Individual dynamics and local heterogeneity provide a microscopic view of the epidemic spreading

The COVID-19 pandemic has caused severe global disasters,highlighting the importance of understanding the details and trends of epidemic transmission in order to introduce efficient intervention measures.While the widely used deterministic compartmental models have qualitatively presented continuous “analytical” insight and captured some transmission features,their treatment usually lacks spatiotemporal variation.Here,we propose a stochastic individual dynamical(SID)model to mimic the random and heterogeneous nature of epidemic propagation.The SID model provides a unifying framework for representing the spatiotemporal variations of epidemic development by tracking the movements of each individual.Using this model,we reproduce the infection curves for COVID-19 cases in different areas globally and find the local dynamics and heterogeneity at the individual level that affect the disease outbreak.The macroscopic trend of virus spreading is clearly illustrated from the microscopic perspective,enabling a quantitative assessment of different interventions.Seemingly,this model is also applicable to studying stochastic processes at the “meter scale”,e.g.,human society’s collective dynamics.

The distribution and ecological risks of antibiotics in surface water in key cities along the lower reaches of the Yellow River:A case study of Kaifeng City,China

A large number of antibiotics have been discharged into rivers by human activities,posing a threat to aquatic ecosystems.The surface water of the Yellow River Basin also suffers antibiotic pollution,which hinders the improvement in the aquatic ecological environment.This study investigated and analyzed the characteristics and assessed the ecological risks of antibiotic pollution in surface water bodies such as canals,rivers and fish ponds in Kaifeng,Henan Province,which is a key city along the lower reaches of the Yellow River.The test results are as follows.A total of 15 types of antibiotics were detected in the surface water.They had a total antibiotic concentration of 12.2-249.9μg/L,of which tetracyclines(TCs)and quinolones accounted for the highest percentages.Six types of quinolones had detection rates of up to 100%,and doxycycline(DC)and oxytetracycline(OTC)had average concentrations of 29.52μg/L1 and 13.71μg/L,respectively.The major canals with water diverted from the Yellow River had total concentrations of quinolones and TCs of 22.0μg/L and 14.9μg/L,respectively,which were higher than those in previous studies.This phenomenon may be related to the decrease in the water flow of the Yellow River during the dry season and the increase in the antibiotic consumption of residents in the context of the Covid-19 outbreak.The upper reaches of the Huiji River in the Xiangfu District had higher antibiotic content than other districts in Kaifeng.Specifically,TCs accounted for 72.38%-91.84%of all antibiotics,and the DC and OTC concentrations were significantly higher than other antibiotics in the upper reaches.As indicated by the ecological risk assessment results,TCs had the highest ecological risks to green algae.Among them,DC had medium-high risks;TC,OTC,and chlortetracycline(CTC)had medium-high risks;trimethoprim(TMP)and lomefloxacin(LOM)had low risks;other TC antibiotics had no risk.Compared with green algae,most antibiotics showed higher ecological risks to daphnia and lower ecological risks to fish.DC and OTC dominate antibiotic pollutants in the surface water in Kaifeng City,and especially in Xiangfu District,where DC and OTC have medium-high risks.The TCs in the major Yellow River showed medium risks to both green algae and daphnia.It can be speculated that the antibiotic pollution in the Yellow River might pose a certain threat to the ecological security of water in Kaifeng City.

The Sunspot Cycle Leads to Origin and Epidemic Mechanism of Novel Coronavirus COVID-19

