Susceptible-infected-removed Research Articles

Brownian snails with removal: epidemics in diffusing populations

Two stochastic models of susceptible/infected/removed (SIR) type are introduced for the spread of infection through a spatially-distributed population. Individuals are initially distributed at random in space, and they move continuously according to independent diffusion processes. The disease may pass from an infected individual to an uninfected individual when they are sufficiently close. Infected individuals are permanently removed at some given rate $\alpha$. Such processes are reminiscent of so-called frog models, but differ through the action of removal, as well as the fact that frogs jump whereas snails slither. Two models are studied here, termed the `delayed diffusion' and the `diffusion' models. In the first, individuals are stationary until they are infected, at which time they begin to move; in the second, all individuals start to move at the initial time $0$. Using a perturbative argument, conditions are established under which the disease infects a.s. only finitely many individuals. It is proved for the delayed diffusion model that there exists a critical value $\alpha_c\in(0,\infty)$ for the survival of the epidemic.

Numerical Assessments Employing Neural Networks for a Novel Drafted Anti-Virus Subcategory in a Nonlinear Fractional-Order SIR Differential System

Whereas computer viruses (CVs) are a terrible threat to individual and corporate computer structures. A considerable attempt has been made to research ways to prevent their negative consequences, to develop anti-virus software that behave as vaccines in desktop computers or strategic network nodes. A further method for combating viral transmission is to develop preventative strategies associated with a given performance of a network that may be described using population models compared to the few employed with epidemiological analyses. An updated variation of such SIR (Susceptible-Infected-Removed) framework is offered here, along with an explanation of whether these parameters correspond to network properties. The novel formed SAIR model is then numerically treated, employing the qualities of stochastic procedure-based numerical computation approaches that use neural networks (NNs). In this research study, we suggest novel fractional-order SAIR (FO-SAIR) differential model that has not previously been published. This study’s aim appeared to be to demonstrate the effects and applicability of such FO-SAIR differential scheme. An FO-SAIR problem is examined using stochastic solvers relyed upon Levenberg-Marquardt backpropagation approach (L-MB) and NNs, specifically L-MBNNs. For solve the FO-SAIR system, three examples with different values under the same fractional order are presented. The statistical methods used to generate numerical answers for the FO-SAIR system are categorised thus obeys: 75% for training, 13% for testing, and 12% for permission. By using Adams-Bashforth-Moulton, the numerical results were contrasted with the reference solutions to determine the accuracy of such L-MBNNs. To confirm overall capability, competence, validity, consistency, and exactness, the numerical performances of these L-MBNNs using error histograms (EHs), state transitions (STs), regression, correlation, and mean square error (MSE) are also shown.

Pathogen.jl: Infectious Disease Transmission Network Modeling with Julia

We introduce Pathogen.jl for simulation and inference of transmission network individual level models (TN-ILMs) of infectious disease spread in continuous time. TN-ILMs can be used to jointly infer transmission networks, event times, and model parameters within a Bayesian framework via Markov chain Monte Carlo (MCMC). We detail our specific strategies for conducting MCMC for TN-ILMs, and our implementation of these strategies in the Julia package, Pathogen.jl, which leverages key features of the Julia language. We provide an example using Pathogen.jl to simulate an epidemic following a susceptible-infectious-removed (SIR) TN-ILM, and then perform inference using observations that were generated from that epidemic. We also demonstrate the functionality of Pathogen.jl with an application of TN-ILMs to data from a measles outbreak that occurred in Hagelloch, Germany, in 1861 (Pfeilsticker 1863; Oesterle 1992).

Differentially targeted seeding reveals unique pathological alpha-synuclein propagation patterns.

