Physica A: Statistical Mechanics and its Applications

Estimation of COVID-19 dynamics and its evolution is a multidisciplinary effort, which requires the unification of heterogeneous disciplines (scientific, mathematics, epidemiological, biological/bio-chemical, virologists and health disciplines to mention the most relevant) to work together in a better understanding of this pandemic. Time series analysis is of great importance to determine both the similarity in the behavior of COVID-19 in certain countries/states and the establishment of models that can analyze and predict the transmission process of this infectious disease. In this contribution, an analysis of the different states of the United States will be carried out to measure the similarity of COVID-19 time series, using dynamic time warping distance (DTW) as a distance metric. A parametric methodology is proposed to jointly analyze infected and deceased persons. This metric allows to compare time series that have a different time length, making it very appropriate for studying the United States, since the virus did not spread simultaneously in all the states/provinces. After a measure of the similarity between the time series of the states of United States was determined, a hierarchical cluster was created, which makes it possible to analyze the behavioral relationships of the pandemic between different states and to discover interesting patterns and correlations in the underlying data of COVID-19 in the United States. With the proposed methodology, nine different clusters were obtained, showing a different behavior in the eastern zone and western zone of the United States. Finally, to make a prediction of the evolution of COVID-19 in the states, Logistic, Gompertz and SIR model was computed. With these mathematical model it is possible to have a more precise knowledge of the evolution and forecast of the pandemic.

Forecast of the peak-out and settling timing of COVID-19 at an early stage should help the people how to cope with the situation. Curve-fitting method with an asymmetric log-normal function has been applied to daily confirmed cases data in various countries. Most of the curve-fitting could show good forecasts, while the reason has not been clearly shown. The K value has recently been proposed which can provide good reasoning of curve-fitting mechanism by corresponding a long and steep slope on the K curve with fitting stability. Since K can be expressed by a time differential of logarithmic total cases, the physical background of the above correspondence was discussed in terms of the growth rate in epidemic entropy.

Using a notably large amount of data in investigating physical and chemical phenomena demands new statistical and computational approaches; besides, the cross-validations require well-established theoretical frameworks. This study aims to validate the statistical efficiency of alternative definitions for the information-theoretic measures, such as transfer entropy, using the so-called (, q)-framework. The primary goal is to find measurements of high-order correlations that preserve information-theoretic properties of information transfer between the components of a dynamical system (such as a protein) due to local operations. Besides, this study aims to decode the information contained in the amino acid sequence establishing a three-dimensional protein structure by comparing the amino acids physical-chemical properties with their ranked role in the protein interaction network topology using new graph-theoretic measures based on the constructed digraph models of (, q) information transfer within a heat flow kernel embedding framework. Moreover, this study aims to use the Deep Graph Convolution Neural Networks for classifying the role of each amino acid in a protein trained upon short equilibrium structure fluctuations at sub-nanosecond time scales. In particular, this study examines the influence of disulphide bridges on the three-dimensional structure of the Bovine Pancreatic Trypsin Inhibitor wild type and mutated analogue protein.

Path of Fixation in evolutionary process highly depends on structure of underlying population. In this paper, we apply a machine learning method to predict the path of fixation in several complex graphs and two regular graphs. In our approach, the path of fixation is not used as the target variable in the machine learning model. Rather, we focus on predicting the probability of progression forward (referred to as{lambda} in the literature) using the machine learning model. By using previous achievements in determining the fixation path for the Moran process, obtaining the path of fixation becomes straightforward. Due to the time and computational resources required for simulating an evolutionary process in a large population, utilizing a machine learning method can help us save both of these valuable resources. This approach can provide insights to researchers studying evolutionary processes in the context of meta-population problems.

