Epidemic Spreading Model Research Articles

Dynamics based on analysis of public data for spreading of disease

The stochastic model for epidemic spreading of the novel coronavirus disease based on the data set supply by the public health agencies in countries as Brazil, United States and India is investigated. We perform a numerical analysis using the stochastic differential equation in Itô’s calculus for the estimating of novel cases daily, as well as analytical calculations solving the correspondent Fokker–Planck equation for the probability density distribution of novel cases, P(N(t), t). Our results display that the model based in the Itô’s diffusion fits well to the results due to uncertainty in the official data and to the number of tests realized in populations of each country.

Immune amnesia induced by measles and its effects on concurrent epidemics.

It has been recently discovered that the measles virus can damage pre-existing immunological memory, destroying B lymphocytes and reducing the diversity of non-specific B cells of the infected host. In particular, this implies that previously acquired immunization from vaccination or direct exposition to other pathogens could be partially erased in a phenomenon named ‘immune amnesia’, whose effects can become particularly worrisome given the actual rise of anti-vaccination movements. Here, we present the first attempt to incorporate immune amnesia into standard models of epidemic spreading by proposing a simple model for the spreading of two concurrent pathogens causing measles and another generic disease. Different analyses confirm that immune amnesia can have important consequences for epidemic spreading, significantly altering the vaccination coverage required to reach herd immunity. We also uncover the existence of novel propagating and endemic phases induced by immune amnesia. Finally, we discuss the meaning and consequences of our results and their relation with, e.g. immunization strategies, together with the possibility that explosive types of transitions may emerge, making immune-amnesia effects particularly dramatic. This work opens the door to further developments and analyses of immune-amnesia effects, contributing also to the theory of interacting epidemics on complex networks.

Epidemic spreading with awareness on multi-layer activity-driven networks

Network structure plays an important role in epidemic spreading process. In this paper, we propose a susceptible–alert–infected–susceptible epidemic spreading model based on coupled activity-driven networks. The critical conditions for epidemic outbreaks are analyzed based on the proposed model. The explicit expressions of the critical conditions are obtained, which are determined by the multi-layer activity-driven network structure associated with propagation parameters. We also analyze the influence of network structure and propagation parameters on the epidemic outbreak critical condition, which may shed some lights on the control of the epidemic spreading in future. The correctness of the theoretical results is corroborated by Monte Carlo simulations.

Study of SEIRD Adaptive-Compartmental Model of COVID-19 Epidemic Spread in Russian Federation Using Optimization Methods

A systemic approach to the study of a new multi-parameter model of the COVID-19 pandemic spread is proposed, which has the ultimate goal of optimizing the manage parameters of the model. The approach consists of two main parts: 1) an adaptive-compartmental model of the epidemic spread, which is a generalization of the classical SEIR model, and 2) a module for adjusting the parameters of this model from the epidemic data using intelligent optimization methods. Data for testing the proposed approach using the pandemic spread in some regions of the Russian Federation were collected on a daily basis from open sources during the first 130 days of the epidemic, starting in March 2020. For this, a so-called data farm was developed and implemented on a local server (an automated system for collecting, storing and preprocessing data from heterogeneous sources, which, in combination with optimization methods, allows most accurately tune the parameters of the model, thus turning it into an intelligent system to support management decisions). Among all model parameters used, the most important are the rate of infection transmission, the government actions and the population reaction.

A Low-Dimensional Network Model for an SIS Epidemic: Analysis of the Super Compact Pairwise Model

Network-based models of epidemic spread have become increasingly popular in recent decades. Despite a rich foundation of such models, few low-dimensional systems for modeling SIS-type diseases have been proposed that manage to capture the complex dynamics induced by the network structure. We analyze one recently introduced model and derive important epidemiological quantities for the system. We derive the epidemic threshold and analyze the bifurcation that occurs, and we use asymptotic techniques to derive an approximation for the endemic equilibrium when it exists. We consider the sensitivity of this approximation to network parameters, and the implications for disease control measures are found to be in line with the results of existing studies.

