement structure can be successfully evaluated from the inverse dispersion characteristics of Rayleigh wave in pavement structure.

Riemann problem and wave interactions for an inhomogeneous Aw-Rascle traffic flow model with extended Chaplygin gas

The Riemann problem and wave interactions are discussed and investigated for an inhomogeneous Aw-Rascle (AR) traffic flow model with extended Chaplygin gas pressure. First, under some variable transformation, the Riemann problem with initial data of two piecewise constants is solved and two different types of Riemann solutions involving rarefaction wave, shock wave and contact discontinuity are obtained. Second, by studying the Riemann problem with three-piecewise-constant initial data, we analyze the interactions of waves and establish the global structures of Riemann solutions. It is shown that, influenced by the source term, the Riemann solutions for the inhomogeneous AR traffic flow model are no longer self-similar, and all the elementary wave curves do not keep straight. Finally, the stability of solution under the small perturbation of initial data is briefly discussed.

EFL Teachers’ Emotions at Online Teaching throughout the COVID-19 Pandemic: Changes and Coping Strategies

The outbreak of COVID-19 in 2020 put the education system worldwide in a critical situation with a sudden shift from the traditional face-to-face to the online mode of instruction. Many studies have been conducted over the past two years to investigate teachers’ struggle with this abrupt transition; however, a complete picture of their emotional battle throughout the whole pandemic has not yet been depicted due to the short study durations. By analyzing rich datasets collected from semi-structured interviews with nine EFL teachers working at the tertiary level, we were able to outline their emotional changes and coping strategies for emotional regulation throughout the span of two years, from the beginning to the end of the mandatory online teaching period. It was found that, in general, the participants’ changes in emotions can be illustrated with a wave curve, which is divided into five phases with quite distinctive characteristics. The findings also highlighted the complexity and changeability of teachers’ emotional experiences, as well as the five major coping strategies utilized by the teachers to enhance their emotional well-being. Finally, several recommendations applicable for both teachers and stakeholders in future crises are proposed.

Comparative Study of Dispersion Curves for LAMB Waves Using Analytical Solutions and Semi-Analytical Methods

Lamb wave dispersion curves are useful for optimizing the inspection scanning distance that can be covered with good sensitivity in many current applications. However, one of the main problems concerning this calculation lies in selecting a numerical method that is computationally accurate and efficient. In this paper, Lamb waves dispersion curves are generated by the Scaled Boundary Finite Element Method, and by the Rayleigh–Lamb equation. For the semi-analytical case, waveguide cross-section discretization was performed using isoparametric elements and high-order spectral elements. The semi-analytical formulations lead to an eigenvalue problem that can be solved efficiently by calculating the couples of wavenumbers and frequencies that guarantee the wave mode propagation, the basis for generating the dispersion curves. These are compared with those obtained from the analytical solution for the symmetric and antisymmetric modes; in both cases, homogeneous plates of constant thickness are considered. The numerical results show good agreement when using a low number of isoparametric elements, or a single spectral element with shape functions of the order of six for computing the dispersion curves and wave structure. The calculation is given with low computational effort, and the relative variation with respect to the analytical reference values is less than 2%.

Load transfer analysis of vertically loaded bored piles in sea reclamation areas considering the effect of the pile-gravel interface roughness

A load transfer model for vertically loaded bored piles in sea reclamation areas with gravel is proposed in this paper. The focus is on quantifying the mobilization of pile-side friction, which is closely related to the shear behaviors of the pile-gravel interface. The surface profile of the gravel particles and the concrete piles are assumed to be circle and wave curves, respectively. The shear displacement and dilatancy calculation are based on the macro and micro geometry relationship between gravel particles and pile surface. The shear stress calculation of the pile-gravel interface is dealt with by empirical elastoplastic equations. A simple slip-line field is also built to identify the critical shear displacement. The finite difference equations are used to derive the load-displacement curves for vertically loaded bored piles in sea reclamation areas with gravel. The model predictions are compared with field observations and particle flow numerical simulation to validate the performance of the proposed method, and the results prove to be reasonable. Moreover, parameter studies are conducted and the results prove that the pile can bear more load when the particle diameter is similar to the pile's rough surface, and both the increases of wave angle and the relative friction coefficient can promote the bearing capacity.