Listed examples of virus transmission epidemics that can be strongly transmitted through the air caused by sunspot change cycle, analyzed the mechanism that promotes the generation of new viruses. From the schematic diagram of the changes in the combined force of the hydrodynamic effect of the sun sweeping the earth and the sweeping force, we obtain the places that are prone to light vortices are 30 degrees north latitude and 30 degrees south latitude on the east coast of the mainland creatively. The curved continental lines are perfect, the range of the light vortex generated is more obviously, and the effect is stronger. And the curved continental lines are perfect, the range of the light vortex generated is more obviously, and the effect is stronger. It is inferred that the light vortex produces the special amplified energy so that can make the virus mutate to produce a new highly infectious novel coronavirus. The earliest known place and time of the novel coronavirus origin are consistent with the reasoning of the new theory. Because the radius and frequency of the light vortex are different, the resulting virus strains are also different. Moreover, the fatality rate in the light vortex area is much higher than that in the non-light vortex area, indicating that the virus’s toxicity and lethality are higher in the light vortex area, so it can explain why Russia, India, and countries in the African equatorial region mortality are much lower than the United States, Italy, Spain and Brazil. Finally, preventive and recommended measures are proposed.

A Preliminary Study on Spatial Spread Risk of Epidemics by Analyzing the Urban Subway Mobility Data

The prevention and treatment of epidemic is always an urgent problem faced by the human being. Due to the special space structure, huge passenger flow and great people mobility, the subway lines have become the areas with high epidemic transmission risks. However, there is no recent study related to epidemic transmission in the subway network on urban-scale. In this article, from the perspective of big data, we study the transmission risk of epidemic in Beijing subway network by using urban subway mobility data. By reintegrating and mining the urban subway mobility data, we preliminary assess the transmission risk in the subway lines from the passenger behaviors, station features, route features and individual case on the basis of subway network structure. This study has certain practical significance for the early stage of epidemic tracking and prevention.

Extinction and Stationary Distribution of a Stochastic SIR Epidemic Model with Jumps

A stochastic susceptible-infective-recovered(SIR)epidemic model with jumps was considered.The contributions of this paper are as follows.(1) The stochastic differential equation(SDE)associated with the model has a unique global positive solution;(2) the results reveal that the solution of this epidemic model will be stochastically ultimately bounded,and the non-linear SDE admits a unique stationary distribution under certain parametric conditions;(3) the coefficients play an important role in the extinction of the diseases.

Dynamical Analysis of the Stochastic COVID-19 Model Using Piecewise Differential Equation Technique

Various data sets showing the prevalence of numerous viral diseases have demonstrated that the transmission is not truly homogeneous.Two examples are the spread of Spanish flu and COVID-19.The aimof this research is to develop a comprehensive nonlinear stochastic model having six cohorts relying on ordinary differential equations via piecewise fractional differential operators.Firstly,the strength number of the deterministic case is carried out.Then,for the stochastic model,we show that there is a critical number RS0 that can predict virus persistence and infection eradication.Because of the peculiarity of this notion,an interesting way to ensure the existence and uniqueness of the global positive solution characterized by the stochastic COVID-19 model is established by creating a sequence of appropriate Lyapunov candidates.Adetailed ergodic stationary distribution for the stochastic COVID-19 model is provided.Our findings demonstrate a piecewise numerical technique to generate simulation studies for these frameworks.The collected outcomes leave no doubt that this conception is a revolutionary doorway that will assist mankind in good perspective nature.

GLOBAL STABILITY OF SIRS EPIDEMIC MODELS WITH A CLASS OF NONLINEAR INCIDENCE RATES AND DISTRIBUTED DELAYS

In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. When the nonlinear inci- dence rate is a saturated incidence rate, our result provides a new global stability condition for a small rate of immunity loss.

Dynamic properties of epidemic spreading on finite size complex networks

The Internet presents a complex topological structure, on which computer viruses can easily spread. By using theoretical analysis and computer simulation methods, the dynamic process of disease spreading on finite size networks with complex topological structure is investigated. On the finite size networks, the spreading process of SIS （susceptibleinfected-susceptible） model is a finite Markov chain with an absorbing state. Two parameters, the survival probability and the conditional infecting probability, are introduced to describe the dynamic properties of disease spreading on finite size networks. Our results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks. Also, knowledge about the dynamic character of virus spreading is helpful for adopting immunity policy.

