The effects of community interactions and quarantine on a complex network

Abstract: An adaptive complex network based on a susceptible-exposed-infectious-quarantine-recovered (SEIQR) framework is implemented to investigate the transmission dynamics of an infectious disease. The topology and its relations with network parameters are discussed. Using the primary outbreak data from the SEIQR network model, a regression model is developed to describe the relation between the quarantine rate and the key epidemiological parameters. We approximate the quarantine rate as a function of the number of individuals visiting communities and hubs, then incorporate it into the adaptive complex network to investigate the disease transmission dynamics. The proposed quantity can be estimated from the outbreak data and hence is more approachable as compared to the constant rate. Our results suggest that contact radius, hub radius, number of hubs, hub capacity and transmission rate may be important determinants to predict the disease spread and severity of outbreaks. Moreover, our results also suggest that during an outbreak, closing down certain public facilities or reducing their capacities and reducing the number of individuals visiting communities or public places, may significantly slow down the disease spread

Modeling epidemics on networks of connected communities

Advances in the fields of mathematics, physics, epidemiology, and computing have led to an incredibly productive period of epidemic modeling. Here I will present the findings of several computational studies aimed at understanding how epidemics spread across networks. I investigate specifically how epidemics spread across networks consisting of two weakly connected sub-networks (communities) with varying internal connectivities, vaccination probabilities, and probabilities of social distancing. I find that, on average, epidemics may spread across communities even for a single cross connection, that crossing over is characterized by multiple time delayed epidemic waves that result in increased epidemic duration. I develop a novel mathematical characterization of networks consisting of an arbitrary number of weakly connected communities and derive a relationship between the reproductive number (R_0) of an epidemic and the Mean Squared Displacement (MSD) of the epidemic, when the spread is viewed as the progression of multiple forward-biased random walkers. Finally, I propose a new compartmental Susceptible Exposed Infected Quarantined Recovered (SEIQR) model for the 2014 Ebola Virus Disease (EVD) outbreak based on differential equations. I extend this model to an immigration SEIQR (iSEIQR) model with a constant rate of immigration and demonstrate homologous behavior in the form of multiple infection waves between a dynamic single community network model with a constant immigration of possible exposed individuals and the two community models discussed elsewhere in this work. The applications of two community network models are discussed, especially in the context of understanding and mitigating regional and transnational epidemic spread. Pharmaceutical and non-pharmaceutical interventions, such as targeted vaccination, public health education (i.e. avoidance), quarantine, and travel restrictions are explored and some mathematical and physical applications of modeling weakly coupled sub-networks are described. Finally, several possible extensions to this work are listed and discussed

Bayesian inference and failure analysis for risk assessment in quality engineering

