Clustering model for transmission of the SARS virus: application to epidemic control and risk assessment

A Deep Learning-Enhanced Compartmental Model and Its Application in Modeling Omicron in China

The mainstream compartmental models require stochastic parameterization to estimate the transmission parameters between compartments, whose calculation depend upon detailed statistics on epidemiological characteristics, which are expensive, economically and resource-wise, to collect. In addition, infectious diseases spread in three dimensions: temporal, spatial, and mobile, i.e., they affect a population through not only the time progression of infection, but also the geographic distribution and physical mobility of the population. However, the parameterization process for the mainstream compartmental models does not effectively capture the spatial and mobile dimensions. As an alternative, deep learning techniques are utilized in estimating these stochastic parameters with greatly reduced dependency on data particularity and with a built-in temporal-spatial-mobile process that models the geographic distribution and physical mobility of the population. In particular, we apply DNN (Deep Neural Network) and LSTM (Long-Short Term Memory) techniques to estimate the transmission parameters in a customized compartmental model, then feed the estimated transmission parameters to the compartmental model to predict the development of the Omicron epidemic in China over the 28 days for the period between 4 June and 1 July 2022. The average levels of predication accuracy of the model are 98% and 92% for the number of infections and deaths, respectively. We establish that deep learning techniques provide an alternative to the prevalent compartmental modes and demonstrate the efficacy and potential of applying deep learning methodologies in predicting the dynamics of infectious diseases.

Applications of Machine Learning (ML) and Mathematical Modeling (MM) in Healthcare with Special Focus on Cancer Prognosis and Anticancer Therapy: Current Status and Challenges

The use of data-driven high-throughput analytical techniques, which has given rise to computational oncology, is undisputed. The widespread use of machine learning (ML) and mathematical modeling (MM)-based techniques is widely acknowledged. These two approaches have fueled the advancement in cancer research and eventually led to the uptake of telemedicine in cancer care. For diagnostic, prognostic, and treatment purposes concerning different types of cancer research, vast databases of varied information with manifold dimensions are required, and indeed, all this information can only be managed by an automated system developed utilizing ML and MM. In addition, MM is being used to probe the relationship between the pharmacokinetics and pharmacodynamics (PK/PD interactions) of anti-cancer substances to improve cancer treatment, and also to refine the quality of existing treatment models by being incorporated at all steps of research and development related to cancer and in routine patient care. This review will serve as a consolidation of the advancement and benefits of ML and MM techniques with a special focus on the area of cancer prognosis and anticancer therapy, leading to the identification of challenges (data quantity, ethical consideration, and data privacy) which are yet to be fully addressed in current studies.

Risk assessment of infectious disease epidemic based on fuzzy Bayesian network

The prevention and control of infectious disease epidemic (IDE) is an important task for every country and region. Risk assessment is significant for the prevention and control of IDE. Fuzzy Bayesian networks (FBN) can capture complex causality and uncertainty. The study developed a novel FBN model, integrating grounded theory, interpretive structural model, and expert weight determination algorithm for the risk assessment of IDE. The algorithm is proposed by the authors for expert weighting in fuzzy environment. The proposed FBN model comprehensively takes into account the risk factors and the interaction among them, and quantifies the uncertainty of IDE risk assessment, so as to make the assessment results more reliable. Taking the epidemic situation of COVID-19 in Wuhan as a case, the application of the proposed model is illustrated. And sensitivity analysis is performed to identify the important risk factors of IDE. Moreover, the effectiveness of the model is checked by the three-criterion-based quantitative validation method including variation connection, consistent effect, and cumulative limitation. Results show that the probability of the outbreak of COVID-19 in Wuhan is as high as 82.26%, which is well-matched with the actual situation. "Information transfer mechanism," "coordination and cooperation among various personnel," "population flow," and "ability of quarantine" are key risk factors. The constructed model meets the above three criteria. The application potential and effectiveness of the developed FBN model are demonstrated. The study provides decision support for preventing and controlling IDE.