Distribution of large-scale detachment faults on mid-ocean ridges in relation to spreading rates

Large-scale detachment faults on mid-ocean ridges （MORs） provide a window into the deeper earth. They have megamullion on their corrugated surfaces, with exposed lower crustal and upper mantle rocks, rela- tively high residual Bouguer gravity anomaly and P-wave velocity, and are commonly associated with ocean- ic core complex. According to 30 detachment faults identified on MORs, we found that their distances to the axis mostly range from 5 to 50 km, half-spreading rates range from 6.8 to 17 mm/a, and activity time ranges from recent to 3 Ma. Most of the detachment faults are developed on the slow spreading Mid-Atlantic Ridge （MAR） and ultra-slow spreading Southwest Indian Ridge （SWIRl, with the dominant half-spreading rates of 7-13 mm/a, especially 10-13 mm/a. Furthermore, they mostly occur at the inside corner of one segment end and result in an asymmetric seafloor spreading. The detachment faults on MORs are mainly controlled by the tectonism and influenced by the magmatism. Long-lived detachment faults tend to be formed where the ridge magma supply is at a moderate level, although the tectonism is a first-order controlling factor. At the slow spreading ridges, detachment faults tend to occur where local magma supply is relatively low, whilst at the ultra-slow spreading ridges, they normally occur where local magma supply is relatively high. These faults are accompanied by hydrothermal activities, with their relationships being useful in the study of hydrothermal polymetallic sulfides and their origin.

Effect of incubation period on epidemic spreading in complex networks

We study the effect of incubation period on epidemic spreading in the Barabasi-Albert scale-free network and the Watts-Strogatz small world network by using a Suspectable-Incubated-Infected-Suspectable model. Our analytical investigations show that the epidemic threshold is independent of incubation period in both networks, which is verified by our large-scale simulation results. We also investigate the effect of incubation period on the epidemic dynamics in a supercritical regime. It is found that with the increase of incubation period Ω, a damped oscillation evolution of ρT （the ratio of persons in incubated state） appears and the time needed to reach a saturation value increases. Moreover, the steady value of ρT increases and approaches to an asymptotic constant with the value of Ω increasing. As a result, the infected ratio ρI decreases with the increase of Ω according to a power law.

The Analysis of an SIRS Epidemic Model with Discrete Delay on Scale-Free Network

A new epidemic SIRS model with discrete delay on scale-free network is presented. We give the formula of the basic reproductive number for the model and prove that the disease dies out when the basic reproductive number is less than unity, while the disease is uniformly persistent when the basic reproductive number is more than unity. Numerical simulations are given to demonstrate the main results.

Modelling the spread of sexually transmitted diseases on scale-free networks

In this paper a new model for the spread of sexually transmitted diseases （STDs） is presented. The dynamic behaviors of the model on a heterogenons scale-free （SF） network are considered, where the absence of a threshold on the SF network is demonstrated, and the stability of the disease-free equilibrium is obtained. Three immunization strategies, uniform immunization, proportional immunization and targeted immunization, are applied in this model. Analytical and simulated results are given to show that the proportional immunization strategy in the model is effective on SF networks.

Epidemic spreading on random surfer networks with infected avoidance strategy

In this paper, we study epidemic spreading on random surfer networks with infected avoidance （IA） strategy. In particular, we consider that susceptible individuals＇ moving direction angles are affected by the current location information received from infected individuals through a directed information network. The model is mainly analyzed by discrete-time numerical simulations. The results indicate that the IA strategy can restrain epidemic spreading effectively. However, when long-distance jumps of individuals exist, the IA strategy＇s effectiveness on restraining epidemic spreading is heavily reduced. Finally, it is found that the influence of the noises from information transferring process on epidemic spreading is indistinctive.

