How complex is COVID-19: Spatiotemporal variation of chaotic nature of the virus in Indian states.

Like other pandemics, COVID-19 also created a huge socioeconomic imbalance and distress in people. Often, every pandemic is characterized as chaotic and complex. Hence, the nature of the virus spread and deaths should be analyzed to prepare for the next similar pandemic. In this analysis, the popular and well-known time series in chaos theory is implemented, and the results are deduced for the states of India. The phase space reconstruction algorithm is implemented, and false nearest neighbor (FNN) method is applied to determine the dimensionality, and also Lyapunov exponent of the time series is estimated. The chaotic nature of COVID-19 cases showed a less severe and low complexity, with the FNN dimension range of 3-5, whereas the COVID-19 deaths showed moderate complexity with FNN dimensions 2-7. Policymakers should take action on medical availability in rural states and control people's movement in highly populated areas.

Nonlinear model of infection wavy oscillation of COVID-19 in Japan based on diffusion kinetics.

The infectious propagation of SARS-CoV-2 is continuing worldwide, and specifically, Japan is facing severe circumstances. Medical resource maintenance and action limitations remain the central measures. An analysis of long-term follow-up reports in Japan shows that the infection number follows a unique wavy oscillation, increasing and decreasing over time. However, only a few studies explain the infection wavy oscillation. This study introduces a novel nonlinear mathematical model of the new infection wavy oscillation by applying the macromolecule diffusion theory. In this model, the diffusion coefficient that depends on population density gives nonlinearity in infection propagation. As a result, our model accurately simulated infection wavy oscillations, and the infection wavy oscillation frequency and amplitude were closely linked with the recovery rate of infected individuals. In conclusion, our model provides a novel nonlinear contact infection analysis framework.

Identifying causality drivers and deriving governing equations of nonlinear complex systems.

Identifying and describing the dynamics of complex systems is a central challenge in various areas of science, such as physics, finance, or climatology. While machine learning algorithms are increasingly overtaking traditional approaches, their inner workings and, thus, the drivers of causality remain elusive. In this paper, we analyze the causal structure of chaotic systems using Fourier transform surrogates and three different inference techniques: While we confirm that Granger causality is exclusively able to detect linear causality, transfer entropy and convergent cross-mapping indicate that causality is determined to a significant extent by nonlinear properties. For the Lorenz and Halvorsen systems, we find that their contribution is independent of the strength of the nonlinear coupling. Furthermore, we show that a simple rationale and calibration algorithm are sufficient to extract the governing equations directly from the causal structure of the data. Finally, we illustrate the applicability of the framework to real-world dynamical systems using financial data before and after the COVID-19 outbreak. It turns out that the pandemic triggered a fundamental rupture in the world economy, which is reflected in the causal structure and the resulting equations.

A new buffering theory of social support and psychological stress.

A dynamical model linking stress, social support, and health has been recently proposed and numerically analyzed from a classical point of view of integer-order calculus. Although interesting observations have been obtained in this way, the present work conducts a fractional-order analysis of that model. Under a periodic forcing of an environmental stress variable, the perceived stress has been analyzed through bifurcation diagrams and two well-known metrics of entropy and complexity, such as spectral entropy and C0 complexity. The results obtained by numerical simulations have shown novel insights into how stress evolves with frequency and amplitude of the perturbation, as well as with initial conditions for the system variables. More precisely, it has been observed that stress can alternate between chaos, periodic oscillations, and stable behaviors as the fractional order varies. Moreover, the perturbation frequency has revealed a narrow interval for the chaotic oscillations, while its amplitude may present different values indicating a low sensitivity regarding chaos generation. Also, the perceived stress has been noted to be highly sensitive to initial conditions for the symptoms of stress-related ill-health and for the social support received from family and friends. This work opens new directions of research whereby fractional calculus might offer more insight into psychology, life sciences, mental disorders, and stress-free well-being.

Model Dynamics and Optimal Control for Intervention Policy of COVID-19 Epidemic with Quarantine and Immigrating Disturbances.