Multiscale homogenization numerical study on the mechanism of interface debonding detection for steel–concrete composite structures with multichannel surface wave measurements

In order to understand the interface debonding detection mechanism for steel–concrete composite structures (SCCSs) efficiently using multichannel analysis of surface waves (MASW) when the heterogeneity and randomness of the mesoscale structure of concrete are considered, mesoscale homogenization numerical analysis on surface wave propagation in SCCSs is carried out. Firstly, for exploring the theoretical dispersion characteristics of surface waves in SCCSs, dispersion curves of both Lamb wave and Rayleigh wave of three different layering scenarios, including single-layer, two-layer, and three-layer composite models where concrete is treated as homogeneous material, are investigated. Meanwhile, the effect of the steel plate thickness on the dispersion curves is studied. Secondly, to evaluate the effect of mesoscale structure variation of concrete in SCCSs on surface waves, a random aggregate method (RAM) is employed to establish the mesoscale model of concrete composed of randomly distributed aggregates with different shapes. Thirdly, for enhancing numerical simulation efficiency on surface wave propagation, an equivalent homogenization approach and Voigt parallel model are developed to establish the mesoscale homogenization models of SCCSs. Dispersion curves from forwarding analysis on surface wave measurement of the mesoscale models are compared with the corresponding theoretical dispersion curves to reveal surface wave attribution and optimum layering scenarios of SCCSs for MASW method. The influence of mesoscale concrete variation on surface wave fields in SCCSs using equivalent homogenization models is investigated comprehensively and compared with that of the corresponding mesoscale models. Finally, the feasibility of the proposed MASW method for interface debonding length estimation is validated, and wavelength selection criteria of excitation signals considering interface dimension, as well as steel plate thickness, are discussed. The results from the mesoscale homogenization numerical study can provide helpful guidance on the practical application of MASW-based debonding detection for SCCSs where concrete is heterogeneous.

Experimental and numerical simulation study of fiber-reinforced high strength concrete at high strain rates

With the widespread use of fiber-reinforced high strength concrete (FRHSC) in military and civil fields, it is necessary to have an accurate understanding of the mechanical properties and failure modes of FRHSC under impact. The dynamic compression experiments were performed on FRHSC using the large-size split Hopkinson pressure bar (SHPB) apparatus. The experimental results were analyzed to determine the reasonable strain rate range of FRHSC under large-size SHPB loading conditions. The strain rate effect, critical strain, and failure mode of FRHSC under dynamic impact were studied. The strain rate and strength parameters in the Holmquist-Johnson-Cook (HJC) model were determined based on the experimental results, and the numerical simulation of SHPB was completed by LS-DYNA. The results revealed that the reasonable strain rate of FRHSC under large-size SHPB loading did not exceed 100 s−1. The material presented an obvious strain rate effect, and the critical strain was almost unchanged with the increased strain rate. Steel fiber improves the toughness of FRHSC. Under quasi-static loading, the tensile-compression ratio of the material was 0.13, and there was no apparent damage under impact. The rationality of the strain rate and strength parameters in the HJC model was verified by comparing the stress wave curve of the pressure bar, the stress-strain curve, and the failure mode of the specimen obtained by experiment and simulation.

Extraction of Group Velocity Dispersion Curves of Surface Waves Using Continuous Wavelet Transform

Surface wave tomography is performed by first estimating surface wave dispersion curves and then inverting them. The objective of this paper is the efficient and reliable estimation of the group velocity dispersion curves of surface waves. In this paper, group velocity dispersion curves of surface waves recorded at a single station with known location of seismic source or between a pair of stations are estimated using continuous wavelet transform (CWT). The advantage of CWT is its multi-resolution property and flexible choice of analyzing function. In the proposed method, the number of CWT filters used are almost half of the total number of filters used in the conventional frequency-time analysis (FTAN) method. The CWT coefficients of the seismogram are the functions of time and scale (analogues to wave period). The arrival time to reach the peak of the envelope function of CWT coefficients is estimated to calculate group velocity of the surface waves. Group velocity dispersion curve of the surface waves is the plot of change of group velocity with the period. Synthetic test data and ambient noise recordings of MesoAmerica Seismic Experiment (MASE) stations are acquired to investigate the performance of the proposed method. It is observed that the proposed method effectively retrieves the weaker surface waves and results the broader band group-velocity dispersion curve when compared to the conventional FTAN method. The proposed method is also found to be computationally efficient.