Identifying Potential Super-Spreaders and Disease Transmission Hotspots Using White-Tailed Deer Scraping Networks

White-tailed deer (Odocoileus virginianus, WTD) spread communicable diseases such the zoonotic coronavirus SARS-CoV-2, which is a major public health concern, and chronic wasting disease (CWD), a fatal, highly contagious prion disease occurring in cervids. Currently, it is not well understood how WTD are spreading these diseases. In this paper, we speculate that "super-spreaders" mediate disease transmission via direct social interactions and indirectly via body fluids exchanged at scrape sites. Super-spreaders are infected individuals that infect more contacts than other infectious individuals within a population. In this study, we used network analysis from scrape visitation data to identify potential super-spreaders among multiple communities of a rural WTD herd. We combined local network communities to form a large region-wide social network consisting of 96 male WTD. Analysis of WTD bachelor groups and random network modeling demonstrated that scraping networks depict real social networks, allowing detection of direct and indirect contacts, which could spread diseases. Using this regional network, we model three major types of potential super-spreaders of communicable disease: in-degree, out-degree, and betweenness potential super-spreaders. We found out-degree and betweenness potential super-spreaders to be critical for disease transmission across multiple communities. Analysis of age structure revealed that potential super-spreaders were mostly young males, less than 2.5 years of age. We also used social network analysis to measure the outbreak potential across the landscape using a new technique to locate disease transmission hotspots. To model indirect transmission risk, we developed the first scrape-to-scrape network model demonstrating connectivity of scrape sites. Comparing scrape betweenness scores allowed us to locate high-risk transmission crossroads between communities. We also monitored predator activity, hunting activity, and hunter harvests to better understand how predation influences social networks and potential disease transmission. We found that predator activity significantly influenced the age structure of scraping communities. We assessed disease-management strategies by social-network modeling using hunter harvests or removal of potential super-spreaders, which fragmented WTD social networks reducing the potential spread of disease. Overall, this study demonstrates a model capable of predicting potential super-spreaders of diseases, outlines methods to locate transmission hotspots and community crossroads, and provides new insight for disease management and outbreak prevention strategies.

How Is the Risk of Major Sudden Infectious Epidemic Transmitted? A Grounded Theory Analysis Based on COVID-19 in China

The outbreak of a sudden infectious epidemic often causes serious casualties and property losses to the whole society. The COVID-19 epidemic that broke out in China at the end of December 2019, spread rapidly, resulting in large groups of confirmed diagnoses, and causing severe damage to China's society. This epidemic even now encompasses the globe. This paper takes the COVID-19 epidemic that has occurred in China as an example, the original data of this paper is derived from 20 Chinese media reports on COVID-19, and the grounded theory is used to analyze the original data to find the risk transmission rules of a sudden infectious epidemic. The results show that in the risk transmission of a sudden infectious epidemic, there are six basic elements: the risk source, the risk early warning, the risk transmission path, the risk transmission victims, the risk transmission inflection point, and the end of risk transmission. After a sudden infectious epidemic breaks out, there are three risk transmission paths, namely, a medical system risk transmission path, a social system risk transmission path, and a psychological risk transmission path, and these three paths present a coupling structure. These findings in this paper suggest that people should strengthen the emergency management of a sudden infectious epidemic by controlling of the risk source, establishing an efficient and scientific risk early warning mechanism and blocking of the risk transmission paths. The results of this study can provide corresponding policy implications for the emergency management of sudden public health events.

Data-driven methods for present and future pandemics: Monitoring, modelling and managing

This survey analyses the role of data-driven methodologies for pandemic modelling and control. We provide a roadmap from the access to epidemiological data sources to the control of epidemic phenomena. We review the available methodologies and discuss the challenges in the development of data-driven strategies to combat the spreading of infectious diseases. Our aim is to bring together several different disciplines required to provide a holistic approach to epidemic analysis, such as data science, epidemiology, and systems-and-control theory. A 3M-analysis is presented, whose three pillars are: Monitoring, Modelling and Managing. The focus is on the potential of data-driven schemes to address three different challenges raised by a pandemic: (i) monitoring the epidemic evolution and assessing the effectiveness of the adopted countermeasures; (ii) modelling and forecasting the spread of the epidemic; (iii) making timely decisions to manage, mitigate and suppress the contagion. For each step of this roadmap, we review consolidated theoretical approaches (including data-driven methodologies that have been shown to be successful in other contexts) and discuss their application to past or present epidemics, such as Covid-19, as well as their potential application to future epidemics.

