Susceptible-infected-recovered Research Articles

A Networked Competitive Multi-Virus SIR Model: Analysis and Observability

This paper proposes a novel discrete-time multi-virus SIR (susceptible-infected-recovered) model that captures the spread of competing SIR epidemics over a population network. First, we provide a sufficient condition for the infection level of all the viruses over the networked model to converge to zero in exponential time. Second, we propose an observation model which captures the summation of all the viruses’ infection levels in each node, which represents the individuals who are infected by different viruses but share similar symptoms. We present a sufficient condition for the model to be locally observable. We propose a Luenberger observer for the system state estimation and show via simulations that the estimation error of the Luenberger observer converges to zero before the viruses die out.

A Graphical Analysis of Mosquito Infection Model with Host and Vector Population

A mosquito infection model was formulated consisting of SIR (Susceptible-Infectious-Recovered) with exposed and carrier class for humans as host and SI (Susceptible-Infectious) with exposed class for mosquitoes as vector. Numerical simulations were carried out for the diseases Malaria, Dengue and Chikungunya. The graphs on susceptible, exposed, carrier, infectious and recovered were given for the different values of parameters involved in the model. The comparative graphical study was done on the state variables.

A nonstandard finite difference scheme for the SVICDR model to predict COVID-19 dynamics.

In the context of 2019 coronavirus disease (COVID-19), considerable attention has been paid to mathematical models for predicting country- or region-specific future pandemic developments. In this work, we developed an SVICDR model that includes a susceptible, an all-or-nothing vaccinated, an infected, an intensive care, a deceased, and a recovered compartment. It is based on the susceptible-infectious-recovered (SIR) model of Kermack and McKendrick, which is based on ordinary differential equations (ODEs). The main objective is to show the impact of parameter boundary modifications on the predicted incidence rate, taking into account recent data on Germany in the pandemic, an exponential increasing vaccination rate in the considered time window and trigonometric contact and quarantine rate functions. For the numerical solution of the ODE systems a model-specific non-standard finite difference (NSFD) scheme is designed, that preserves the positivity of solutions and yields the correct asymptotic behaviour.

A General Epidemic Model and Its Application to Mask Design Considering Different Preferences towards Masks

While most masks have a limited effect on personal protection, how effective are they for collective protection? How to enlighten the design of masks from the perspective of collective dynamics? In this paper, we assume three preferences in the population: (i) never wearing a mask; (ii) wearing a mask if and only if infected; (iii) always wearing a mask. We study the epidemic transmission in an open system within the Susceptible‐Infected‐Recovered (SIR) model framework. We use agent‐based Monte Carlo simulation and mean‐field differential equations to investigate the model, respectively. Ternary heat maps show that wearing masks is always beneficial in curbing the spread of the epidemic. Based on the model, we investigate the potential implications of different mask designs from the perspective of collective dynamics. The results show that strengthening the filterability of the mask from the face to the outside is more effective in most parameter spaces because it acts on individuals with both preferences (ii) and (iii). However, when the fraction of individuals always wearing a mask achieves a critical point, strengthening the filterability from outside to the face becomes more effective because of the emerging hidden reality that the infected individuals become too few to utilize the filterability from their face to outside fully.

Study on the contagion mechanism of associated credit risk with corporate senior executives’ alertness

Associate credit risk is a kind of credit risk among the associated credit enterprises formed by credit-related enterprises. Based on the mean field theory of complex network and the classical model Susceptible–Infected–Recovered (SIR) of risk propagation dynamics, this paper explores the influence mechanism of the influence of corporate senior executives’ alertness promoted by risk information on the contagion of associated credit risk. The results show that the corporate senior executives’ alertness does not change the contagion threshold of associated credit risk.