Parkinson’s disease is a progressive neurodegenerative disorder characterized by the intracellular accumulation of insoluble alpha-synuclein aggregates into Lewy bodies and neurites. Increasing evidence indicates that Parkinson’s disease progression results from the spread of pathologic alpha-synuclein through neuronal networks. However, the exact mechanisms underlying the propagation of abnormal proteins in the brain are only partially understood. The objective of this study was first to describe the long-term spatiotemporal distributions of Lewy-related pathology in mice injected with alpha-synuclein preformed fibrils and then to recreate these patterns using a computational model that simulates in silico the spread of pathologic alpha-synuclein.In this study, 87 2–3-month-old non-transgenic mice were injected with alpha-synuclein preformed fibrils to generate a comprehensive post-mortem dataset representing the long-term spatiotemporal distributions of hyperphosphorylated alpha-synuclein, an established marker of Lewy pathology, across the 426 regions of the Allen Mouse Brain Atlas. The mice were injected into either the caudoputamen, nucleus accumbens or hippocampus, and followed over 24 months with pathologic alpha-synuclein quantified at seven intermediate time points. The pathologic patterns observed at each time point in this high-resolution dataset were then compared to those generated using a Susceptible-Infected-Removed (SIR) computational model, an agent-based model that simulates the spread of pathologic alpha-synuclein for every brain region taking simultaneously into account the effect of regional brain connectivity and Snca gene expression.Our histopathological findings showed that differentially targeted seeding of pathological alpha-synuclein resulted in unique propagation patterns over 24 months and that most brain regions were permissive to pathology. We found that the SIR model recreated the observed distributions of pathology over 24 months for each injection site. Null models showed that both Snca gene expression and connectivity had a significant influence on model fit.In sum, our study demonstrates that the combination of normal alpha-synuclein concentration and brain connectomics contributes to making brain regions more vulnerable to the pathological process, providing support for a prion-like spread of pathologic alpha-synuclein. We propose that this rich dataset and the related computational model will help test new hypotheses regarding mechanisms that may alter the spread of pathologic alpha-synuclein in the brain.

A single-agent extension of the SIR model describes the impact of mobility restrictions on the COVID-19 epidemic

Mobility restrictions are successfully used to contain the diffusion of epidemics. In this work we explore their effect on the epidemic growth by investigating an extension of the Susceptible-Infected-Removed (SIR) model in which individual mobility is taken into account. In the model individual agents move on a chessboard with a Lévy walk and, within each square, epidemic spreading follows the standard SIR model. These simple rules allow to reproduce the sub-exponential growth of the epidemic evolution observed during the Covid-19 epidemic waves in several countries and which cannot be captured by the standard SIR model. We show that we can tune the slowing-down of the epidemic spreading by changing the dynamics of the agents from Lévy to Brownian and we investigate how the interplay among different containment strategies mitigate the epidemic spreading. Finally we demonstrate that we can reproduce the epidemic evolution of the first and second COVID-19 waves in Italy using only 3 parameters, i.e , the infection rate, the removing rate, and the mobility in the country. We provide an estimate of the peak reduction due to imposed mobility restrictions, i. e., the so-called flattening the curve effect. Although based on few ingredients, the model captures the kinetic of the epidemic waves, returning mobility values that are consistent with a lock-down intervention during the first wave and milder limitations, associated to a weaker peak reduction, during the second wave.

When and why direct transmission models can be used for environmentally persistent pathogens.

Variants of the susceptible-infected-removed (SIR) model of Kermack & McKendrick (1927) enjoy wide application in epidemiology, offering simple yet powerful inferential and predictive tools in the study of diverse infectious diseases across human, animal and plant populations. Direct transmission models (DTM) are a subset of these that treat the processes of disease transmission as comprising a series of discrete instantaneous events. Infections transmitted indirectly by persistent environmental pathogens, however, are examples where a DTM description might fail and are perhaps better described by models that comprise explicit environmental transmission routes, so-called environmental transmission models (ETM). In this paper we discuss the stochastic susceptible-exposed-infected-removed (SEIR) DTM and susceptible-exposed-infected-removed-pathogen (SEIR-P) ETM and we show that the former is the timescale separation limit of the latter, with ETM host-disease dynamics increasingly resembling those of a DTM when the pathogen’s characteristic timescale is shortened, relative to that of the host population. Using graphical posterior predictive checks (GPPC), we investigate the validity of the SEIR model when fitted to simulated SEIR-P host infection and removal times. Such analyses demonstrate how, in many cases, the SEIR model is robust to departure from direct transmission. Finally, we present a case study of white spot disease (WSD) in penaeid shrimp with rates of environmental transmission and pathogen decay (SEIR-P model parameters) estimated using published results of experiments. Using SEIR and SEIR-P simulations of a hypothetical WSD outbreak management scenario, we demonstrate how relative shortening of the pathogen timescale comes about in practice. With atttempts to remove diseased shrimp from the population every 24h, we see SEIR and SEIR-P model outputs closely conincide. However, when removals are 6-hourly, the two models’ mean outputs diverge, with distinct predictions of outbreak size and duration.