The outbreak of COVID-19 has an undeniable global impact, both socially and economically. March 11th, 2020, COVID-19 was declared as a pandemic worldwide. Many governments, worldwide, have imposed strict lockdown measures to minimize the spread of COVID-19. However, these measures cannot last forever; therefore, many countries are already considering relaxing the lockdown measures. This study, quantitatively, investigated the impact of this relaxation in the United States, Germany, the United Kingdom, Italy, Spain, and Canada. A modified version of the SIR model is used to model the reduction in lockdown based on the already available data. The results showed an inevitable second wave of COVID-19 infection following loosening the current measures. The study tries to reveal the predicted number of infected cases for different reopening dates. Additionally, the predicted number of infected cases for different reopening dates is reported.

The analysis of computer simulation data requires efficient statistical and computational approaches, based on well-established theoretical frameworks. This study aims to introduce such approaches for topological data analysis within the persistent homology framework and to describe the manifold of the protein structure dynamics within the differential geometry of the directed graphs framework. Furthermore, the asymmetric kernel-directed graphs determined by the transfer entropy will describe the information flow in this manifold. The primary goal is to characterise changes in the topology of the protein structure due to the mutations. Moreover, this study aims to define the embedded manifold of dimension m of the amino acid sequence interaction network using the graphs Laplacian matrix for determining the local embedded vector fields and coordinate vectors in this manifold for each amino acid as the vertices of either a directed or undirected graph. Furthermore, this study strives to show that encoding the amino acid sequence information in an m-dimensional manifold is statistically efficient by decoding that information in a much lower-dimensional space. Then, using the topological data analysis, we can observe protein structure dynamics changes in a multidimensional manifold, for example, due to amino acid mutations. The analysis showed that short equilibrium structure fluctuations at a few nanoseconds enable the construction of such a manifold. As a case study, the influence of the mutation of the two disulphide bridges on the three-dimensional structure of the Bovine Pancreatic Trypsin Inhibitor protein is investigated.

The cumulative records of COVID-19 are rapidly increasing day by day in India. The key question prevailing in minds of all is when will it get over? There have been several attempts in literature to address this question using time series, Machine learning, epidemiological and statistical models. However due to high level of uncertainty in the domain and lack of big historical data, the performance of these models suffer. In this work, we present an intuitive model that uses a combination of epidemiological model (SEIR) and mathematical curve fitting method to forecast spread of COVID-19 in India in future. By using the combination model, we get characteristics benefits of these models under limited knowledge and historical data about the novel Coronavirus. Instead of fixing parameters of the standard SEIR model before simulation, we propose to learn them from the real data set consisting of progression of Corona spread in India. The learning of model is carefully designed by understanding that available data set consist of records of cases under full, partial to zero lockdown phases in India. Hence, we make two separate predictions by our propose model. One under the situation of full lockdown in India and, other with partial to zero restrictions in India. With continued strict lockdown after May 03, 2020, our model predicted May 14, 2020 as the date of peak of Coronavirus in India. However, in current scenario of partial to zero lockdown phase in India, the peak of Coronavirus cases is predicted to be July 31, 2020. These two predictions presented in this work provide awareness among citizens of India on importance of control measures such as full, partial and zero lockdown and the spread of Corona disease infection rate. In addition to this, it is a beneficial study for the government of India to plan the things ahead.

The main purpose of the study is to introduce the wavelength models developed to measure the size of outbreaks based on the COVID-19 example. In this way, the wavelengths of the outbreaks can be calculated, ensuring that the outbreaks are valid, reliable and easy to follow at the national and international level. Wavelength models consist of approved case, death, recovered case and net wavelength models. Thus, the size of the outbreak can be measured both individually and as a whole. COVID-19 cases of 181 countries were used to demonstrate the application of the models. The prominent findings in the applied wavelength models are as follows: the countries with the highest case wavelength are USA, Italy, Spain and Germany, respectively. However, Italy ranks first in the death wavelength, followed by Spain, the USA and France. On the other hand, China has taken the first place in the recovered case wavelength. This country was followed by Spain and Germany and Italy, respectively. Based on all these wavelength models mentioned, net wavelength lengths are calculated. According to the findings of net wavelengths obtained, Canada ranked first, followed by United Kingdom, USA and Italy, respectively.