Small-world effects in a modified epidemiological model with mutation and permanent immune mechanism

Pandemic with mutation and permanent immune spreading in a small-world network described is studied by a modified SIR model, with consideration of mutation-immune mechanism. First, a novel mutation-immune model is proposed to modify the classical SIR model to simulate the transmission of mutable viruses that can be permanently immunized in small-world networks. Then, the influences of the size, coordination number and disorder parameter of the small-world network on the spread of the epidemic are analyzed in detail. Finally, the influences of mutation cycle and infection rate on epidemic transmission in small-world network are investigated further. The results show that the structure of the small-world network and the virus mutation cycle have an important impact on the spread of the epidemic. For viruses that can be permanently immunized, virus mutation is equivalent to making the immune cycle of human beings from infinite to finite. The dynamical behavior of the modified SIR epidemic model changes from an irregular, low-amplitude evolution at small disorder parameter to a spontaneous state of wide amplitude oscillations at large disorder parameter. Moreover, similar transition can also be found in increasing mutation cycle parameter. The maximum valid variation mutation decreases with the increase of disorder parameter and coordination number, but increase with respect to system size. In addition above, as the infection rate increases, the fraction of the infected increases and then decreases. As the mutation cycle increases, the time-average fraction of the infected and the infection rate corresponding to the maximum time-average fraction of the infected also decrease. As one conclusion, the results could give a deep understanding Pandemic with mutation and permanent immune spreading, from viewpoint of small-world network.

Modeling and prediction of the 2019 coronavirus disease spreading in China incorporating human migration data

This study integrates the daily intercity migration data with the classic Susceptible-Exposed-Infected-Removed (SEIR) model to construct a new model suitable for describing the dynamics of epidemic spreading of Coronavirus Disease 2019 (COVID-19) in China. Daily intercity migration data for 367 cities in China were collected from Baidu Migration, a mobile-app based human migration tracking data system. Early outbreak data of infected, recovered and death cases from official source (from January 24 to February 16, 2020) were used for model fitting. The set of model parameters obtained from best data fitting using a constrained nonlinear optimisation procedure was used for estimation of the dynamics of epidemic spreading in the following months. The work was completed on February 19, 2020. Our results showed that the number of infections in most cities in China would peak between mid February to early March 2020, with about 0.8%, less than 0.1% and less than 0.01% of the population eventually infected in Wuhan, Hubei Province and the rest of China, respectively. Moreover, for most cities outside and within Hubei Province (except Wuhan), the total number of infected individuals is expected to be less than 300 and 4000, respectively.

Modeling and prediction of the 2019 coronavirus disease spreading in China incorporating human migration data

This study integrates the daily intercity migration data with the classic Susceptible-Exposed-Infected-Removed (SEIR) model to construct a new model suitable for describing the dynamics of epidemic spreading of Coronavirus Disease 2019 (COVID-19) in China. Daily intercity migration data for 367 cities in China were collected from Baidu Migration, a mobile-app based human migration tracking data system. Early outbreak data of infected, recovered and death cases from official source (from January 24 to February 16, 2020) were used for model fitting. The set of model parameters obtained from best data fitting using a constrained nonlinear optimisation procedure was used for estimation of the dynamics of epidemic spreading in the following months. The work was completed on February 19, 2020. Our results showed that the number of infections in most cities in China would peak between mid February to early March 2020, with about 0.8%, less than 0.1% and less than 0.01% of the population eventually infected in Wuhan, Hubei Province and the rest of China, respectively. Moreover, for most cities outside and within Hubei Province (except Wuhan), the total number of infected individuals is expected to be less than 300 and 4000, respectively.

Heatmap centrality: A new measure to identify super-spreader nodes in scale-free networks

The identification of potential super-spreader nodes within a network is a critical part of the study and analysis of real-world networks. Motivated by a new interpretation of the "shortest path" between two nodes, this paper explores the properties of the heatmap centrality by comparing the farness of a node with the average sum of farness of its adjacent nodes in order to identify influential nodes within the network. As many real-world networks are often claimed to be scale-free, numerical experiments based upon both simulated and real-world undirected and unweighted scale-free networks are used to illustrate the effectiveness of the proposed "shortest path" based measure with regards to its CPU run time and ranking of influential nodes.