A dynamic model called SqEAIIR for the COVID-19 epidemic is investigated with the effects of vaccination, quarantine and precaution promotion when the traveling and immigrating individuals are considered as unknown disturbances. By utilizing only daily sampling data of isolated symptomatic individuals collected by Mexican government agents, an equivalent model is established by an adaptive fuzzy-rules network with the proposed learning law to guarantee the convergence of the model's error. Thereafter, the optimal controller is developed to determine the adequate intervention policy. The main theorem is conducted to demonstrate the setting of all designed parameters regarding the closed-loop performance. The numerical systems validate the efficiency of the proposed scheme to control the epidemic and prevent the overflow of requiring healthcare facilities. Moreover, the sufficient performance of the proposed scheme is achieved with the effect of traveling and immigrating individuals.

On nonlinear dynamics of COVID-19 disease model corresponding to nonsingular fractional order derivative.

This manuscript is devoted to investigate the mathematical model of fractional-order dynamical system of the recent disease caused by Corona virus. The said disease is known as Corona virus infectious disease (COVID-19). Here we analyze the modified SEIR pandemic fractional order model under nonsingular kernel type derivative introduced by Atangana, Baleanu and Caputo ([Formula: see text]) to investigate the transmission dynamics. For the validity of the proposed model, we establish some qualitative results about existence and uniqueness of solution by using fixed point approach. Further for numerical interpretation and simulations, we utilize Adams-Bashforth method. For numerical investigations, we use some available clinical data of the Wuhan city of China, where the infection initially had been identified. The disease free and pandemic equilibrium points are computed to verify the stability analysis. Also we testify the proposed model through the available data of Pakistan. We also compare the simulated data with the reported real data to demonstrate validity of the numerical scheme and our analysis.

The Temporal Lagged Relationship Between Meteorological Factors and Scrub Typhus With the Distributed Lag Non-linear Model in Rural Southwest China.

Background: Meteorological factors can affect the emergence of scrub typhus for a period lasting days to weeks after their occurrence. Furthermore, the relationship between meteorological factors and scrub typhus is complicated because of lagged and non-linear patterns. Investigating the lagged correlation patterns between meteorological variables and scrub typhus may promote an understanding of this association and be beneficial for preventing disease outbreaks. Methods: We extracted data on scrub typhus cases in rural areas of Panzhihua in Southwest China every week from 2008 to 2017 from the China Information System for Disease Control and Prevention. The distributed lag non-linear model (DLNM) was used to study the temporal lagged correlation between weekly meteorological factors and weekly scrub typhus. Results: There were obvious lagged associations between some weather factors (rainfall, relative humidity, and air temperature) and scrub typhus with the same overall effect trend, an inverse-U shape; moreover, different meteorological factors had different significant delayed contributions compared with reference values in many cases. In addition, at the same lag time, the relative risk increased with the increase of exposure level for all weather variables when presenting a positive association. Conclusions: The results found that different meteorological factors have different patterns and magnitudes for the lagged correlation between weather factors and scrub typhus. The lag shape and association for meteorological information is applicable for developing an early warning system for scrub typhus.

Evaluation of the effects of meteorological factors on COVID-19 prevalence by the distributed lag nonlinear model.

BACKGROUND: Although numerous studies have explored the impact of meteorological factors on the epidemic of COVID-19, their relationship remains controversial and needs to be clarified. METHODS: We assessed the risk effect of various meteorological factors on COVID-19 infection using the distributed lag nonlinear model, based on related data from July 1, 2020, to June 30, 2021, in eight countries, including Portugal, Greece, Egypt, South Africa, Paraguay, Uruguay, South Korea, and Japan, which are in Europe, Africa, South America, and Asia, respectively. We also explored associations between COVID-19 prevalence and individual meteorological factors by the Spearman's rank correlation test. RESULTS: There were significant non-linear relationships between both temperature and relative humidity and COVID-19 prevalence. In the countries located in the Northern Hemisphere with similar latitudes, the risk of COVID-19 infection was the highest at temperature below 5 â„ƒ. In the countries located in the Southern Hemisphere with similar latitudes, their highest infection risk occurred at around 15 â„ƒ. Nevertheless, in most countries, high temperature showed no significant association with reduced risk of COVID-19 infection. The effect pattern of relative humidity on COVID-19 depended on the range of its variation in countries. Overall, low relative humidity was correlated with increased risk of COVID-19 infection, while the high risk of infection at extremely high relative humidity could occur in some countries. In addition, relative humidity had a longer lag effect on COVID-19 than temperature. CONCLUSIONS: The effects of meteorological factors on COVID-19 prevalence are nonlinear and hysteretic. Although low temperature and relative humidity may lower the risk of COVID-19, high temperature or relative humidity could also be associated with a high prevalence of COVID-19 in some regions.