The non-linear impact of data handling on network diffusion models

SummaryMany computational models rely on real-world data, and the steps required in moving from data collection, to data preparation, to model calibration, and input are becoming increasingly complex. Errors in data can lead to errors in model output that might invalidate conclusions in extreme cases. While the challenge of errors in data collection have been analyzed in the literature, here we highlight the importance of data handling in the modeling and simulation process, and how particular data handling errors can lead to errors in model output. We develop a framework for assessing the impact of potential data errors for models of spreading processes on networks, a broad class of models that capture many important real-world phenomena (e.g., epidemics, rumor spread, etc.). We focus on the susceptible-infected-removed (SIR) and Threshold models and examine how systematic errors in data handling impact the predicted spread of a virus (or information). Our results demonstrate that data handling errors can have significant impact on model conclusions especially in critical regions of a system.

Modeling the effect of the vaccination campaign on the COVID-19 pandemic

Population-wide vaccination is critical for containing the SARS-CoV-2 (COVID-19) pandemic when combined with restrictive and prevention measures. In this study we introduce SAIVR, a mathematical model able to forecast the COVID-19 epidemic evolution during the vaccination campaign. SAIVR extends the widely used Susceptible-Infectious-Removed (SIR) model by considering the Asymptomatic (A) and Vaccinated (V) compartments. The model contains several parameters and initial conditions that are estimated by employing a semi-supervised machine learning procedure. After training an unsupervised neural network to solve the SAIVR differential equations, a supervised framework then estimates the optimal conditions and parameters that best fit recent infectious curves of 27 countries. Instructed by these results, we performed an extensive study on the temporal evolution of the pandemic under varying values of roll-out daily rates, vaccine efficacy, and a broad range of societal vaccine hesitancy/denial levels. The concept of herd immunity is questioned by studying future scenarios which involve different vaccination efforts and more infectious COVID-19 variants.

Identifiability and predictability of integer- and fractional-order epidemiological models using physics-informed neural networks.

We analyze a plurality of epidemiological models through the lens of physics-informed neural networks (PINNs) that enable us to identify time-dependent parameters and data-driven fractional differential operators. In particular, we consider several variations of the classical susceptible-infectious-removed (SIR) model by introducing more compartments and fractional-order and time-delay models. We report the results for the spread of COVID-19 in New York City, Rhode Island and Michigan states and Italy, by simultaneously inferring the unknown parameters and the unobserved dynamics. For integer-order and time-delay models, we fit the available data by identifying time-dependent parameters, which are represented by neural networks. In contrast, for fractional differential models, we fit the data by determining different time-dependent derivative orders for each compartment, which we represent by neural networks. We investigate the structural and practical identifiability of these unknown functions for different datasets, and quantify the uncertainty associated with neural networks and with control measures in forecasting the pandemic.

Susceptible-Infected-Removed Mathematical Model under Deep Learning in Hospital Infection Control of Novel Coronavirus Pneumonia.

Objective This research aimed to explore the application of a mathematical model based on deep learning in hospital infection control of novel coronavirus (COVID-19) pneumonia. Methods First, the epidemic data of Beijing, China, were utilized to make a definite susceptible-infected-removed (SIR) model fitting to determine the estimated value of the COVID-19 removal intensity β, which was then used to do a determined SIR model and a stochastic SIR model fitting for the hospital. In addition, the reasonable β and γ estimates of the hospital were determined, and the spread of the epidemic in hospital was simulated, to discuss the impact of basal reproductive number changes, isolation, vaccination, and so forth on COVID-19. Results There was a certain gap between the fitting of SIR to the remover and the actual data. The fitting of the number of infections was accurate. The growth rate of the number of infections decreased after measures, such as isolation, were taken. The effect of herd immunity was achieved after the overall immunity reached 70.9%. Conclusion The SIR model based on deep learning and the stochastic SIR fitting model were accurate in judging the development trend of the epidemic, which can provide basis and reference for hospital epidemic infection control.

Prediction System-Based Community Partition for Tuberculosis Outbreak Spread

In this work, our goal is to design and investigate a new simulation system based on detection communities for control and prediction of TB outbreak. The latter is mainly based on four subsystems, namely: Susceptible-Infected-Removed (SIR) system, detection community system, visualization system and prediction system. The SIR including reservoir within Small World (SW) network system is applied to take better advantage of its modeling property and understanding epidemic spread. In order to characterize the influence of communities’ structure, we use Louvain method to identify communities in human complex network. Then, we propose a predictive approach for identifying the hottest outbreak communities based on communities’ detection, as well as mapping areas at risk. Current results show the performance of the proposed system and the important role of detection communities in the process of epidemic spreading and prediction.

Machine learning predictions of COVID-19 second wave end-times in Indian states.