On new computations of the fractional epidemic childhood disease model pertaining to the generalized fractional derivative with nonsingular kernel

<abstract><p>The present research investigates the Susceptible-Infected-Recovered (SIR) epidemic model of childhood diseases and its complications with the Atangana-Baleanu fractional derivative operator in the Caputo sense (ABC). With the aid of the Elzaki Adomian decomposition method (EADM), the approximate solutions of the aforesaid model are discussed by exerting the Adomian decomposition method. By employing the fixed point postulates and the Picard–Lindelöf approach, the stability, existence, and uniqueness consequences of the model are demonstrated. Furthermore, we illustrate the essential hypothesis for disease control in order to find the role of unaware infectives in the spread of childhood diseases. Besides that, simulation results and graphical illustrations are presented for various fractional-orders. A comparison analysis is shown with the previous findings. It is hoped that ABC fractional derivative and the projected algorithm will provide new venues in futuristic studies to manipulate and analyze several epidemiological models.</p></abstract>

When and How to Adjust Non-Pharmacological Interventions Concurrent with Booster Vaccinations Against COVID-19 — Guangdong, China, 2022

IntroductionWith the large-scale roll-out of the coronavirus disease 2019 (COVID-19) booster vaccination effort (a vaccine dose given 6 months after completing primary vaccination) in China, we explore when and how China could lift non-pharmacological interventions (NPIs) against COVID-19 in 2022.MethodsUsing a modified susceptible-infectious-recovered (SIR) mathematical model, we projected the COVID-19 epidemic situation and required medical resources in Guangdong Province, China.ResultsIf the number of people entering from overseas recovers to 20% of the number in 2019, the epidemic in 2022 could be controlled at a low level by a containment (215 local cases) or suppression strategy (1,397 local cases). A mitigation strategy would lead to 21,722 local cases. A coexistence strategy would lead to a large epidemic with 6,850,083 local cases that would overwhelm Guangdong’s medical system. With 50% or 100% recovery of the 2019 level of travelers from overseas, the epidemic could also be controlled with containment or suppression, but enormous resources, including more hotel rooms for border quarantine, will be required. However, coexistence would lead to an uncontrollable epidemic with 12,922,032 local cases.DiscussionWith booster vaccinations, the number of travelers from overseas could increase slightly in 2022, but a suppression strategy would need to be maintained to ensure a controllable epidemic.

A death, infection, and recovery (DIR) model to forecast the COVID-19 spread

BackgroundThe SARS-Cov-2 virus (commonly known as COVID-19) has resulted in substantial casualties in many countries. The first case of COVID-19 was reported in China towards the end of 2019. Cases started to appear in several other countries (including Pakistan) by February 2020. To analyze the spreading pattern of the disease, several researchers used the Susceptible-Infectious-Recovered (SIR) model. However, the classical SIR model cannot predict the death rate. ObjectiveIn this article, we present a Death-Infection-Recovery (DIR) model to forecast the virus spread over a window of one (minimum) to fourteen (maximum) days. Our model captures the dynamic behavior of the virus and can assist authorities in making decisions on non-pharmaceutical interventions (NPI), like travel restrictions, lockdowns, etc. MethodThe size of training dataset used was 134 days. The Auto Regressive Integrated Moving Average (ARIMA) model was implemented using XLSTAT (add-in for Microsoft Excel), whereas the SIR and the proposed DIR model was implemented using python programming language. We compared the performance of DIR model with the SIR model and the ARIMA model by computing the Percentage Error and Mean Absolute Percentage Error (MAPE). ResultsExperimental results demonstrate that the maximum% error in predicting the number of deaths, infections, and recoveries for a period of fourteen days using the DIR model is only 2.33%, using ARIMA model is 10.03% and using SIR model is 53.07%. ConclusionThis percentage of error obtained in forecasting using DIR model is significantly less than the% error of the compared models. Moreover, the MAPE of the DIR model is sufficiently below the two compared models that indicates its effectiveness.

Impact of media coverage on a fractional-order SIR epidemic model

In this work, we formulated and analyzed a fractional-order epidemic model of infectious disease (such as SARS, 2019-nCoV and COVID-19) concerning media effect. The model is based on classical susceptible-infected-recovered (SIR) model. Basic properties regarding positivity, boundedness and non-negative solutions are discussed. Basic reproduction number [Formula: see text] of the system has been calculated using next-generation matrix method and it is seen that the disease-free equilibrium is locally as well as globally asymptotically stable if [Formula: see text], otherwise unstable. The existence of endemic equilibrium point is established using the Lambert W function. The condition for global stability has been derived. Numerical simulation suggests that fractional order and media have a large effect on our system dynamics. When media impact is stronger enough, our fractional-order system stabilizes the oscillation.