Prediction of COVID-19 spreading profiles in South Korea, Italy and Iran by data-driven coding

This work applies a data-driven coding method for prediction of the COVID-19 spreading profile in any given population that shows an initial phase of epidemic progression. Based on the historical data collected for COVID-19 spreading in 367 cities in China and the set of parameters of the augmented Susceptible-Exposed-Infected-Removed (SEIR) model obtained for each city, a set of profile codes representing a variety of transmission mechanisms and contact topologies is formed. By comparing the data of an early outbreak of a given population with the complete set of historical profiles, the best fit profiles are selected and the corresponding sets of profile codes are used for prediction of the future progression of the epidemic in that population. Application of the method to the data collected for South Korea, Italy and Iran shows that peaks of infection cases are expected to occur before mid April, the end of March and the end of May 2020, and that the percentage of population infected in each city or region will be less than 0.01%, 0.5% and 0.5%, for South Korea, Italy and Iran, respectively.

A review of mathematical modeling, artificial intelligence and datasets used in the study, prediction and management of COVID-19

In the past few months, several works were published in regards to the dynamics and early detection of COVID-19 via mathematical modeling and Artificial intelligence (AI). The aim of this work is to provide the research community with comprehensive overview of the methods used in these studies as well as a compendium of available open source datasets in regards to COVID-19. In all, 61 journal articles, reports, fact sheets, and websites dealing with COVID-19 were studied and reviewed. It was found that most mathematical modeling done were based on the Susceptible-Exposed-Infected-Removed (SEIR) and Susceptible-infected-recovered (SIR) models while most of the AI implementations were Convolutional Neural Network (CNN) on X-ray and CT images. In terms of available datasets, they include aggregated case reports, medical images, management strategies, healthcare workforce, demography, and mobility during the outbreak. Both Mathematical modeling and AI have both shown to be reliable tools in the fight against this pandemic. Several datasets concerning the COVID-19 have also been collected and shared open source. However, much work is needed to be done in the diversification of the datasets. Other AI and modeling applications in healthcare should be explored in regards to this COVID-19.

Modelling Strong Control Measures for Epidemic Propagation With Networks-A COVID-19 Case Study

We show that precise knowledge of epidemic transmission parameters is not required to build an informative model of the spread of disease. We propose a detailed model of the topology of the contact network under various external control regimes and demonstrate that this is sufficient to capture the salient dynamical characteristics and to inform decisions. Contact between individuals in the community is characterised by a contact graph, the structure of that contact graph is selected to mimic community control measures. Our model of city-level transmission of an infectious agent (SEIR model) characterises spread via a (a) scale-free contact network (no control); (b) a random graph (elimination of mass gatherings); and (c) small world lattice (partial to full lockdown-"social" distancing). This model exhibits good qualitative agreement between simulation and data from the 2020 pandemic spread of a novel coronavirus. Estimates of the relevant rate parameters of the SEIR model are obtained and we demonstrate the robustness of our model predictions under uncertainty of those estimates. The social context and utility of this work is identified, contributing to a highly effective pandemic response in Western Australia.

The influence of society's mesoscopic structure on the rate of epidemic spreading

In this study, we investigate the role of the mesoscopic structural properties of a scale-free social network on the contagion spreading. We focus on both the exponent of power-law community size distribution function (β) and the mixing parameter (μ). Findings show that increasing β reduces the rate of epidemic spreading. On the other hand, increasing μ increases the rate of epidemic spreading. Two innovating parameters, Temperature and cos θ, are introduced here to analyze these effects.

Behavior of susceptible-vaccinated-infected-recovered epidemics with diversity in the infection rate of individuals

We study a susceptible-vaccinated-infected-recovered (SVIR) epidemic-spreading model with diversity of infection rate of the individuals. By means of analytical arguments as well as extensive computer simulations, we demonstrate that the heterogeneity in infection rate can either impede or accelerate the epidemic spreading, which depends on the amount of vaccinated individuals introduced in the population as well as the contact pattern among the individuals. Remarkably, as long as the individuals with different capability of acquiring the disease interact with unequal frequency, there always exist a cross point for the fraction of vaccinated, below which the diversity of infection rate hinders the epidemic spreading and above which expedites it. The overall results are robust to the SVIR dynamics defined on different population models; the possible applications of the results are discussed.