The impact of meteorological factors and PM2.5 on COVID-19 transmission.

In this study, we analysed the relationship between meteorological factors and the number of patients with coronavirus disease 2019 (COVID-19). The study period was from 12 April 2020 to 13 October 2020, and daily meteorological data and the daily number of patients with COVID-19 in each state of the United States were collected. Based on the number of COVID-19 patients in each state of the United States, we selected four states (California, Florida, New York, Texas) for analysis. One-way analysis of variance ( ANOVA), scatter plot analysis, correlation analysis and distributed lag nonlinear model (DLNM) analysis were used to analyse the relationship between meteorological factors and the number of patients with COVID-19. We found that the significant influencing factors of the number of COVID-19 cases differed among the four states. Specifically, the number of COVID-19 confirmed cases in California and New York was negatively correlated with AWMD (P < 0.01) and positively correlated with AQI, PM2.5 and TAVG (P < 0.01) but not significantly correlated with other factors. Florida was significantly correlated with TAVG (positive) (P < 0.01) but not significantly correlated with other factors. The number of COVID-19 cases in Texas was only significantly negatively associated with AWND (P < 0.01). The influence of temperature and PM2.5 on the spread of COVID-19 is not obvious. This study shows that when the wind speed was 2 m/s, it had a significant positive correlation with COVID-19 cases. The impact of meteorological factors on COVID-19 may be very complicated. It is necessary to further explore the relationship between meteorological factors and COVID-19. By exploring the influence of meteorological factors on COVID-19, we can help people to establish a more accurate early warning system.

The evolution of happiness pre and peri-COVID-19: A Markov Switching Dynamic Regression Model.

Happiness levels often fluctuate from one day to the next, and an exogenous shock such as a pandemic can likely disrupt pre-existing happiness dynamics. This paper fits a Marko Switching Dynamic Regression Model (MSDR) to better understand the dynamic patterns of happiness levels before and during a pandemic. The estimated parameters from the MSDR model include each state's mean and duration, volatility and transition probabilities. Once these parameters have been estimated, we use the one-step method to predict the unobserved states' evolution over time. This gives us unique insights into the evolution of happiness. Furthermore, as maximising happiness is a policy priority, we determine the factors that can contribute to the probability of increasing happiness levels. We empirically test these models using New Zealand's daily happiness data for May 2019 -November 2020. The results show that New Zealand seems to have two regimes, an unhappy and happy regime. In 2019 the happy regime dominated; thus, the probability of being unhappy in the next time period (day) occurred less frequently, whereas the opposite is true for 2020. The higher frequency of time periods with a probability of being unhappy in 2020 mostly correspond to pandemic events. Lastly, we find the factors positively and significantly related to the probability of being happy after lockdown to be jobseeker support payments and international travel. On the other hand, lack of mobility is significantly and negatively related to the probability of being happy.

Immune-viral dynamics modeling for SARS-CoV-2 drug development.

Coronavirus disease 2019 (COVID-19) global pandemic is caused by severe acute respiratory syndrome-coronavirus 2 (SARS-CoV-2) viral infection, which can lead to pneumonia, lung injury, and death in susceptible populations. Understanding viral dynamics of SARS-CoV-2 is critical for development of effective treatments. An Immune-Viral Dynamics Model (IVDM) is developed to describe SARS-CoV-2 viral dynamics and COVID-19 disease progression. A dataset of 60 individual patients with COVID-19 with clinical viral load (VL) and reported disease severity were assembled from literature. Viral infection and replication mechanisms of SARS-CoV-2, viral-induced cell death, and time-dependent immune response are incorporated in the model to describe the dynamics of viruses and immune response. Disease severity are tested as a covariate to model parameters. The IVDM was fitted to the data and parameters were estimated using the nonlinear mixed-effect model. The model can adequately describe individual viral dynamics profiles, with disease severity identified as a covariate on infected cell death rate. The modeling suggested that it takes about 32.6 days to reach 50% of maximum cell-based immunity. Simulations based on virtual populations suggested a typical mild case reaches VL limit of detection (LOD) by 13 days with no treatment, a moderate case by 17 days, and a severe case by 41 days. Simulations were used to explore hypothetical treatments with different initiation time, disease severity, and drug effects to demonstrate the usefulness of such modeling in informing decisions. Overall, the IVDM modeling and simulation platform enables simulations for viral dynamics and treatment efficacy and can be used to aid in clinical pharmacokinetic/pharmacodynamic (PK/PD) and dose-efficacy response analysis for COVID-19 drug development.