Modeling indoor-level non-pharmaceutical interventions during the COVID-19 pandemic: A pedestrian dynamics-based microscopic simulation approach

Mathematical modeling of epidemic spreading has been widely adopted to estimate the threats of epidemic diseases (i.e., the COVID-19 pandemic) as well as to evaluate epidemic control interventions. The indoor place is considered to be a significant epidemic spreading risk origin, but existing widely-used epidemic spreading models are usually limited for indoor places since the dynamic physical distance changes between people are ignored, and the empirical features of the essential and non-essential travel are not differentiated. In this paper, we introduce a pedestrian-based epidemic spreading model that is capable of modeling indoor transmission risks of diseases during people's social activities. Taking advantage of the before-and-after mobility data from the University of Maryland COVID-19 Impact Analysis Platform, it's found that people tend to spend more time in grocery stores once their travel frequencies are restricted to a low level. In other words, an increase in dwell time could balance the decrease in travel frequencies and satisfy people's demands. Based on the pedestrian-based model and the empirical evidence, combined non-pharmaceutical interventions from different operational levels are evaluated. Numerical simulations show that restrictions on people's travel frequency and open hours of indoor places may not be universally effective in reducing average infection risks for each pedestrian who visit the place. Entry limitations can be a widely effective alternative, whereas the decision-maker needs to balance the decrease in risky contacts and the increase in queue length outside the place that may impede people from fulfilling their travel needs. The results show that a good coordination among the decision-makers can contribute to the improvement of the performance of combined non-pharmaceutical interventions, and it also benefits the short-term and long-term interventions in the future.

Dynamics Analysis of a Wireless Rechargeable Sensor Network for Virus Mutation Spreading.

Virus spreading problems in wireless rechargeable sensor networks (WSNs) are becoming a hot topic, and the problem has been studied and discussed in recent years. Many epidemic spreading models have been introduced for revealing how a virus spreads and how a virus is suppressed. However, most of them assumed the sensors are not rechargeable sensors. In addition, most of existing works do not consider virus mutation problems. This paper proposes a novel epidemic model, including susceptible, infected, variant, low-energy and dead states, which considers the rechargeable sensors and the virus mutation factor. The stability of the proposed model is first analyzed by adopting the characteristic equation and constructing Lyapunov functions methods. Then, an optimal control problem is formulated to control the virus spread and decrease the cost of the networks by applying Pontryagin’s maximum principle. Finally, all of the theoretical results are confirmed by numerical simulation.

Chase-Escape percolation on the 2D square lattice

Chase-escape percolation is a variation of the standard epidemic spread models. In this model, each site can be in one of three states: unoccupied, occupied by a single prey, or occupied by a single predator. Prey particles spread to neighboring empty sites at rate p, and predator particles spread only to neighboring sites occupied by prey particles at rate 1, killing the prey particle that existed at that site. It was found that the prey can survive forever with non-zero probability, if p>pc with pc<1. Earlier simulations showed that pc is very close to 1∕2. Using Monte Carlo simulations in D=2, we estimate the value of pc to be 0.49451±0.00001 and the critical exponents are consistent with the undirected percolation universality class. We check that at pc, the correlation functions at large length scales are rotationally invariant. We define a discrete-time parallel-update version of the model, which brings out the relation between chase-escape and undirected bond percolation. We further show that for all p<pc, in D dimensions, the probability that the number of predators in the absorbing configuration is greater than s is bounded from below by exp(−Kp−1s1∕D), where K is some p-independent constant. This is in contrast to the exponentially decaying cluster size distribution in the standard percolation theory. Even so, the scaling function for the cluster size distribution for p near pc decays exponentially: the stretched exponential behavior dominates for s≫s∗, but s∗ diverges near pc. We also study the problem starting from an initial condition with predator particles on all lattice points of the line y=0 and prey particles on the line y=1. In this case, for pc<p<1, the center of mass of the fluctuating prey and predator fronts travel at the same speed. This speed is strictly smaller than the speed of an Eden front with the same value of p, but with no predators. This is caused by the prey sites at the leading edge being eaten up by predators. The fluctuations of the front follow KPZ scaling both above and below the depinning transition at p=1.

Detection of Xylella fastidiosa in almond orchards by synergic use of an epidemic spread model and remotely sensed plant traits