Controlling epidemic spread by social distancing: do it well or not at all

BACKGROUND

Existing epidemiological models have largely tended to neglect the impact of individual behaviour on the dynamics of diseases. However, awareness of the presence of illness can cause people to change their behaviour by, for example, staying at home and avoiding social contacts. Such changes can be used to control epidemics but they exact an economic cost. Our aim is to study the costs and benefits of using individual-based social distancing undertaken by healthy individuals as a form of control.

METHODS

Our model is a standard SIR model superimposed on a spatial network, without and with addition of small-world interactions. Disease spread is controlled by allowing susceptible individuals to temporarily reduce their social contacts in response to the presence of infection within their local neighbourhood. We ascribe an economic cost to the loss of social contacts, and weigh this against the economic benefit gained by reducing the impact of the epidemic. We study the sensitivity of the results to two key parameters, the individuals' attitude to risk and the size of the awareness neighbourhood.

RESULTS

Depending on the characteristics of the epidemic and on the relative economic importance of making contacts versus avoiding infection, the optimal control is one of two extremes: either to adopt a highly cautious control, thereby suppressing the epidemic quickly by drastically reducing contacts as soon as disease is detected; or else to forego control and allow the epidemic to run its course. The worst outcome arises when control is attempted, but not cautiously enough to cause the epidemic to be suppressed. The next main result comes from comparing the size of the neighbourhood of which individuals are aware to that of the neighbourhood within which transmission can occur. The control works best when these sizes match and is particularly ineffective when the awareness neighbourhood is smaller than the infection neighbourhood. The results are robust with respect to inclusion of long-range, small-world links which destroy the spatial structure, regardless of whether individuals can or cannot control them. However, addition of many non-local links eventually makes control ineffective.

CONCLUSIONS

These results have implications for the design of control strategies using social distancing: a control that is too weak or based upon inaccurate knowledge, may give a worse outcome than doing nothing.

Staged progression model for epidemic spread on homogeneous and heterogeneous networks

In this paper, epidemic spread with the staged progression model on homogeneous and heterogeneous networks is studied. First, the epidemic threshold of the simple staged progression model is given. Then the staged progression model with birth and death is also considered. The case where infectivity is a nonlinear function of the nodes' degree is discussed, too. Finally, the analytical results are verified by numerical simulations.

Stability of the spreading in small-world network with predictive controller

In this Letter, we apply the predictive control strategy to suppress the propagation of diseases or viruses in small-world network. The stability of small-world spreading model with predictive controller is investigated. The sufficient and necessary stability condition is given, which is closely related to the controller parameters and small-world rewiring probability p. Our simulations discover a phenomenon that, with the fixed predictive controller parameters, the spreading dynamics become more and more stable when p decreases from a larger value to a smaller one, and the suitable controller parameters can effectively suppress the spreading behaviors even when p varies within the whole spectrum, and the unsuitable controller parameters can lead to oscillation when p lies within a certain range.

Transmission and control of an emerging influenza pandemic in a small-world airline network

The avian influenza virus H5N1 and the 2009 swine flu H1N1 are potentially serious pandemic threats to human health, and air travel readily facilitates the spread of infectious diseases. However, past studies have not yet incorporated the effects of air travel on the transmission of influenza in the construction of mathematical epidemic models. Therefore, this paper focused on the human-to-human transmission of influenza, and investigated the effects of air travel activities on an influenza pandemic in a small-world network. These activities of air travel include passengers' consolidation, conveyance and distribution in airports and flights. Dynamic transmission models were developed to assess the expected burdens of the pandemic, with and without control measures. This study also investigated how the small-world properties of an air transportation network facilitate the spread of influenza around the globe. The results show that, as soon as the influenza is spread to the top 50 global airports, the transmission is greatly accelerated. Under the constraint of limited resources, a strategy that first applies control measures to the top 50 airports after day 13 and then soon afterwards to all other airports may result in remarkable containment effectiveness. As the infectiousness of the disease increases, it will expand the scale of the pandemic, and move the start time of the pandemic ahead.