A novel social distance model reveals the sidewall effect at bottlenecks.

Intermittent and periodic outbreaks of infectious diseases have had profound and lasting effects on societies throughout human history. During the global spread of SARS-CoV-2 and the resulting coronavirus disease (COVID-19), social distance has been imposed worldwide to limit the spread of the virus. An additional deliberate intention of keeping a minimum safety distance from neighbors can fundamentally alter the "social force" between individuals. Here, we introduce a new "social distance" term inspired by gas molecular dynamics and integrate it into an existing agent-based social force model to describe the dynamics of crowds under social-distanced conditions. The advantage of this "social distance" term over the simple increasing of the repulsive range of other alternatives is that the fundamental crowd properties are precisely described by our model parameters. We compare the new model with the Helbing and Molnar's classical model and experimental data, and show that this new model is superior in reproducing experimental data. We demonstrate the usability of this model with a bottleneck motion base case. The new model shows that the bottleneck effect can be significantly alleviated through small wall modifications. Lastly, we explain the mechanism of this improvement and conclude that this improvement is due to spatial asymmetry.

Optimal control strategies on COVID-19 infection to bolster the efficacy of vaccination in India.

The Novel Coronavirus which emerged in India on January/30/2020 has become a catastrophe to the country on the basis of health and economy. Due to rapid variations in the transmission of COVID-19, an accurate prediction to determine the long term effects is infeasible. This paper has introduced a nonlinear mathematical model to interpret the transmission dynamics of COVID-19 infection along with providing vaccination in the precedence. To minimize the level of infection and treatment burden, the optimal control strategies are carried out by using the Pontryagin's Maximum Principle. The data validation has been done by correlating the estimated number of infectives with the real data of India for the month of March/2021. Corresponding to the model, the basic reproduction number [Formula: see text] is introduced to understand the transmission dynamics of COVID-19. To justify the significance of parameters we determined the sensitivity analysis of [Formula: see text] using the parameters value. In the numerical simulations, we concluded that reducing [Formula: see text] below unity is not sufficient enough to eradicate the COVID-19 disease and thus, it is required to increase the vaccination rate and its efficacy by motivating individuals to take precautionary measures.

PM2.5 Monitoring: Use Information Abundance Measurement and Wide and Deep Learning.

This article devises a photograph-based monitoring model to estimate the real-time PM2.5 concentrations, overcoming currently popular electrochemical sensor-based PM2.5 monitoring methods' shortcomings such as low-density spatial distribution and time delay. Combining the proposed monitoring model, the photographs taken by various camera devices (e.g., surveillance camera, automobile data recorder, and mobile phone) can widely monitor PM2.5 concentration in megacities. This is beneficial to offering helpful decision-making information for atmospheric forecast and control, thus reducing the epidemic of COVID-19. To specify, the proposed model fuses Information Abundance measurement and Wide and Deep learning, dubbed as IAWD, for PM2.5 monitoring. First, our model extracts two categories of features in a newly proposed DS transform space to measure the information abundance (IA) of a given photograph since the growth of PM2.5 concentration decreases its IA. Second, to simultaneously possess the advantages of memorization and generalization, a new wide and deep neural network is devised to learn a nonlinear mapping between the above-mentioned extracted features and the groundtruth PM2.5 concentration. Experiments on two recently established datasets totally including more than 100 000 photographs demonstrate the effectiveness of our extracted features and the superiority of our proposed IAWD model as compared to state-of-the-art relevant computing techniques.