The early detection of Xylella fastidiosa (Xf) infections is critical to the management of this dangerous plan pathogen across the world. Recent studies with remote sensing (RS) sensors at different scales have shown that Xf-infected olive trees have distinct spectral features in the visible and infrared regions (VNIR). However, further work is needed to integrate remote sensing in the management of plant disease epidemics. Here, we research how the spectral changes picked up by different sets of RS plant traits (i.e., pigments, structural or leaf protein content), can help capture the spatial dynamics of Xf spread. We coupled a spatial spread model with the probability of Xf-infection predicted by a RS-driven support vector machine (RS-SVM) model. Furthermore, we analyzed which RS plant traits contribute most to the output of the prediction models. For that, in almond orchards affected by Xf (n = 1426 trees), we conducted a field campaign simultaneously with an airborne campaign to collect high-resolution thermal images and hyperspectral images in the visible-near-infrared (VNIR, 400–850 nm) and short-wave infrared regions (SWIR, 950–1700 nm). The best performing RS-SVM model (OA = 75%; kappa = 0.50) included as predictors leaf protein content, nitrogen indices (NIs), fluorescence and a thermal indicator (Tc), alongside pigments and structural parameters. Leaf protein content together with NIs contributed 28% to the explanatory power of the model, followed by chlorophyll (22%), structural parameters (LAI and LIDFa), and chlorophyll indicators of photosynthetic efficiency. Coupling the RS model with an epidemic spread model increased the accuracy (OA = 80%; kappa = 0.48). In the almond trees where the presence of Xf was assayed by qPCR (n = 318 trees), the combined RS-spread model yielded an OA of 71% and kappa = 0.33, which is higher than the RS-only model and visual inspections (both OA = 64–65% and kappa = 0.26–31). Our work demonstrates how combining spatial epidemiological models and remote sensing can lead to highly accurate predictions of plant disease spatial distribution.

Employing Fuzzy Logic to Analyze the Structure of Complex Biological and Epidemic Spreading Models

Complex networks constitute a new field of scientific research that is derived from the observation and analysis of real-world networks, for example, biological, computer and social ones. An important subset of complex networks is the biological, which deals with the numerical examination of connections/associations among different nodes, namely interfaces. These interfaces are evolutionary and physiological, where network epidemic models or even neural networks can be considered as representative examples. The investigation of the corresponding biological networks along with the study of human diseases has resulted in an examination of networks regarding medical supplies. This examination aims at a more profound understanding of concrete networks. Fuzzy logic is considered one of the most powerful mathematical tools for dealing with imprecision, uncertainties and partial truth. It was developed to consider partial truth values, between completely true and completely false, and aims to provide robust and low-cost solutions to real-world problems. In this manuscript, we introduce a fuzzy implementation of epidemic models regarding the Human Immunodeficiency Virus (HIV) spreading in a sample of needle drug individuals. Various fuzzy scenarios for a different number of users and different number of HIV test samples per year are analyzed in order for the samples used in the experiments to vary from case to case. To the best of our knowledge, analyzing HIV spreading with fuzzy-based simulation scenarios is a research topic that has not been particularly investigated in the literature. The simulation results of the considered scenarios demonstrate that the existence of fuzziness plays an important role in the model setup process as well as in analyzing the effects of the disease spread.

Coupled Dynamic Model of Resource Diffusion and Epidemic Spreading in Time-Varying Multiplex Networks

In the real world, individual resources are crucial for patients when epidemics outbreak. Thus, the coupled dynamics of resource diffusion and epidemic spreading have been widely investigated when the recovery of diseases significantly depends on the resources from neighbors in static social networks. However, the social relationships of individuals are time-varying, which affects such coupled dynamics. For that, we propose a coupled resource-epidemic (RNR-SIS) dynamic model (coupled model for short) on a time-varying multiplex network to synchronously simulate the resource diffusion and epidemic spreading in dynamic social networks. The equilibrium analysis of the coupled model is conducted in a general scenario where the resource generation varies between susceptible and infected states and the recovery rate changes between resourceful and noresource states. By using the microscopic Markov chain approach and Monte Carlo simulations, we determine a probabilistic framework of the intralayer and interlayer dynamic processes of the coupled model and obtain the outbreak threshold of epidemic spreading. Meanwhile, the experimental results show the trivially asymmetric interactions between resource diffusion and epidemic spreading. They also indicate that the stronger activity heterogeneity and the larger contact capacity of individuals in the resource layer can more greatly promote resource diffusion, effectively suppressing epidemic spreading. However, these two individual characters in the epidemic layer can cause more resource depletion, which greatly promotes epidemic spreading. Furthermore, we also find that the contact capacity finitely impacts the coupled dynamics of resource diffusion and epidemic spreading.

Prediction and control of COVID-19 spreading based on a hybrid intelligent model.

The coronavirus (COVID-19) is a highly infectious disease that emerged in the late December 2019 in Wuhan, China. It caused a worldwide outbreak and a major threat to global health. It is important to design prediction and control strategies to restrain its exploding. In this study, a hybrid intelligent model is proposed to simulate the spreading of COVID-19. First, considering the effect of control measures, such as government investment, media publicity, medical treatment, and law enforcement in epidemic spreading. Then, the infection rates are optimized by genetic algorithm (GA) and a modified susceptible-infected-quarantined-recovered (SIQR) epidemic spreading model is proposed. In addition, the long short-term memory (LSTM) is imbedded into the SIQR model to design the hybrid intelligent model to further optimize other parameters of the system model, which can obtain the optimal predictive model and control measures. Simulation results show that the proposed hybrid intelligence algorithm has good predictive ability. This study provide a reliable model to predict cases of infection and death, and reasonable suggestion to control COVID-19.