ХВИЛІ ЗСУВУ В ШАРУВАТО-ПЕРІОДИЧНІЙ СТРУКТУРІ «П'ЄЗОЕЛЕКТРИК - ЩІЛИНА»

A large number of scientific works are devoted to the problems of propagation of waves of different physical nature in periodic and heterogeneous media. The main problem considered in the article was the study of the shear wave in the layered-periodic structure "piezoelectric - gap". The statement is given and the problem of the propagation of volumetric acoustoelectric elastic shear waves in a regularly layered piezoelectric-slit medium is solved. Dispersion relations were obtained, which allow to investigate the possibility of propagation of wave fields with an arbitrary geometry of the period of the structure. A comparison of the spectra of the dispersion curves for volumetric acoustoelectric waves in a regularly layered space was carried out. The obtained dispersion relations were also analyzed numerically, and the results are presented in the form of graphs. Graphs of the limits of the boundaries of the transmission zones for various types of geometry of the generating layer package are given. As a result of numerical experiments, the possibility of the existence of transmission zones for bulk acoustic-electric waves in regularly layered media of the "piezoelectric - slot" type was established.

Periodic waves for the cubic-quintic nonlinear Schrodinger equation: Existence and orbital stability

&lt;p style='text-indent:20px;'&gt;In this paper, we prove existence and orbital stability results of periodic standing waves for the cubic-quintic nonlinear Schrödinger equation. We use the implicit function theorem to construct a smooth curve of explicit periodic waves with &lt;i&gt;dnoidal&lt;/i&gt; profile and such construction can be used to prove that the associated period map is strictly increasing in terms of the energy levels. The monotonicity is also useful to obtain the behaviour of the non-positive spectrum for the associated linearized operator around the wave. Concerning the stability, we prove that the dnoidal waves are orbitally stable in the energy space restricted to the even functions.&lt;/p&gt;

Cluster analysis of epidemic curves of the third Covid-19 epidemics wave in different regions of Poland

Purpose: The purpose of the analysis was to divide Polish regions (as a single region we mean “powiat”) into categories according to the way in which their population passed the third wave of COVID-19 epidemics and the attempt of linking the resultant classifications with other factors. Design/methodology/approach On the basis of data about daily COVID-19 cases per 10,000 inhabitants in regions, weekly averages in every day were calculated. The curves of these averages for each region were approximated by a polynomial function. Then, for the majority of created functions, five characteristic "points" were determined: a maximum of the function together with a maximum and a minimum of its first derivative and two maxima of its second derivative, which are all located the closest to the function maximum. On the basis of coordinates of these points, regions were grouped by using of K-means method. Finally, the mean levels of various factors in obtained categories were analyzed as well as different classification models determined on this basis. Findings: The performed analysis allowed to construct predictive models of the approximate shape of the epidemic curve in a given region. These models can be used in more-depth analysis of epidemics evolution. Research limitations/implications: These models can be used in more-depth analysis of epidemics evolution. Originality/value: By using cross-validation test, the number of clusters equal to five was determined. Mean values of the mentioned coordinates in each cluster allowed to determine an approximate shape of characteristic epidemic curve for a given group of regions. Only among some clusters there was a significant difference in population density, the percentage of population living in cities and the approximate percentage of inhabitants vaccinated after the third wave of COVID-19 epidemics. Nevertheless, on the basis of these factors and the age structure of the population, decision trees which classify most of the wave categories with a satisfactory accuracy were determined. Keywords: Cluster analysis, decision tree, epidemic curve, method of K-means, region. Category of the paper: Research paper.