A Mathematical Model of COVID-19 with Vaccination and Treatment.

We formulate and theoretically analyze a mathematical model of COVID-19 transmission mechanism incorporating vital dynamics of the disease and two key therapeutic measures-vaccination of susceptible individuals and recovery/treatment of infected individuals. Both the disease-free and endemic equilibrium are globally asymptotically stable when the effective reproduction number R 0(v) is, respectively, less or greater than unity. The derived critical vaccination threshold is dependent on the vaccine efficacy for disease eradication whenever R 0(v) > 1, even if vaccine coverage is high. Pontryagin's maximum principle is applied to establish the existence of the optimal control problem and to derive the necessary conditions to optimally mitigate the spread of the disease. The model is fitted with cumulative daily Senegal data, with a basic reproduction number R 0 = 1.31 at the onset of the epidemic. Simulation results suggest that despite the effectiveness of COVID-19 vaccination and treatment to mitigate the spread of COVID-19, when R 0(v) > 1, additional efforts such as nonpharmaceutical public health interventions should continue to be implemented. Using partial rank correlation coefficients and Latin hypercube sampling, sensitivity analysis is carried out to determine the relative importance of model parameters to disease transmission. Results shown graphically could help to inform the process of prioritizing public health intervention measures to be implemented and which model parameter to focus on in order to mitigate the spread of the disease. The effective contact rate b, the vaccine efficacy ε, the vaccination rate v, the fraction of exposed individuals who develop symptoms, and, respectively, the exit rates from the exposed and the asymptomatic classes σ and ϕ are the most impactful parameters.

The Impact of the Declaration of the State of Emergency on the Spread of COVID-19: A Modeling Analysis.

When encountering the outbreak and early spreading of COVID-19, the Government of Japan imposed gradually upgraded restriction policies and declared the state of emergency in April 2020 for the first time. To evaluate the efficacy of the countering strategies in different periods, we constructed a SEIADR (susceptible-exposed-infected-asymptomatic-documented-recovered) model to simulate the cases and determined corresponding spreading coefficients. The effective reproduction number R t was obtained to evaluate the measures controlling the COVID-19 conducted by the Government of Japan during different stages. It was found that the strict containing strategies during the state of emergency period drastically inhibit the COVID-19 trend. R t was decreased to 1.1123 and 0.8911 in stages 4 and 5 (a state of emergency in April and May 2020) from 3.5736, 2.0126, 3.0672 in the previous three stages when the containing strategies were weak. The state of emergency was declared again in view of the second wave of massive infections in January 2021. We estimated the cumulative infected cases and additional days to contain the COVID-19 transmission for the second state of emergency using this model. R t was 1.028 which illustrated that the strategies were less effective than the previous state of emergency. Finally, the overall infected population was predicted using combined isolation and testing intensity; the effectiveness and the expected peak time were evaluated. If using the optimized control strategies in the current stage, the spread of COVID-19 in Japan could be controlled within 30 days. The total confirmed cases should reduce to less than 4.2 × 105 by April 2021. This model study suggested stricter isolating measures may be required to shorten the period of the state of emergency.

LUNAR :Drug Screening for Novel Coronavirus Based on Representation Learning Graph Convolutional Network.

An outbreak of COVID-19 that began in late 2019 was caused by a novel coronavirus(SARS-CoV-2). It has become a global pandemic. As of June 9, 2020, it has infected nearly 7 million people and killed more than 400,000, but there is no specific drug. Therefore, there is an urgent need to find or develop more drugs to suppress the virus. Here, we propose a new nonlinear end-to-end model called LUNAR. It uses graph convolutional neural networks to automatically learn the neighborhood information of complex heterogeneous relational networks and combines the attention mechanism to reflect the importance of the sum of different types of neighborhood information to obtain the representation characteristics of each node. Finally, through the topology reconstruction process, the feature representations of drugs and targets are forcibly extracted to match the observed network as much as possible. Through this reconstruction process, we obtain the strength of the relationship between different nodes and predict drug candidates that may affect the treatment of COVID-19 based on the known targets of COVID-19. These selected candidate drugs can be used as a reference for experimental scientists and accelerate the speed of drug development. LUNAR can well integrate various topological structure information in heterogeneous networks, and skillfully combine attention mechanisms to reflect the importance of neighborhood information of different types of nodes, improving the interpretability of the model. The area under the curve(AUC) of the model is 0.949 and the accurate recall curve (AUPR) is 0.866 using 10-fold cross-validation. These two performance indexes show that the model has superior predictive performance. Besides, some of the drugs screened out by our model have appeared in some clinical studies to further illustrate the effectiveness of the model.