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University LondonFailure is the state of not achieving a desired or intended goal. Failure analysis planning in the context of risk assessment is an approach that helps to reduce total cost, increase production capacity, and produce higher-quality products. One of the most common issues that businesses confront are defective products. This issue not only results in monetary loss, but also in a loss of status. Companies must improve their production quality and reduce the quantity of faulty products in order to continue operating in a healthy and profitable manner in today’s very competitive environment. On the other hand, there is the ongoing COVID-19 pandemic, which has thrown the world’s natural order into disarray, and has been designated a Public Health Emergency of International Concern by the World Health Organization. The demand for quality control is rapidly increasing. Failure analysis is thus an useful tool for identifying common failures, their likely causes, and their impact on the health system, as well as plotting strategies to limit COVID-19 transmission. It is now more vital than ever to enhance failure analysis methods. The traditional FMEA (Failure mode and effects analysis) is one of the most widely used approaches for identifying and classifying failure modes (FMs) and failure causes (FCs). It is a risk analysis tool for coping with possible failures and is widely used in the reliability engineering, safety engineering and quality engineering. To prioritize risks of different failure modes, FMEA uses the risk priority number (RPN), which is the product of three risk measures: severity (S), occurrence (O) and detection (D). Traditional FMEA, on the other hand, has drawbacks, such as the inability to cope with uncertain failure data, such as expert subjective evaluations, the failure events’ conditionality, RPN has a high degree of subjectivity, comparing various RPNs is challenging, potential errors may be ignored in the conventional FMEA process, etc. To overcome these limitations, I present an integrated Bayesian approach to FMEA in this thesis. In this proposed approach, I worked with experts in quality engineering and used Bayesian inference to estimate the FMEA risk parameters: S, O and D. The proposed approach is intended to become more practical and less subjective as more data is added. Bayesian statistics is a statistical theory that is based on the Bayesian interpretation of probability, which states that probability expresses a degree of belief or information (knowledge) about an event. Bayesian statistics addresses the issues with uncertainties found in frequentist statistics, such as the distribution of contributing factors, the implications of using specific distributions and specifies that there is some prior probability. A prior can be derived from previous information, such as previous experiments, but it can also be derived from a trained subject-matter expert’s purely subjective assessment. Frequentist statistics (also known as classical statistics) has several limitations, including a lack of uncertainty information in predictions, no built-in regularisation, and no consideration of prior knowledge. Due to the availability of powerful computers and new algorithms, Bayesian methods have seen increased use within statistics in the twenty-first century, and this thesis highlights the effective use of Bayesian analyses to address the shortcomings of the current FMEA with the revamped Bayesian FMEA. As a demonstration of the approach, three case studies are presented. The first case study is a Bayesian risk assessment approach of the modified SEIR (susceptible-exposed-infectious-recovered) model for the transmission dynamics of COVID-19 with an exponentially distributed. The effective reproduction number is estimated based on laboratory-confirmed cases and death data using Bayesian inference and analyse the impact of the community spread of COVID-19 across the United Kingdom. The value of effective reproduction number models the average number of infections caused by a case of an infectious disease in a population that includes not only susceptible people. The FMEA is then applied to evaluate the effectiveness of the action measures taken to manage the COVID-19 pandemic. In the FMEA, the focus was on COVID-19 infections and therefore the failure mode is taken as positive cases. The model is applied to COVID-19 data showing the effectiveness of interventions adopted to control the epidemic by reducing the effective reproduction number of COVID-19. The risk measures were estimated from the case fatality rate (S), the posterior median of the effective reproduction number (O) and the current corrective measures used by government policies (D). The second case study is a Bayesian risk assessment of a coordinate measuring machine (CMM) process using failure mode, effects and criticality analysis (FMECA) and an augmented form error model. The form error is defined as the deviation of a manufactured part from its design or ideal shape, and it is a key characteristic to evaluate in quality engineering and manufacturing. The form error is presented as a probabilistic model using symmetric unimodal distributions. Bayesian inference is then used to identify influence factors associated with the measurement process due to form error, environmental, human and random effects. A risk assessment is then performed by combining Bayesian inference, FMECA and conformity testing, to quantify and minimise the risk of wrong decisions. In the FMECA, the focus was on CMM measurement process and I identified four major FMs that can occur: probe, mechanical, environmental and measurement performance failure. Eleven FCs were also observed, each of which was linked to one of the four FMs. The risk measures were estimated from the posterior probability of failure causes associated with the CMM measurement process (O), the severity of a specific consumer’s risk (S) and the detectability of failures from the posterior standard deviation of the form error model (D). The third case study is a Bayesian risk assessment of a CMM measurement process using an autoregressive (AR) form error model and a combined Fault tree analysis (FTA) and FMEA approach to predict significant failure modes and causes. The main idea is to estimate and predict the form error based on CMM data using Gibbs sampling and analyse the impact of the CMM measurement process on product conformity testing. The FTA is used to compare the actual and predicted form error data from the Bayesian AR plot to determine the likelihood of the CMM measurement process failing using binary data. The acquired binary data is then classified into four states (true positive, true negative, false positive, and false negative) using a confusion matrix, which is subsequently utilized to calculate key classification measures (i.e., error rate, prediction rate, prevalence rate, sensitivity rate, etc). The classification measures were then used to assess the FMEA risk measures S, O, and D, which were critical for determining the RPN and making decisions. Analytical and numerical methods are used in all case studies to highlight the practical implications of our findings and are meant to be practical without complex computing. The proposed methodologies can find applications in numerous disciplines and wide quality engineering

Machine learning in drug supply chain management during disease outbreaks: a systematic review

The drug supply chain is inherently complex. The challenge is not only the number of stakeholders and the supply chain from producers to users but also production and demand gaps. Downstream, drug demand is related to the type of disease outbreak. This study identifies the correlation between drug supply chain management and the use of predictive parameters in research on the spread of disease, especially with machine learning methods in the last five years. Using the Publish or Perish 8 application, there are 71 articles that meet the inclusion criteria and keyword search requirements according to Kitchenham's systematic review methodology. The findings can be grouped into three broad groupings of disease outbreaks, each of which uses machine learning algorithms to predict the spread of disease outbreaks. The use of parameters for prediction with machine learning has a correlation with drug supply management in the coronavirus disease case. The area of drug supply risk management has not been heavily involved in the prediction of disease outbreaks

Exploring the impact of social stress on the adaptive dynamics of COVID-19: Typing the behavior of na\"ive populations faced with epidemics