The approximation of an isolated epidemic process wave using a combination of exponents

The most commonly used methods for the medium- and long-term forecasting of epidemic processes are based on the classical SIR (susceptible – infected – recovered) model and its numerous modifications. In this approach, the dynamics of the epidemic is approximated using the solutions of differential or discrete equations. The forecasting methods based on the approximation of data by functions of a given class are usually focused on obtaining a short-term forecast. They are not used for the long-term forecasts of epidemic processes due to their insufficient efficiency for forecasting nonstationary processes. In this paper, we formulated a hypothesis that the primary waves of the COVID-19 pandemic, which took place in a number of European countries, including the Republic of Belarus, in the spring-summer of 2020 are isolated and therefore can be regarded as processes close to stationary. On the basis of this hypothesis, a method of approximating isolated epidemic process waves by means of generalized logistic functions with an increased number of exponents was proposed. The developed approach was applied to predict the number of infected people in the Republic of Belarus for the period until August 2020 based on data from the beginning of the epidemic until June 12, 2020.

An algorithm for the direct estimation of the parameters of the SIR epidemic model from the I(t) dynamics.

The discrete SIR (Susceptible–Infected–Recovered) model is used in many studies to model the evolution of epidemics. Here, we consider one of its dynamics—the exponential decrease in infected cases I(t). By considering only the I(t) dynamics, we extract three parameters: the exponent of the initial exponential increase gamma ; the maximum value I_{max }; and the exponent of the final decrease varGamma . From these three parameters, we show mathematically how to extract all relevant parameters of the SIR model. We test this procedure on numerical data and then apply the methodology to real data received from the COVID-19 situation in France. We conclude that, based on the hospitalized data and the ICU (Intensive Care Unit) cases, two exponentials are found, for the initial increase and the decrease in I(t). The parameters found are larger than reported in the literature, and they are associated with a susceptible population which is limited to a sub-sample of the total population. This may be due to the fact that the SIR model cannot be applied to the covid-19 case, due to its strong hypotheses such as mixing of all the population, or also to the fact that the parameters have changed over time, due to the political initiatives such as social distanciation and lockdown.

New and simple mathematical description of epidemics including consecutive waves

AbstractThe Bateman linear differential equations describing in time nuclear levels interconnected by transitions (in general, each with its own rate) are adapted to the epidemiology case where only two infection and recovery rates are used. Time‐dependent functions describing successive generations of infected people are thus derived. Closed mathematical expressions allow an easy calculation/prediction of the properties of these generations and therefore of the whole epidemics. The main limitation consists in reaching the point when the number of susceptible to the infection people substantially decreases. As testing ground, reasonable descriptions of the newly registered COVID‐19 cases per day is achieved for Europe and the United States till December 2020, including several so‐called Pandemic waves. The approach of the present work, by using transmission from one generation of infected people to a new generation allows a much more detailed tracking of the Pandemic spread than the approaches used so far. For example, the most widely used Susceptible Infectious Recovered (SIR) models (and their variants) use instead transitions from one big compartment of susceptible people to another new one of infected people followed by recovery leading to a third compartment. Clear correlations are found between features of the Pandemic process and the emergence of new SARS‐CoV‐2 variants, with some of them (especially the variant) immediately influencing the spread of the infection disease in the Pandemic wave of Autumn of 2020.

A novel method for identifying influential nodes in complex networks based on gravity model

How to identify influential nodes in complex networks is an essential issue in the study of network characteristics. A number of methods have been proposed to address this problem, but most of them focus on only one aspect. Based on the gravity model, a novel method is proposed for identifying influential nodes in terms of the local topology and the global location. This method comprehensively examines the structural hole characteristics and K-shell centrality of nodes, replaces the shortest distance with a probabilistically motivated effective distance, and fully considers the influence of nodes and their neighbors from the aspect of gravity. On eight real-world networks from different fields, the monotonicity index, susceptible-infected-recovered (SIR) model, and Kendall’s tau coefficient are used as evaluation criteria to evaluate the performance of the proposed method compared with several existing methods. The experimental results show that the proposed method is more efficient and accurate in identifying the influence of nodes and can significantly discriminate the influence of different nodes.

