Ulam-Hyers stability of tuberculosis and COVID-19 co-infection model under Atangana-Baleanu fractal-fractional operator.

The intention of this work is to study a mathematical model for fractal-fractional tuberculosis and COVID-19 co-infection under the Atangana-Baleanu fractal-fractional operator. Firstly, we formulate the tuberculosis and COVID-19 co-infection model by considering the tuberculosis recovery individuals, the COVID-19 recovery individuals, and both disease recovery compartment in the proposed model. The fixed point approach is utilized to explore the existence and uniqueness of the solution in the suggested model. The stability analysis related to solve the Ulam-Hyers stability is also investigated. This paper is based on Lagrange's interpolation polynomial in the numerical scheme, which is validated through a specific case with a comparative numerical analysis for different values of the fractional and fractal orders.

Fractal dimension based geographical clustering of COVID-19 time series data.

Understanding the local dynamics of COVID-19 transmission calls for an approach that characterizes the incidence curve in a small geographical unit. Given that incidence curves exhibit considerable day-to-day variation, the fractal structure of the time series dynamics is investigated for the Flanders and Brussels Regions of Belgium. For each statistical sector, the smallest administrative geographical entity in Belgium, fractal dimensions of COVID-19 incidence rates, based on rolling time spans of 7, 14, and 21 days were estimated using four different estimators: box-count, Hall-Wood, variogram, and madogram. We found varying patterns of fractal dimensions across time and location. The fractal dimension is further summarized by its mean, variance, and autocorrelation over time. These summary statistics are then used to cluster regions with different incidence rate patterns using k-means clustering. Fractal dimension analysis of COVID-19 incidence thus offers important insight into the past, current, and arguably future evolution of an infectious disease outbreak.

Changes in EEG Measures of a Recipient of the mRNA COVID-19 Vaccine - A Case Study.

The current study is aimed to evaluate the effect of COVID-19 vaccine on human EEG and the persistence of the effect. Within a one-year-long resting EEG study period, the healthy male subject was administered two Comirnaty doses three weeks apart to prevent COVID-19. Fourteen recordings were acquired from the subject in one year: twelve reference and two post-vaccination recordings after administrating the second dose of Comirnaty. The changes in absolute powers of EEG frequency bands, EEG spectral asymmetry index (SASI), and Higuchi's fractal dimension (HFD) were analyzed. The results indicated a statistically significant increase in absolute gamma power, SASI and HFD values on the fifth day after the vaccination, while the EEG had restored its normal character on the twelfth day after vaccination. These measures seem to have higher sensitivity for the detection of the effects of the vaccine Clinical Relevance- This is the first study evaluating COVID-19 vaccine effect on healthy human EEG. The study indicated that the vaccine disturbs EEG but the impact is not long-lasting.

Peptide-Induced Fractal Assembly of Silver Nanoparticles for Visual Detection of Disease Biomarkers.

We report the peptide-programmed fractal assembly of silver nanoparticles (AgNPs) in a diffusion-limited aggregation (DLA) mode, and this change in morphology generates a significant color change. We show that peptides with specific repetitions of defined amino acids (i.e., arginine, histidine, or phenylalanine) can induce assembly and coalescence of the AgNPs (20 nm) into a hyperbranched structure (AgFSs) (∼2 µm). The dynamic process of this assembly was systematically investigated, and the extinction of the nanostructures can be modulated from 400 to 600 nm by varying the peptide sequences and molar ratio. According to this rationale, two strategies of SARS-CoV-2 detection were investigated. The activity of the main protease (Mpro) involved in SARS-CoV-2 was validated with a peptide substrate that can bridge the AgNPs after the proteolytic cleavage. A sub-nanomolar limit of detection (0.5 nM) and the capacity to distinguish by the naked eye in a wide concentration range (1.25-30 nM) were achieved. Next, a multichannel sensor-array based on multiplex peptides that can visually distinguish SARS-CoV-2 proteases from influenza proteases in doped human samples was investigated.

Fractal fractional based transmission dynamics of COVID-19 epidemic model.

We investigate the dynamical behavior of Coronavirus (COVID-19) for different infections phases and multiple routes of transmission. In this regard, we study a COVID-19 model in the context of fractal-fractional order operator. First, we study the COVID-19 dynamics with a fractal fractional-order operator in the framework of Atangana-Baleanu fractal-fractional operator. We estimated the basic reduction number and the stability results of the proposed model. We show the data fitting to the proposed model. The system has been investigated for qualitative analysis. Novel numerical methods are introduced for the derivation of an iterative scheme of the fractal-fractional Atangana-Baleanu order. Finally, numerical simulations are performed for various orders of fractal-fractional dimension.

Gaussian Barebone Salp Swarm Algorithm with Stochastic Fractal Search for medical image segmentation: A COVID-19 case study.

An appropriate threshold is a key to using the multi-threshold segmentation method to solve image segmentation problems, and the swarm intelligence (SI) optimization algorithm is one of the popular methods to obtain the optimal threshold. Moreover, Salp Swarm Algorithm (SSA) is a recently released swarm intelligent optimization algorithm. Compared with other SI optimization algorithms, the optimization solution strategy of the SSA still needs to be improved to enhance further the solution accuracy and optimization efficiency of the algorithm. Accordingly, this paper designs an effective segmentation method based on a non-local mean 2D histogram and 2D Kapur's entropy called SSA with Gaussian Barebone and Stochastic Fractal Search (GBSFSSSA) by combining Gaussian Barebone and Stochastic Fractal Search mechanism. In GBSFSSSA, the Gaussian Barebone and Stochastic Fractal Search mechanism effectively balance the global search ability and local search ability of the basic SSA. The CEC2017 competition data set is used to prove the algorithm's performance, and GBSFSSSA shows an absolute advantage over some typical competitive algorithms. Furthermore, the algorithm is applied in image segmentation of COVID-19 CT images, and the results are analyzed based on three different metrics: peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and feature similarity (FSIM), which can lead to the conclusion that the overall performance of GBSFSSSA is better than the comparison algorithm and can effectively improve the segmentation of medical images. Therefore, it is justified that GBSFSSSA is a reliable and effective method in solving the multi-threshold image segmentation problem.