In the context of natural disasters, human responses inevitably intertwine with natural factors. The COVID-19 pandemic, as a significant stress factor, has brought to light profound variations among different countries in terms of their adaptive dynamics in addressing the spread of infection outbreaks across different regions. This emphasizes the crucial role of cultural characteristics in natural disaster analysis. The theoretical understanding of large-scale epidemics primarily relies on mean-field kinetic models. However, conventional SIR-like models failed to fully explain the observed phenomena at the onset of the COVID-19 outbreak. These phenomena included the unexpected cessation of exponential growth, the reaching of plateaus, and the occurrence of multi-wave dynamics. In situations where an outbreak of a highly virulent and unfamiliar infection arises, it becomes crucial to respond swiftly at a non-medical level to mitigate the negative socio-economic impact. Here we present a theoretical examination of the first wave of the epidemic based on a simple SIRSS model (SIR with Social Stress). We conduct an analysis of the socio-cultural features of na\"ive population behaviors across various countries worldwide. The unique characteristics of each country/territory are encapsulated in only a few constants within our model, derived from the fitted COVID-19 statistics. These constants also reflect the societal response dynamics to the external stress factor, underscoring the importance of studying the mutual behavior of humanity and natural factors during global social disasters. Based on these distinctive characteristics of specific regions, local authorities can optimize their strategies to effectively combat epidemics until vaccines are developed.Comment: 29 pages, 16 figures, 1 table, 2 appendice

Least-Squares Finite Element Method for a Meso-Scale Model of the Spread of COVID-19

This paper investigates numerical properties of a flux-based finite element method for the discretization of a SEIQRD (susceptible-exposed-infected-quarantined-recovered-deceased) model for the spread of COVID-19. The model is largely based on the SEIRD (susceptible-exposed-infected-recovered-deceased) models developed in recent works, with additional extension by a quarantined compartment of the living population and the resulting first-order system of coupled PDEs is solved by a Least-Squares meso-scale method. We incorporate several data on political measures for the containment of the spread gathered during the course of the year 2020 and develop an indicator that influences the predictions calculated by the method. The numerical experiments conducted show a promising accuracy of predictions of the space-time behavior of the virus compared to the real disease spreading data.Peer Reviewe

Numerical Simulation and Design of COVID-19 Forecasting Framework Using Efficient Data Analytics Methodologies

The COVID-19 pandemic hit globally in December 2019 when a certain virus strain from Wuhan, China started proliferating throughout the world. By the end of March 2020, lockdowns and curfews were imposed all over the world halting trade, commerce, education, and various other essential activities. It has been nearly a year since the WHO declared a pandemic but there is still a consistent rise of the cases even with the administration of various types of vaccines and preventive measure. One of the main struggles that the healthcare workers face is to find out the how the virus is spreading amongst a community. The knowledge of this can be used to stop the spread of virus. This is a very important step towards getting things back into momentum to restore activities globally. Many attempts have been made under epidemiology to study the spread of COVID and many mathematical models have emerged as a result that can help with this. A popular model that is used for estimating the effective reproduction number (Rt) has the shortcoming that it cannot simultaneously forecast the future number of cases. This work explores an extension of another model, the SIR-model, in which the model parameters are fitted to recorded data. This makes the model adaptive, opening up the possibilities for estimating the Rt daily and making predictions of future number of confirmed cases. The paper use this adaptive SIR-model (aSIR) to estimate the Rt and create forecasts of new cases in India. The paper purpose is to determine how precise aSIR-models are at estimating the Rt (when compared with FHM’s model). It will also analyze how accurate aSIR-models are at simultaneously forecasting the future spread of Covid-19 in India. The coronavirus spread can be mathematically modelled using factors such as the number of susceptible people, exposed people, infected people, asymptotic people and the number of recovered people. The Khan-Atangana system is an integer-order coronavirus model that uses the above-mentioned factors. Since the coronavirus model depends on the initial conditions, the Khan-Atangana model uses the Atangana-Baleanu operate as it has a non-variant and non-local kernel. Instead, we replace the equations with fractional-order derivatives using the Grünwald-Letnikov derivative. The fractional order derivatives need to be fed with initial conditions and are useful to determine the spread due to their non-local nature. This project proposes to solve these fractional-order derivatives using numerical methods and analyse the stability of this epidemiological model

SUIHTER: A new mathematical model for COVID-19. Application to the analysis of the second epidemic outbreak in Italy

The COVID-19 epidemic is the last of a long list of pandemics that have affected humankind in the last century. In this paper, we propose a novel mathematical epidemiological model named SUIHTER from the names of the seven compartments that it comprises: susceptible uninfected individuals (S), undetected (both asymptomatic and symptomatic) infected (U), isolated (I), hospitalized (H), threatened (T), extinct (E), and recovered (R). A suitable parameter calibration that is based on the combined use of least squares method and Markov Chain Monte Carlo (MCMC) method is proposed with the aim of reproducing the past history of the epidemic in Italy, surfaced in late February and still ongoing to date, and of validating SUIHTER in terms of its predicting capabilities. A distinctive feature of the new model is that it allows a one-to-one calibration strategy between the model compartments and the data that are daily made available from the Italian Civil Protection. The new model is then applied to the analysis of the Italian epidemic with emphasis on the second outbreak emerged in Fall 2020. In particular, we show that the epidemiological model SUIHTER can be suitably used in a predictive manner to perform scenario analysis at national level.Comment: 25 page