Epidemics on networks with preventive rewiring

AbstractA stochastic SIR (susceptible infective recovered) model is considered for the spread of an epidemic on a network, described initially by an Erdős–Rényi random graph, in which susceptible individuals connected to infectious neighbors may drop or rewire such connections. A novel construction of the model is used to derive a deterministic model for epidemics started with a positive fraction initially infected and prove convergence of the scaled stochastic model to that deterministic model as the population size . For epidemics initiated by a single infective that take off, we prove that for part of the parameter space, in the limit as , the final fraction infected is discontinuous in the infection rate at its threshold , thus not converging to 0 as . The discontinuity is particularly striking when rewiring is necessarily to susceptible individuals in that jumps from 0 to 1 as passes through .

Controlling Infectious Diseases: The Decisive Phase Effect on a Seasonal Vaccination Strategy

The study of epidemiological systems has generated deep interest in exploring the dynamical complexity of common infectious diseases driven by seasonally varying contact rates. Mathematical modeling and field observations have shown that, under seasonal variation, the incidence rates of some endemic infectious diseases fluctuate dramatically and the dynamics is often characterized by chaotic oscillations in the absence of specific vaccination programs. In fact, the existence of chaotic behavior has been precisely stated in the literature as a noticeable feature in the dynamics of the classical Susceptible-Infected-Recovered (SIR) seasonally forced epidemic model. However, in the context of epidemiology, chaos is often regarded as an undesirable phenomenon associated with the unpredictability of infectious diseases. As a consequence, the problem of converting chaotic motions into regular motions becomes particularly relevant. In this article, we consider the so-called phase control method applied to the seasonally forced SIR epidemic model to suppress chaos. Interestingly, this method of controlling chaos has a clear meaning as a weak perturbation on a seasonal vaccination strategy. Numerical simulations show that the phase difference between the two periodic forces — contact rate and vaccination — plays a very important role in controlling chaos.

Validation Method of the Mathematical Model for SARS-Cov-2 Pandemic from Data Mining and Statistical Analysis

Nowadays, in 2020, we live during the most dangerous global pandemic that has been reported since the Spanish Flu, which occurred between 1918 and 1920. According to World Health Organization (WHO) records, the pandemic caused by the Sars-Cov-2 virus began in December 2019 and is present in all continents and almost all countries, surpassing more than 79 million infected and 1.7 million deaths by December 2020. Several mathematical models applied to Epidemiology have been adopted over time. One of the most widely adopted is the Susceptible-Infected-Recovered (SIR), developed in India by Kermack and Mckendrick in 1927. In our research, a comprehensive collection of data on the SARS-Cov-2 pandemic was made from reports by WHO, Dadax Limited (Chinese data company), and Johns Hopkins University in the United States of America (USA). Facts were collected from many different countries, regarding the number of confirmed, recovered, and death cases. In this article, we constructed a mathematical model that describes the evolution of the pandemic from the similarity with models already adopted in the field of nuclear physics. For the validation of the mathematical model, we chose information from Germany due to the reliability of the available information. Thus, a statistical analysis was executed to qualify the performance of the method and the predictive character of the mathematical model. To date, 11,716 raw data have been collected, of which we performed data mining relevant to use in this research.

Epidemic Spreading in a Social Network With Facial Masks Wearing Individuals

In this paper, we present a susceptible-infected-recovered (SIR) model with individuals wearing facial masks and individuals who do not. The disease transmission rates, the recovering rates and the fraction of individuals who wear masks are all time dependent in the model. We develop a progressive estimation of the disease transmission rates and the recovering rates based on the COVID-19 data published by John Hopkins University. We determine the fraction of individual who wear masks by a maximum likelihood estimation, which maximizes the transition probability of a stochastic susceptible-infected-recovered model. The transition probability is numerically difficult to compute if the number of infected individuals is large. We develop an approximation for the transition probability based on central limit theorem and mean field approximation. We show through numerical study that our approximation works well. We develop a bond percolation analysis to predict the eventual fraction of population who are infected, assuming that parameters of the SIR model do not change anymore. We predict the outcome of COVID-19 pandemic using our theory.