Linear and non-linear dynamics of the epidemics: System identification based parametric prediction models for the pandemic outbreaks.

Coronavirus disease 2019 (COVID-19) has endured constituting formidable economic, social, educational, and phycological challenges for the societies. Moreover, during pandemic outbreaks, the hospitals are overwhelmed with patients requiring more intensive care units and intubation equipment. Therein, to cope with these urgent healthcare demands, the state authorities seek ways to develop policies based on the estimated future casualties. These policies are mainly non-pharmacological policies including the restrictions, curfews, closures, and lockdowns. In this paper, we construct three model structures of the SpInItIbD-N (suspicious Sp, infected In, intensive care It, intubated Ib, and dead D together with the non-pharmacological policies N) holding two key targets. The first one is to predict the future COVID-19 casualties including the intensive care and intubated ones, which directly determine the need for urgent healthcare facilities, and the second one is to analyse the linear and non-linear dynamics of the COVID-19 pandemic under the non-pharmacological policies. In this respect, we have modified the non-pharmacological policies and incorporated them within the models whose parameters are learned from the available data. The trained models with the data released by the Turkish Health Ministry confirmed that the linear SpInItIbD-N model yields more accurate results under the imposed non-pharmacological policies. It is important to note that the non-pharmacological policies have a damping effect on the pandemic casualties and this can dominate the non-linear dynamics. Herein, a model without pharmacological or non-pharmacological policies might have more dominant non-linear dynamics. In addition, the paper considers two machine learning approaches to optimize the unknown parameters of the constructed models. The results show that the recursive neural network has superior performance for learning nonlinear dynamics. However, the batch least squares outperforms in the presence of linear dynamics and stochastic data. The estimated future pandemic casualties with the linear SpInItIbD-N model confirm that the suspicious, infected, and dead casualties converge to zero from 200000, 1400, 200 casualties, respectively. The convergences occur in 120 days under the current conditions.

Rise and Decay of the COVID-19 Epidemics in the USA and the State of New York in the First Half of 2020: A Nonlinear Physics Perspective Yielding Novel Insights.

As of December 2020, since the beginning of the year 2020, the COVID-19 pandemic has claimed worldwide more than 1 million lives and has changed human life in unprecedented ways. Despite the fact that the pandemic is far from over, several countries managed at least temporarily to make their first-wave COVID-19 epidemics to subside to relatively low levels. Combining an epidemiological compartment model and a stability analysis as used in nonlinear physics and synergetics, it is shown how the first-wave epidemics in the state of New York and nationwide in the USA developed through three stages during the first half of the year 2020. These three stages are the outbreak stage, the linear stage, and the subsiding stage. Evidence is given that the COVID-19 outbreaks in these two regions were due to instabilities of the COVID-19 free states of the corresponding infection dynamical systems. It is shown that from stage 1 to stage 3, these instabilities were removed, presumably due to intervention measures, in the sense that the COVID-19 free states were stabilized in the months of May and June in both regions. In this context, stability parameters and key directions are identified that characterize the infection dynamics in the outbreak and subsiding stages. Importantly, it is shown that the directions in combination with the sign-switching of the stability parameters can explain the observed rise and decay of the epidemics in the state of New York and the USA. The nonlinear physics perspective provides a framework to obtain insights into the nature of the COVID-19 dynamics during outbreak and subsiding stages and allows to discuss possible impacts of intervention measures. For example, the directions can be used to determine how different populations (e.g., exposed versus symptomatic individuals) vary in size relative to each other during the course of an epidemic. Moreover, the timeline of the computationally obtained stages can be compared with the history of the implementation of intervention measures to discuss the effectivity of such measures.