The estimate of the remaining time of an ongoing wave of epidemic spreading is a critical issue. Due to the variations of a wide range of parameters in an epidemic, for simple models such as Susceptible-Infected-Removed (SIR) model, it is difficult to estimate such a time scale. On the other hand, multidimensional data with a large set attributes are precisely what one can use in statistical learning algorithms to make predictions. Here we show, how the predictability of the SIR model changes with various parameters using a supervised learning algorithm. We then estimate the condition in which the model gives the least error in predicting the duration of the first wave of the COVID-19 pandemic in different states in India. Finally, we use the SIR model with the above mentioned optimal conditions to generate a training data set and use it in the supervised learning algorithm to estimate the end-time of the ongoing second wave of the pandemic in different states in India.

Model-based ensembles: Lessons learned from retrospective analysis of COVID-19 infection forecasts across 10 countries

Mathematical models of different types and data intensities are highly used by researchers, epidemiologists, and national authorities to explore the inherently unpredictable progression of COVID-19, including the effects of different non-pharmaceutical interventions. Regardless of model complexity, forecasts of future COVID-19 infections, deaths and hospitalization are associated with large uncertainties, and critically depend on the quality of the training data, and in particular how well the recorded national or regional numbers of infections, deaths and recoveries reflect the the actual situation. In turn, this depends on, e.g., local test and abatement strategies, treatment capacities and available technologies. Other influencing factors including temperature and humidity, which are suggested by several authors to affect the spread of COVID-19 in some countries, are generally only considered by the most complex models and further serve to inflate the uncertainty. Here we use comparative and retrospective analyses to illuminate the aggregated effect of these systematic biases on ensemble-based model forecasts. We compare the actual progression of active infections across ten of the most affected countries in the world until late November 2020 with “re-forecasts” produced by two of the most commonly used model types: (i) a compartment-type, susceptible–infected–removed (SIR) model; and (ii) a statistical (Holt-Winters) time series model. We specifically examine the sensitivity of the model parameters, estimated systematically from different subsets of the data and thereby different time windows, to illustrate the associated implications for short- to medium-term forecasting and for probabilistic projections based on (single) model ensembles as inspired by, e.g., weather forecasting and climate research. Our findings portray considerable variations in forecasting skill in between the ten countries and demonstrate that individual model predictions are highly sensitive to parameter assumptions. Significant skill is generally only confirmed for short-term forecasts (up to a few weeks) with some variation across locations and periods.

On the optimal control of SIR model with Erlang-distributed infectious period: isolation strategies.

Mathematical models are formal and simplified representations of the knowledge related to a phenomenon. In classical epidemic models, a major simplification consists in assuming that the infectious period is exponentially distributed, then implying that the chance of recovery is independent on the time since infection. Here, we first attempt to investigate the consequences of relaxing this assumption on the performances of time-variant disease control strategies by using optimal control theory. In the framework of a basic susceptible–infected–removed (SIR) model, an Erlang distribution of the infectious period is considered and optimal isolation strategies are searched for. The objective functional to be minimized takes into account the cost of the isolation efforts per time unit and the sanitary costs due to the incidence of the epidemic outbreak. Applying the Pontryagin’s minimum principle, we prove that the optimal control problem admits only bang–bang solutions with at most two switches. In particular, the optimal strategy could be postponing the starting intervention time with respect to the beginning of the outbreak. Finally, by means of numerical simulations, we show how the shape of the optimal solutions is affected by the different distributions of the infectious period, by the relative weight of the two cost components, and by the initial conditions.

Dynamic Robustness of Open-Source Project Knowledge Collaborative Network Based on Opinion Leader Identification.

A large amount of semantic content is generated during designer collaboration in open-source projects (OSPs). Based on the characteristics of knowledge collaboration behavior in OSPs, we constructed a directed, weighted, semantic-based knowledge collaborative network. Four social network analysis indexes were created to identify the key opinion leader nodes in the network using the entropy weight and TOPSIS method. Further, three degradation modes were designed for (1) the collaborative behavior of opinion leaders, (2) main knowledge dissemination behavior, and (3) main knowledge contribution behavior. Regarding the degradation model of the collaborative behavior of opinion leaders, we considered the propagation characteristics of opinion leaders to other nodes, and we created a susceptible–infected–removed (SIR) propagation model of the influence of opinion leaders’ behaviors. Finally, based on empirical data from the Local Motors open-source vehicle design community, a dynamic robustness analysis experiment was carried out. The results showed that the robustness of our constructed network varied for different degradation modes: the degradation of the opinion leaders’ collaborative behavior had the lowest robustness; this was followed by the main knowledge dissemination behavior and the main knowledge contribution behavior; the degradation of random behavior had the highest robustness. Our method revealed the influence of the degradation of collaborative behavior of different types of nodes on the robustness of the network. This could be used to formulate the management strategy of the open-source design community, thus promoting the stable development of OSPs.