Model and Dynamic Behavior of Malware Propagation over Wireless Sensor Networks

Based on the inherent characteristics of wireless sensor networks (WSN), the dynamic behavior of malware propagation in flat WSN is analyzed and investigated. A new model is proposed using 2-D cellular automata (CA), which extends the traditional definition of CA and establishes whole transition rules for malware propagation in WSN. Meanwhile, the validations of the model are proved through theoretical analysis and simulations. The theoretical analysis yields closed-form expressions which show good agreement with the simulation results of the proposed model. It is shown that the malware propaga-tion in WSN unfolds neighborhood saturation, which dominates the effects of increasing infectivity and limits the spread of the malware. MAC mechanism of wireless sensor networks greatly slows down the speed of malware propagation and reduces the risk of large-scale malware prevalence in these networks. The proposed model can describe accurately the dynamic behavior of malware propagation over WSN, which can be applied in developing robust and efficient defense system on WSN.

Global behavior of epidemic transmission on heterogeneous networks via two distinct routes

In the study of epidemic spreading two natural questions are: whether the spreading of epidemics on heterogenous networks have multiple routes, and whether the spreading of an epidemic is a local or global behavior? In this paper, we answer the above two questions by studying the SIS model on heterogenous networks, and give the global conditions for the endemic state when two distinct routes with uniform rate of infection are considered. The analytical results are also verified by numerical simulations.

Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization

We examine epidemic thresholds for disease spread using susceptible-infected-susceptible models on scale-free networks with variable infectivity. Infectivity between nodes is modeled as a piecewise linear function of the node degree (rather than the less realistic linear transformation considered previously). With this nonlinear infectivity, we derive conditions for the epidemic threshold to be positive. The effects of various immunization schemes including ring and targeted vaccination are studied and compared. We find that both targeted and ring immunization strategies compare favorably to a proportional scheme in terms of effectiveness.

Network-Based Analysis of Beijing SARS Data

In this paper, we analyze Beijing SARS data using methods developed from the complex network analysis literature. Three kinds of SARS-related networks were constructed and analyzed, including the patient contact network, the weighted location (district) network, and the weighted occupation network. We demonstrate that a network-based data analysis framework can help evaluate various control strategies. For instance, in the case of SARS, a general randomized immunization control strategy may not be effective. Instead, a strategy that focuses on nodes (e.g., patients, locations, or occupations) with high degree and strength may lead to more effective outbreak control and management.

Behaviors of susceptible-infected epidemics on scale-free networks with identical infectivity

In this paper, we propose a susceptible-infected model with identical infectivity, in which, at every time step, each node can only contact a constant number of neighbors. We implemented this model on scale-free networks, and found that the infected population grows in an exponential form with the time scale proportional to the spreading rate. Furthermore, by numerical simulation, we demonstrated that the targeted immunization of the present model is much less efficient than that of the standard susceptible-infected model. Finally, we investigate a fast spreading strategy when only local information is available. Different from the extensively studied path-finding strategy, the strategy preferring small-degree nodes is more efficient than that preferring large-degree nodes. Our results indicate the existence of an essential relationship between network traffic and network epidemic on scale-free networks.

Congruent epidemic models for unstructured and structured populations: analytical reconstruction of a 2003 SARS outbreak

Both the threat of bioterrorism and the natural emergence of contagious diseases underscore the importance of quantitatively understanding disease transmission in structured human populations. Over the last few years, researchers have advanced the mathematical theory of scale-free networks and used such theoretical advancements in pilot epidemic models. Scale-free contact networks are particularly interesting in the realm of mathematical epidemiology, primarily because these networks may allow meaningfully structured populations to be incorporated in epidemic models at moderate or intermediate levels of complexity. Moreover, a scale-free contact network with node degree correlation is in accord with the well-known preferred mixing concept. The present author describes a semi-empirical and deterministic epidemic modeling approach that (a) focuses on time-varying rates of disease transmission in both unstructured and structured populations and (b) employs probability density functions to characterize disease progression and outbreak controls. Given an epidemic curve for a historical outbreak, this modeling approach calls for Monte Carlo calculations (that define the average new infection rate) and solutions to integro-differential equations (that describe outbreak dynamics in an aggregate population or across all network connectivity classes). Numerical results are obtained for the 2003 SARS outbreak in Taiwan and the dynamical implications of time-varying transmission rates and scale-free contact networks are discussed in some detail.