COVID-19 Outbreak: Model-Driven Impact Analysis Comparing Oman and Pakistan

Motivated by the rapid spread of COVID-19 all across the globe, we haveperformed simulations of a system dynamic epidemic spread model in differentpossible situations. The simulation, not only captures the model dynamic of thespread of the virus, but also, takes care of population and mobility data. Themodel is calibrated based on epidemic data and events as they happened. Thesimulation results are quite disturbing, indicating that, during a process of stringent social distancing and testing strategies, a small perturbation can lead toquite undesirable outcomes. The simulation results, although consistent in expected outcomes across changing parameters’ values, also indicate a substantialmismatch with real numbers. An analysis of what can be the reason of this mismatch is also performed. Within these contradictions, a comparative analysisof COVID-19 outbreak between two geographically close but demographicallyvery different countries – that is Oman and Pakistan – is performed.

A Markovian random walk model of epidemic spreading.

We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time Markovian walk governed by his specific transition matrix. With this assumption, we first derive an upper bound for the reproduction numbers. Then, we assume that a walker is in one of the states: susceptible, infectious, or recovered. An infectious walker remains infectious during a certain characteristic time. If an infectious walker meets a susceptible one on the same node, there is a certain probability for the susceptible walker to get infected. By implementing this hypothesis in computer simulations, we study the space-time evolution of the emerging infection patterns. Generally, random walk approaches seem to have a large potential to study epidemic spreading and to identify the pertinent parameters in epidemic dynamics.

Dynamics of cascades on burstiness-controlled temporal networks

Burstiness, the tendency of interaction events to be heterogeneously distributed in time, is critical to information diffusion in physical and social systems. However, an analytical framework capturing the effect of burstiness on generic dynamics is lacking. Here we develop a master equation formalism to study cascades on temporal networks with burstiness modelled by renewal processes. Supported by numerical and data-driven simulations, we describe the interplay between heterogeneous temporal interactions and models of threshold-driven and epidemic spreading. We find that increasing interevent time variance can both accelerate and decelerate spreading for threshold models, but can only decelerate epidemic spreading. When accounting for the skewness of different interevent time distributions, spreading times collapse onto a universal curve. Our framework uncovers a deep yet subtle connection between generic diffusion mechanisms and underlying temporal network structures that impacts a broad class of networked phenomena, from spin interactions to epidemic contagion and language dynamics.

Modeling epidemic spread in transportation networks: A review

The emergence of novel infectious diseases has become a serious global problem. Convenient transportation networks lead to rapid mobilization in the context of globalization, which is an important factor underlying the rapid spread of infectious diseases. Transportation systems can cause the transmission of viruses during the epidemic period, but they also support the reopening of economies after the epidemic. Understanding the mechanism of the impact of mobility on the spread of infectious diseases is thus important, as is establishing the risk model of the spread of infectious diseases in transportation networks. In this study, the basic structure and application of various epidemic spread models are reviewed, including mathematical models, statistical models, network-based models, and simulation models. The advantages and limitations of model applications within transportation systems are analyzed, including dynamic characteristics of epidemic transmission and decision supports for management and control. Lastly, research trends and prospects are discussed. It is suggested that there is a need for more in-depth research to examine the mutual feedback mechanism of epidemics and individual behavior, as well as the proposal and evaluation of intervention measures. The findings in this study can help evaluate disease intervention strategies, provide decision supports for transport policy during the epidemic period, and ameliorate the deficiencies of the existing system.

The Prediction of COVID-19 Using LSTM Algorithms

As COVID-19 enters the pandemic stage, the resulting infections, deaths and economic shocks are emerging. To minimize anxiety and uncertainty about socio-economic damage caused by the COVID-19 pandemic, it is necessary to reasonably predict the economic impact of future disease trends by scientific means. Based on previous cases of epidemic (such as influenza) and economic trends, this study has established an epidemic disease spread model and economic situation prediction model. Based on this model, the author also predict the economic impact of future COVID-19 spread. The results of this study are as follows. First, the deep learning-based economic impact prediction model, which was built based on historical infectious disease data, was verified with verification data to ensure 77% accuracy in predicting inflation rates. Second, based on the economic impact prediction model of the deep learning-based infectious disease, the author presented the COVID-19 trend and future economic impact prediction results for the next 1 year. Currently, most of the published studies on COVID-19 are on the prediction of disease spread by statistical mathematical calculations. This study is expected to be used as an empirical reference to efficient and preemptive decision making by predicting the spread of diseases and economic conditions related to COVID-19 using deep learning technology and historical infectious disease data.