The novel coronal virus has spread across more than 213 countries within the space of six months causing devastating public health hazard and monumental economic loss. In the absence of clinically approved pharmaceutical intervention, attentions are shifted to non-pharmaceutical controls to mitigate the burden of the novel pandemic. In this regard, a ten mutually exclusive compartmental mathematical model is developed to investigate possible effects of both pharmaceutical and non-pharmaceutical controls incorporating both private and governments quarantine and treatments. Several reproduction numbers were calculated and used to determine the impact of both control measures as well as projected benefits of social distancing, treatments and vaccination. We investigate and compare the possible impact of social distancing incorporating different levels of vaccination, with vaccination programme incorporating different levels of treatment. Using the officially published South African COVID-19 data, the numerical simulation shows that the community reproduction threshold will be 30 when there is no social distancing but will drastically reduced to 5 (about 83% reduction) when social distancing is enforced. Furthermore, when there is vaccination with perfect efficacy, the community reproduction threshold will be 4 which increases to 12 (about 67% increment) with-out vaccination. We also established that the implementation of both interventions is enough to curtail the spread of COVID-19 pandemic in South Africa which is in confirmation with the recommendation of the world health organization.

Current research is an attempt to understand the CoVID-19 pandemic curve through statistical approach of probability density function with associated skewness and kurtosis measures, change point detection and polynomial fitting to estimate infected population along with 30 days projection. The pandemic curve has been explored for above average affected countries, six regions and global scale during 64 days of 22nd January to 24th March, 2020. The global cases infection as well as recovery rate curves remained in the ranged of 0 - 9.89 and 0 - 8.89%, respectively. The confirmed cases probability density curve is high positive skewed and leptokurtic with mean global infected daily population of 6620. The recovered cases showed bimodal positive skewed curve of leptokurtic type with daily recovery of 1708. The change point detection helped to understand the CoVID-19 curve in term of sudden change in term of mean or mean with variance. This pointed out disease curve is consist of three phases and last segment that varies in term of day lengths. The mean with variance based change detection is better in differentiating phases and associated segment length as compared to mean. Global infected population might rise in the range of 0.750 to 4.680 million by 24th April 2020, depending upon the pandemic curve progress beyond 24th March, 2020. Expected most affected countries will be USA, Italy, China, Spain, Germany, France, Switzerland, Iran and UK with at least infected population of over 0.100 million. Infected population polynomial projection errors remained in the range of -78.8 to 49.0%.

By means of density functional theory (DFT), influence of solvent molecules on polymer brushes is investigated. Osmotic pressure of solvent molecules gives rise to a stronger stretching of the brush chains in perpendicular direction. This suggests that the osmotic pressure of solvent molecules is a driving force in increasing thickness of brush layer.

We propose a novel mutation mechanism for points and ordinary or palindromic sequences of DNA and RNA. We adopted non-Hermitian approaches based on quantum mechanics. Hermiticity is in the limelight of any physical structure with quantum character, like DNA, or RNA, as it creates quantum stability in that it yields real eigenvalues and orthonormal states. We show that, through the mutation mechanism we constructed based on non-Hermitian physics, the deterioration of the Hermitian character of the original DNA states, nucleotides, does not create a stability problem. We show that Weyls perturbation theory helps us determine the stability of mutated DNA or RNA. We prove that mutations made in the laboratory with conventional nucleotides using non-Hermitian physics methods are not different from mutations that occur spontaneously in nature. This result may help to reveal the quantum nature of genetic diseases in the near future and may shape the molecular approaches.

The collective intelligence of animal groups is a complex algorithm for computer scientist and a many-body problem for physics of living system. We show how the time evolution of features in such a system, like number of ants in particular state for colonies, can be mapped to many-body problems in non-equilibrium statistical mechanics. There exist role transitions of active and passive ant between distributed functions, including exploration, assessing, recruiting and transportation in the house-hunting process. Theoretically, such a process can be approximately described as birth-death process where large number of particles living in the Fock space and particles of one sub-type transfer to a different sub-type with some probability. Started from the master equation with constrain of the quorum criterion, we express the evolution operator as a functional integral mapping from operators acting on Fock space in number representation to functional space in coherent state representation. We then read out the action from the evolution operator, and we use least action principal equations of motion, which are the number field equations. The equations we get are couple ordinary differential equations, which can faithfully describe the original master equation, and hence fully describe the system. This method provides us differential equation-based algorithm, which allow us explore parameter space with respect to more complicated agent-based algorithm. The algorithm also allows exploring stochastic process with memory in a Markovian way, which provide testable prediction on collective decision making.