Epidemiological spread models of Parkinson’s disease support the prion‐like role of alpha‐synuclein

AbstractBackgroundParkinson’s disease (PD) is a progressive neurodegenerative condition marked by brain atrophy in multiple cortical and subcortical regions. It is now known to be caused by the prion‐like propagation of misfolded alpha‐synuclein, supporting Braak’s hypothesis. The pattern of neurodegeneration is now thought to be explained by a combination of brain connectivity and local vulnerability.MethodWe used MRI and clinical data from the Parkinson Progression Markers Initiative to map the progression of brain atrophy over one, two and four years and related it to brain functional and structural connectivity, cell type expression and gene ontology enrichment analyses. We use two methods to measure atoprhy: cortical thickness measures and deformation based morphometry. We will compare these results to pathology in wild‐type mice sacrificed at different time‐points after injection of alpha‐synuclein preformed fibrils. In both cases we use a spreading model inspired by infectious‐disease epidemiology to map the propagation of misfolded alpha‐synuclein. This Susceptible‐Infectious‐Recovered (SIR) model assumes that alpha‐synuclein molecules become misfolded, propagate along the connectome, and cause tissue damage when they accumulate.Result1) The pattern of brain atrophy in de novo PD is compatible with a propagating process with an epicenter in the substantia nigra. 2) The SIR model recapitulates the observed atrophy pattern, and supports connectivity‐based propagation. 3) In addition, the SIR model suggests that brain areas with higher alpha‐synuclein concentration appear to be more susceptible to injury but also more likely to act as disease propagators. 4) Progression over four years is also explained by connectivity. 5) Gene ontology analyses suggest that synapses are especially targeted by neurodegeneration. 6) Studies in mice, where the injection site of alpha‐synuclein preformed fibrils is determined by the investigator, also confirm the connectivity by local vulnerability model.ConclusionHuman and animal studies support the Braak hypothesis of a “toxic agent” propagating from the brainstem to the cortex, accounting for the stereotyped progression of PD manifestations. Data from gene expression studies and animal experiments confirm the important role of prion‐like alpha‐synuclein in PD pathogenesis.

Introductory Models of COVID-19 in the United States

ABSTRACT Students develop and test simple kinetic models of the spread of coronavirus disease 2019 (COVID-19) caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus. Microsoft Excel is used as the modeling platform because it is nonthreatening to students and it is widely available. Students develop finite difference models and implement them in the cells of preformatted spreadsheets following a guided inquiry pedagogy that introduces new model parameters in a scaffolded step-by-step manner. That approach allows students to investigate the implications of new model parameters in a systematic way. Students fit the resulting models to reported cases per day data for the United States using least squares techniques with Excel's Solver. Using their own spreadsheets, students discover for themselves that the initial exponential growth of COVID-19 can be explained by a simplified unlimited growth model and by the susceptible-infected-recovered (SIR) model. They also discover that the effects of social distancing can be modeled using a Gaussian transition function for the infection rate coefficient and that the summer surge was caused by prematurely relaxing social distancing and then reimposing stricter social distancing. Students then model the effect of vaccinations and validate the resulting susceptible-infected-recovered-vaccinated (SIRV) model by showing that it successfully predicts the reported cases per day data from Thanksgiving through the holiday period up to 14 February 2021. The same SIRV model is then extended and successfully fits the fourth peak up to 1 June 2021, caused by further relaxation of social distancing measures. Finally, students extend the model up to the present day (27 August 2021) and successfully account for the appearance of the delta variant of the SARS-CoV-2 virus. The fitted model also predicts that the delta variant peak will be comparatively short, and the cases per day data should begin to fall off in early September 2021, counter to current expectations. This case study makes an excellent capstone experience for students interested in scientific modeling.

On the use of aggregated human mobility data to estimate the reproduction number

The reproduction number of an infectious disease, such as CoViD-19, can be described through a modified version of the susceptible-infected-recovered (SIR) model with time-dependent contact rate, where mobility data are used as proxy of average movement trends and interpersonal distances. We introduce a theoretical framework to explain and predict changes in the reproduction number of SARS-CoV-2 in terms of aggregated individual mobility and interpersonal proximity (alongside other epidemiological and environmental variables) during and after the lockdown period. We use an infection-age structured model described by a renewal equation. The model predicts the evolution of the reproduction number up to a week ahead of well-established estimates used in the literature. We show how lockdown policies, via reduction of proximity and mobility, reduce the impact of CoViD-19 and mitigate the risk of disease resurgence. We validate our theoretical framework using data from Google, Voxel51, Unacast, The CoViD-19 Mobility Data Network, and Analisi Distribuzione Aiuti.