Analysis, Prediction, and Control of Epidemics: A Survey from Scalar to Dynamic Network Models

During the ongoing COVID-19 pandemic, mathematical models of epidemic spreading have emerged as powerful tools to produce valuable predictions of the evolution of the pandemic, helping public health authorities decide which intervention policies should be implemented. The study of these models -- grounded in the systems theory and often analyzed using control-theoretic tools -- is an extremely important research area for many researchers from different fields, including epidemiology, engineering, physics, mathematics, computer science, sociology, economics, and management. In this survey, we review the history and present the state of the art in the modeling, analysis, and control of epidemic dynamics. We discuss different approaches to epidemic modeling, either deterministic or stochastic, ranging from the first implementations of scalar systems of differential equations to describing the epidemic spreading at the population level, and to more recent models on dynamic networks, which capture the spatial spread and the time-varying nature of human interactions.

ҚАРАҒАНДЫ ОБЛЫСЫНЫҢ МЫСАЛЫНДА ТУБЕРКУЛЕЗ ІНДЕТІН АҚПАРАТТЫҚ МОДЕЛЬДЕУ ЖҮЙЕСІН ҚОЛДАНУ

Zonation of the territory of Karaganda region (Central Kazakhstan) on the level of tuberculosis incidence has not been carried out so far. The long-term dynamics of tuberculosis incidence in Karaganda region in the context of its districts was studied. Choice of mathematical model of epidemic spread. The optimization problem is solved with the help of stochastic method: genetic algorithm. Epidemic modeling in the information system. Building maps. Approbation of the information system model on the basis of officially available statistical data.

Spatiotemporal imaging phenotypes of tau pathology in Alzheimer’s disease

AbstractBackgroundThe Braak staging scheme describes a stereotypical spread of tau pathology in Alzheimer’s disease (AD). However, apparent subtypes described at autopsy and clinical variants of AD both suggest variability in the pattern of tau spreading across the population. To address this discrepancy, we applied a validated spatiotemporal clustering algorithm to a large, multisite dataset of tau‐PET images. We verified these findings both longitudinally and on a separate tau‐PET dataset using a different radiotracer, and we characterized the phenotype and potential biological determinants of each subtype.MethodSubtype and Stage Inference (SuStaIn, Young et al., 2018 ) is a data‐driven, probabilistic algorithm that combines disease progression modeling with clustering to extract distinct spatiotemporal patterns (subtypes) from large cross‐sectional datasets. We applied SuStaIn to a multisite dataset (n=1143) of [18F]‐flortaucipir tau‐PET baseline scans to identify spatiotemporal subtypes of tau spreading. We investigated differences in demographic, cognitive and genetic measures. In a subsample of individuals with multiple tau‐PET scans over time (n=536), we tested longitudinal subtype stability and change in disease stage over time. We verified these subtypes in a second single‐site dataset (n=509) of [18F]‐RO948 tau‐PET scans. Finally we used the Epidemic Spreading Model (ESM, Iturria‐Medina et al., 2014) and imaging or transcriptomic analysis to determine if anatomical brain networks or specific cell‐types, respectively, could explain the differing spatial patterns across subtypes.ResultIn those subjects with significant tau‐PET signal in the brain, SuStaIn identified four spatiotemporal subtypes of tau‐PET spreading: Typical (worse memory, more APOE4 carriers), limbic‐sparing (younger, less APOE4 carriers), posterior (worse visuospatial cognition), and lateral‐temporal (worse language and executive function scores; Fig 1A, Fig 2). These same four subtypes were observed in a separate cohort using a different radiotracer (similarity 0.7–0.9; Fig 1B). 86% of subjects exhibited the same subtype at multiple visits (Fig 1C), and of that group, 83% advanced in disease stage or remained stable within model uncertainty. The ESM suggested different epicenters for each subtype, and each subtype pattern exhibited a different profile of cell‐type enrichment (Fig 3).ConclusionFour stable tau‐spreading phenotypes were observed with distinct cognitive profiles, which may be characterized by vulnerability of different corticolimbic networks involving distinct cell classes.