We consider a simple model for the COVID-19 pandemic to analyse the relative effectiveness of several stages of the lockdown in Belgium, as well as of several phases of its relaxation. We also make a future projection of different types of measures relative to different stages of the already experienced lockdown.

AO_SCPLOWBSTRACTC_SCPLOWThis paper deals with an advanced analytical epidemic diffusion model which is capable to predict the status of epidemic impacts. This newly propose model well describes an epidemic growth and it could be widely applied into various topics including pathology, epidemiology, business and data sciences. The Advanced Analytical Epidemic Diffusion Model (AAEDM) is a dynamic diffusion prediction model which is theoretically intuitive and its tractable closed formula could be easily adapted into versatile Bigdata driven analytics including the machine learning system. This dynamic model is still an analytical model but the periods of prediction are segmented for adapting the values from the dataset when the data is available. The epidemiologically vital parameters which effect on the AAEDM are also introduced in this paper. The evaluation of this theoretical model based on the Covid-19 data in Korea has been accomplished with relative fair future prediction accuracies. Although this analytical model has been designed from a basic exponential growth model, the performance of the AAEDM is competitive with other Bigdata based simulation models. Since the AAEDM is relatively simple and handy, anyone can use this model into analyzing outbreak situations in his daily life.

Diagnose the infected patient as soon as possible in the coronavirus 2019 (COVID-19) outbreak which is declared as a pandemic by the world health organization (WHO) is extremely important. Experts recommend CT imaging as a diagnostic tool because of the weak points of the nucleic acid amplification test (NAAT). In this study, the detection of COVID-19 from CT images, which give the most accurate response in a short time, was investigated in the classical computer and firstly in quantum computers. Using the quantum transfer learning method, we experimentally perform COVID-19 detection in different quantum real processors (IBMQx2, IBMQ-London and IBMQ-Rome) of IBM, as well as in different simulators (Pennylane, Qiskit-Aer and Cirq). By using a small number of data sets such as 126 COVID-19 and 100 Normal CT images, we obtained a positive or negative classification of COVID-19 with 90% success in classical computers, while we achieved a high success rate of 94-100% in quantum computers. Also, according to the results obtained, machine learning process in classical computers requiring more processors and time than quantum computers can be realized in a very short time with a very small quantum processor such as 4 qubits in quantum computers. If the size of the data set is small; Due to the superior properties of quantum, it is seen that according to the classification of COVID-19 and Normal, in terms of machine learning, quantum computers seem to outperform traditional computers.

The novel coronavirus disease 2019 (COVID-19) has created a serious threat to global health. We developed a new quantum machine learning (QML) assisted diagnostic method that can provide an accurate diagnosis to aid decision processes of medical providers. One of the key elements in our method was to implement the quantum variational method to efficiently classify data, taking crucial multiple correlations among the features into account. We established and fine-tuned this quantum classifier by using a group of data drawn from publicly available COVID-19 cases. We have shown that QML is capable of processing patient information efficiently and accurately for the diagnosis of COVID-19.

Developing antiviral drugs is an exigent task since viruses mutate to overcome the effect of antiviral drugs. As a result, the efficacy of most antiviral drugs is short-lived. To include this effect, we modify the Neumann and Dahari model. Considering the fact that the efficacy of the antiviral drug varies in time, the differential equations introduced in the previous model systems are rewritten to study the correlation between the viral load and antiviral drug. The effect of antiviral drug that either prevents infection or stops the production of a virus is explored. First, the efficacy of the drug is considered to decreases monotonously as time progresses. In this case, our result depicts that when the efficacy of the drug is low, the viral load decreases and increases back in time revealing the effect of the antiviral drugs is short-lived. On the other hand, for the antiviral drug with high efficacy, the viral load, as well as the number of infected cells, monotonously decreases while the number of uninfected cells increases. The dependence of the critical drug efficacy on time is also explored. Moreover, the correlation between viral load, the antiviral drug, and CTL response is also explored. In this case, not only the dependence for the basic reproduction ratio on the model parameters is explored but also we analyze the critical drug efficacy as a function of time. We show that the term related to the basic reproduction ratio increases when the CTL response step up. A simple analytically solvable mathematical model is also presented to analyze the correlation between viral load and antiviral drugs.