Agent-based analysis of contagion events according to sourcing locations.

The first human infected with the Covid-19 virus was traced to a seafood market in Wuhan, China. Research shows that there are comparable types of viruses found in different and mutually distant areas. This raises several questions: what if the virus originated in another location? How will future waves of epidemics behave if they originate from different locations with a smaller/larger population than Wuhan? To explore these questions, we implement an agent-based model within fractal cities. Cities radiate gravitational social attraction based on their Zipfian population. The probability and predictability of contagion events are analyzed by examining fractal dimensions and lacunarity. Results show that weak gravitational forces of small locations help dissipate infections across country quicker if the pathogen had originated from that location. Gravitational forces of large cities help contain infections within them if they are the starting locations for the pathogen. Greater connectedness and symmetry allow for a more predictable epidemic outcome since there are no obstructions to spreading. To test our hypothesis, we implement datasets from two countries, Sierra Leone and Liberia, and two diseases, Ebola and Covid-19, and obtain the same results.

Updated fractal assessment of Italian Covid-19 disease.

.

Assessing the ratio between new Covid-19 cases and new tests for Sars-Cov-2 in Italy by fractal investigation.

AIM: processing the heterogeneous data on the Italian Covid-19 epidemic by fractal investigation on the trend curve of the ratio between new Covid19 cases/new Sars-Cov-2 tests. METHODS: New cases of Covid-19 disease and new tests were calculated from raw data freely available on the Italian governing website. The effectiveness of Italian government Decrees aiming to obtain lock-down was assessed by fractal investigation. Self-similarity parameters of presumed fractal shapes obtained 6 days after each Decree were estimated, when possible. Self-organized criticality was also assessed to check for chaos involvement in disturbing the fractal shapes. Shapes were then compared and were used to estimate the number of new tests for Sars-Cov-2 that Italy would be able to perform. RESULTS: The full lock-down changed the biocomplexity of the Covid-19 epidemic in Italy. If the biocomplexity of Covid-19 did not change after the lock-down, Italy should have been able to perform at least 25490 tests daily (±8940) on average, while real data show that a larger number of tests were done (p<0.001) (thereby obtaining the lowering of contagions). If the same biocomplexity was observed before full lock down, Italy would be able to perform 7088 tests daily (±5163) on average, while real data show that a lower number of tests were done (p=0.029) (thereby observing the worsening of contagions). CONCLUSION: in case of heterogeneous data, fractal investigation would be prove useful for assessing and estimating trends.

Identification of an Epidemiological Model to Simulate the COVID-19 Epidemic Using Robust Multiobjective Optimization and Stochastic Fractal Search.

Traditionally, the identification of parameters in the formulation and solution of inverse problems considers that models, variables, and mathematical parameters are free of uncertainties. This aspect simplifies the estimation process, but does not consider the influence of relatively small changes in the design variables in terms of the objective function. In this work, the SIDR (Susceptible, Infected, Dead, and Recovered) model is used to simulate the dynamic behavior of the novel coronavirus disease (COVID-19), and its parameters are estimated by formulating a robust inverse problem, that is, considering the sensitivity of design variables. For this purpose, a robust multiobjective optimization problem is formulated, considering the minimization of uncertainties associated with the estimation process and the maximization of the robustness parameter. To solve this problem, the Multiobjective Stochastic Fractal Search algorithm is associated with the Effective Mean concept for the evaluation of robustness. The results obtained considering real data of the epidemic in China demonstrate that the evaluation of the sensitivity of the design variables can provide more reliable results.

Time series and fractal analyses of wheezing: a novel approach.

Since the outbreak of the pandemic Coronavirus Disease 2019, the world is in search of novel non-invasive methods for safer and early detection of lung diseases. The pulmonary pathological symptoms reflected through the lung sound opens a possibility of detection through auscultation and of employing spectral, fractal, nonlinear time series and principal component analyses. Thirty-five signals of vesicular and expiratory wheezing breath sound, subjected to spectral analyses shows a clear distinction in terms of time duration, intensity, and the number of frequency components. An investigation of the dynamics of air molecules during respiration using phase portrait, Lyapunov exponent, sample entropy, fractal dimension, and Hurst exponent helps in understanding the degree of complexity arising due to the presence of mucus secretions and constrictions in the respiratory airways. The feature extraction of the power spectral density data and the application of principal component analysis helps in distinguishing vesicular and expiratory wheezing and thereby, giving a ray of hope in accomplishing an early detection of pulmonary diseases through sound signal analysis.

A fractal kinetics SI model can explain the dynamics of COVID-19 epidemics.

The COVID-19 pandemic has already had a shocking impact on the lives of everybody on the planet. Here, we present a modification of the classical SI model, the Fractal Kinetics SI model which is in excellent agreement with the disease outbreak data available from the World Health Organization. The fractal kinetic approach that we propose here originates from chemical kinetics and has successfully been used in the past to describe reaction dynamics when imperfect mixing and segregation of the reactants is important and affects the dynamics of the reaction. The model introduces a novel epidemiological parameter, the "fractal" exponent h which is introduced in order to account for the self-organization of the societies against the pandemic through social distancing, lockdowns and flight restrictions.