Spreading behavior of SIS epidemic model on networks with dynamical topology

Based on the two-dimensional regular lattice,a modified SIS(Susceptible-Infected-Susceptible)epidemic model with motion rules is presented to study the spreading behavior on networks with dynamical topology.The mean-field theory is utilized to analyze the critical threshold(λc)of epidemic spreading under the randomly mixing conditions.It is found that λc is only related with the population density within the lattice.Large-scale numerical simulations are carried out to verify the mean-field results,and it is observed that the long-range probability p largely affects the epidemic spreading behavior.In addition,the effect of the dual time scales on epidemic spreading is also investigated by the simulations,and it is shown that the dual time scales accelerate the dynamic spreading behavior.The results indicate that the model with motion can help us to further understand the real epidemics.

Traffic-driven epidemic spreading and its control strategies

Many epidemics or viruses in real life spread by taking advantage of other dynamic processes, e.g., the computer virus propagates with the transmission of packets. In this paper, we survey the recent progress in the study of Traffic-Driven Epidemic Spreading (TDES) on complex networks. First, we introduce several typical TDES models. Then, we analyze the key factors which have significant impact on the epidemic threshold, such as the traffic congestion and routing protocols. Furthermore, we discuss the control of the TDES by focusing on the network structure optimization and the immunization strategies. Finally, we put some issues that need to be further explored in the future.

Hereditary Immunity and the Origin of Atherosclerosis

This paper tries to present new confirmation for the opinion about the infectious origin of atherosclerosis from the viewpoint of the current knowledge of hereditary immunity. The performed integrative investigation included the reinterpretation of known clinical and epidemiological observations, supported by immunological, molecular ecological, genetic, and genomic discoveries. The revealed body of firstly achieved information is compatible with the concept that infectious agents contribute the clue step to the development of atherosclerosis over its initial stage performed during the triggering of the arterial endothelial wall by the molecular agent of proposed infectious origin.

A cellular automata model of epidemics of a heterogeneous susceptibility

In this paper we present a model with spatial heterogeneity based on cellular automata （CA）. In the model we consider the relevant heterogeneity of host （susceptible） mixing and the natural birth rate. We divide the susceptible population into three groups according to the immunity of each individual based on the classical susceptible-infectedremoved （SIR） epidemic models, and consider the spread of an infectious disease transmitted by direct contact among humans and vectors that have not an incubation period to become infectious. We test the local stability and instability of the disease-free equilibrium by the spectrum radii of Jacobian. The simulation shows that the structure of the nearest neighbour size of the cell （or the degree of the scale-free networks） plays a very important role in the spread properties of infectious disease. The positive equilibrium of the infections versus the neighbour size follows the third power law if an endemic equilibrium point exists. Finally, we analyse the feature of the infection waves for the homogeneity and heterogeneous cases respectively.

Global stability of a susceptible-infected-susceptible epidemic model on networks with individual awareness

Recent research results indicate that individual awareness can play an important influence on epidemic spreading in networks. By local stability analysis, a significant conclusion is that the embedded awareness in an epidemic network can increase its epidemic threshold. In this paper, by using limit theory and dynamical system theory, we further give global stability analysis of a susceptible-infected-susceptible （SIS） epidemic model on networks with awareness. Results show that the obtained epidemic threshold is also a global stability condition for its endemic equilibrium, which implies the embedded awareness can enhance the epidemic threshold globally. Some numerical examples are presented to verify the theoretical results.

Epidemic Propagation: An Automaton Model as the Continuous SIR Model

The use of the SIR model to predict the time evolution of an epidemic is very frequent and has spatial information about its propagation which may be very useful to contrast its spread. In this paper we take a particular cellular automaton model that well reproduces the time evolution of the disease given by the SIR model;setting the automaton is generally an annoying problem because we need to run a lot of simulations, compare them to the solution of the SIR model and, finally, decide the parameters to use. In order to make this procedure easier, we will show a fast method that, in input, requires the parameters of the SIR continuous model that we want to reproduce, whereas, in output, it yields the parameters to use in the cellular automaton model. The problem of computing the most suitable parameters for the reticular model is reduced to the problem of finding the roots of a polynomial Equation.