The outbreak of COVID-19 is first identified in China, which later spread to various parts of the globe and was pronounced pandemic by the World Health Organization (WHO). The disease of transmissible person-to-person pneumonia caused by the extreme acute respiratory coronavirus 2 syndrome (SARS-COV-2, also known as COVID-19), has sparked a global warning. Thermal screening, quarantining, and later lockdown were methods employed by various nations to contain the spread of the virus. Though exercising various possible plans to contain the spread help in mitigating the effect of COVID-19, projecting the rise and preparing to face the crisis would help in minimizing the effect. In the scenario, this study attempts to use Machine Learning tools to forecast the possible rise in the number of cases by considering the data of daily new cases. To capture the uncertainty, three different techniques: (i) Decision Tree algorithm, (ii) Support Vector Machine algorithm, and (iii) Gaussian process regression are used to project the data and capture the possible deviation. Based on the projection of new cases, recovered cases, deceased cases, medical facilities, population density, number of tests conducted, and facilities of services, are considered to define the criticality index (CI). CI is used to classify all the districts of the country in the regions of high risk, low risk, and moderate risk. An online dashpot is created, which updates the data on daily bases for the next four weeks. The prospective suggestions of this study would aid in planning the strategies to apply the lockdown/ any other plan for any country, which can take other parameters to define the CI.

Dynamical systems on graphs allow to describe multiple phenomena from different areas of Science. In particular, many complex systems in Ecology are studied by this approach. In this paper we analize the mathematical framework for the study of the structural stability of each stationary point, feasible or not, introducing a generalization for this concept, defined as Global Structural Stability. This approach would fit with the proper mathematical concept of structural stability, in which we find a full description of the complex dynamics on the phase space due to nonlinear dynamics. This fact can be analyzed as an informational field grounded in a global attractor whose structure can be completely characterized. These attractors are stable under perturbation and suppose the minimal structurally stable sets. We also study in detail, mathematically and computationally, the zones characterizing different levels of biodiversity in bipartite graphs describing mutualistic antagonistic systems of population dynamics. In particular, we investigate the dependence of the region of maximal biodiversity of a system on its connectivity matrix. On the other hand, as the network topology does not completely determine the robustness of the dynamics of a complex network, we study the correlation between structural stability and several graph measures. A systematic study on synthetic and biological graphs is presented, including 10 mutualistic networks of plants and seed-dispersal and 1000 random synthetic networks. We compare the role of centrality measures and modularity, concluding the importance of just cooperation strength among nodes when describing areas of maximal biodiversity. Indeed, we show that cooperation parameters are the central role for biodiversity while other measures act as secondary supporting functions. Author summaryWe introduce the concept of Global Structural Stability as a proper mathematical concept to fully understand biodiversity in some ecological systems. Our concept retakes the definitions in the classical works of R. Thom [1] and Andronov-Pontryagin [2]. Moreover, there exists a close relation between the structure of a complex network, described as a graph, and its associated dynamics. Mutualistic networks introduce cooperation links between two groups of species, as plant and pollinators or seed-dispersal. The understanding of organizational aspects leading to maximizing biodiversity is one of the more important research areas in Theoretical and Applied Ecology. In this work we introduce a systematic study on different graph measures in order to identify optimal organization for maximal biodiversity (defined as structural stability). Our results conclude that, for mutualistic systems, the strength in cooperation parameters are the core fact, i.e., cooperation is the real fact optimizing biodiversity among other possible structural configurations.