Retrospective analysis of interventions to epidemics using dynamic simulation of population behavior

Retrospective analyses of interventions to epidemics, in which the effectiveness of strategies implemented are compared to hypothetical alternatives, are valuable for performing the cost–benefit calculations necessary to optimize infection countermeasures. SIR (susceptible–infected–removed) models are useful in this regard but are limited by the challenge of deciding how and when to update the numerous parameters as the epidemic changes in response to population behaviors. Behaviors of particular interest include facemask adoption (at various levels) and social distancing. We present a method that uses a “dynamic spread function” to systematically capture the continuous variation in the population behavior and the gradual change in infection evolution, resulting from interventions. No parameter updates are made by the user. We use the tool to quantify the reduction in infection rate realizable from the population of New York City adopting different facemask strategies during COVID-19. Assuming a baseline facemask of 67% filtration efficiency, calculations show that increasing the efficiency to 80% could have reduced the roughly 5000 new infections per day occurring at the peak of the epidemic to around 4000. Population behavior that may not be varied as part of the retrospective analysis, such as social distancing in a facemask analysis, are automatically captured as part of the calibration of the dynamic spread function.

Prediction of COVID-19 evolution in Binh Duong province using SIR epidemiological model

With the fast growth of the COVID-19 pandemic, in-silico studies based on the susceptible-infected-removed (SIR) epidemiological model are very critical to provide reliable predictions of the COVID-19 evolution that can effectively support governments to issue the right measures to prevent and control the pandemic. In this study, the evolution of the COVID-19 in the Binh Duong province is investigated using the SIR model implemented in R-Studio software, in which the homemade computer codes based on the SIR model are developed using R language to automatically detect the optimal parameters in the model, including the reproduction ratio R0, the infection coefficient β, and the recovery coefficient γ. The SIR predictions indicate that the number of new positive cases per day in the Binh Duong province is only 40 new cases by November 30, 2021, and the total number of new cases per day becomes zero by middle February 2021. Besides, the Binh Duong province only has 1126 infected cases by November 30, 2021, which reduces to 203 cases at the end of December 2021. Through the SIR results, the COVID-19 pandemic in the Binh Duong is predicted to be ended at the end of December 2021.

National interest may require distributing COVID-19 vaccines to other countries

As immunization campaigns are accelerating, understanding how to distribute the scarce doses of vaccines is of paramount importance and a quantitative analysis of the trade-offs involved in domestic-only versus cooperative distribution is still missing. In this study we use a network Susceptible-Infected-Removed (SIR) model to show circumstances under which it is in a country’s self-interest to ensure other countries can obtain COVID-19 vaccines rather than focusing only on vaccination of their own residents. In particular, we focus our analysis on the United States and estimate the internal burden of COVID-19 disease under different scenarios about vaccine cooperation. We show that in scenarios in which the US has reached the threshold for domestic herd immunity, the US may find it optimal to donate doses to other countries with lower vaccination coverage, as this would allow for a sharp reduction in the inflow of infected individuals from abroad.

SIR (Susceptible–Infectious–Removed) Model of Epidemiology as an Extended Example for Chemical Kinetics Students

The basic SIR (susceptible–infectious–removed) model of epidemiology is presented in chemical kinetic terms with a simple two-reaction mechanism. The conditions for the development of epidemics, the course of a simple closed epidemic, and the bases of several mitigation strategies are described in terms of the underlying first- and second-order rate coefficients. Connections are made with the terminology used in epidemiology and in recent news reports on the COVID-19 pandemic.

Spatial dynamics and optimization method for a rumor propagation model in both homogeneous and heterogeneous environment.

Considering the influence of environmental capacity and forgetting on rumor spreading, we improve the traditional SIR (susceptible–infected–removed) rumor propagation model and give two dynamic models of rumor propagation in heterogeneous environment and homogeneous environment, respectively. The main purpose of this paper is to make a dynamic analysis of rumor propagation models. In the spatial heterogeneous environment, we have analyzed the uniform persistence of the rumor propagation model and the asymptotic behavior of the positive equilibrium point when the diffusion rate of rumor–susceptible tends to zero. In the spatial homogeneous environment, we discuss the stability of rumor propagation model. Further, optimal control and the necessary optimality conditions are obtained by using the maximum principle. Finally, we study the Hopf bifurcation phenomenon through inducing time delay in the reaction–diffusion model. In addition, the existence of Hopf bifurcation is verified and the influence of diffusion coefficients is studied by numerical simulations.