Travel behavior adjustment based epidemic spreading model and prediction for COVID-19

Owing to the continuous variant of the COVID-19 virus, the present epidemic may persist for a long time, and each breakout displays strongly region/time-dependent characteristics. Predicting each specific burst is the basic task for the corresponding strategies. However, the refinement of prevention and control measures usually means the limitation of the existing records of the evolution of the spread, which leads to a special difficulty in making predictions. Taking into account the interdependence of people' s travel behaviors and the epidemic spreading, we propose a modified logistic model to mimic the COVID-19 epidemic spreading, in order to predict the evolutionary behaviors for a specific bursting in a megacity with limited epidemic related records. It continuously reproduced the COVID-19 infected records in Shanghai, China in the period from March 1 to June 28, 2022. From December 7, 2022 when Mainland China adopted new detailed prevention and control measures, the COVID-19 epidemic broke out nationwide, and the infected people themselves took "ibuprofen” widely to relieve the symptoms of fever. A reasonable assumption is that the total number of searches for the word "ibuprofen” is a good representation of the number of infected people. By using the number of searching for the word "ibuprofen” provided on Baidu, a famous searching platform in Mainland China, we estimate the parameters in the modified logistic model and predict subsequently the epidemic spreading behavior in Shanghai, China starting from December 1, 2022. This situation lasted for 72 days. The number of the infected people increased exponentially in the period from the beginning to the 24th day, reached a summit on the 31st day, and decreased exponentially in the period from the 38th day to the end. Within the two weeks centered at the summit, the increasing and decreasing speeds are both significantly small, but the increased number of infected people each day was significantly large. The characteristic for this prediction matches very well with that for the number of metro passengers in Shanghai. It is suggested that the relevant departments should establish a monitoring system composed of some communities, hospitals, etc. according to the sampling principle in statistics to provide reliable prediction records for researchers. © 2023 Chinese Physical Society.

Digital cities and the spread of COVID-19: Characterizing the impact of non-pharmaceutical interventions in five cities in Spain.

Mathematical modeling has been fundamental to achieving near real-time accurate forecasts of the spread of COVID-19. Similarly, the design of non-pharmaceutical interventions has played a key role in the application of policies to contain the spread. However, there is less work done regarding quantitative approaches to characterize the impact of each intervention, which can greatly vary depending on the culture, region, and specific circumstances of the population under consideration. In this work, we develop a high-resolution, data-driven agent-based model of the spread of COVID-19 among the population in five Spanish cities. These populations synthesize multiple data sources that summarize the main interaction environments leading to potential contacts. We simulate the spreading of COVID-19 in these cities and study the effect of several non-pharmaceutical interventions. We illustrate the potential of our approach through a case study and derive the impact of the most relevant interventions through scenarios where they are suppressed. Our framework constitutes a first tool to simulate different intervention scenarios for decision-making.

A dynamic design strategy of epidemic spreading parameters based on data driven

When modeling and fitting various kinds of epidemic outbreaks, the value of parameters has always been an important practical problem for many scholars. In the existing studies, most of the authors select a fixed parameter by referring to the relevant literature or combined with medical experiments. With the help of Euler difference transformation and the characteristics of the solution of linear equations, we innovatively propose a dynamic update strategy of epidemic diffusion parameters based on data-driven in this study in order to overcome the above limitation. The method can help decision-makers to calculate the optimal parameters of epidemic spread by combining the real-time update data. A case study is conducted with the COVID-19 data of Wuhan. The results show that the dynamic parameter update strategy designed in this paper can effectively improve the accuracy of the evolution prediction of epidemic outbreaks, which provides an important decision support for the accurate allocation of government emergency resources. © 2023 Northeast University. All rights reserved.

The coevolution of the spread of a disease and competing opinions in multiplex networks.

The COVID-19 pandemic has resulted in a proliferation of conflicting opinions on physical distancing across various media platforms, which has had a significant impact on human behavior and the transmission dynamics of the disease. Inspired by this social phenomenon, we present a novel UAP-SIS model to study the interaction between conflicting opinions and epidemic spreading in multiplex networks, in which individual behavior is based on diverse opinions. We distinguish susceptibility and infectivity among individuals who are unaware, pro-physical distancing and anti-physical distancing, and we incorporate three kinds of mechanisms for generating individual awareness. The coupled dynamics are analyzed in terms of a microscopic Markov chain approach that encompasses the aforementioned elements. With this model, we derive the epidemic threshold which is related to the diffusion of competing opinions and their coupling configuration. Our findings demonstrate that the transmission of the disease is shaped in a significant manner by conflicting opinions, due to the complex interaction between such opinions and the disease itself. Furthermore, the implementation of awareness-generating mechanisms can help to mitigate the overall prevalence of the epidemic, and global awareness and self-awareness can be interchangeable in certain instances. To effectively curb the spread of epidemics, policymakers should take steps to regulate social media and promote physical distancing as the mainstream opinion.

Coupled disease-vaccination behavior dynamic analysis and its application in COVID-19 pandemic.

Predicting the evolutionary dynamics of the COVID-19 pandemic is a complex challenge. The complexity increases when the vaccination process dynamic is also considered. In addition, when applying a voluntary vaccination policy, the simultaneous behavioral evolution of individuals who decide whether and when to vaccinate must be included. In this paper, a coupled disease-vaccination behavior dynamic model is introduced to study the coevolution of individual vaccination strategies and infection spreading. We study disease transmission by a mean-field compartment model and introduce a non-linear infection rate that takes into account the simultaneity of interactions. Besides, the evolutionary game theory is used to investigate the contemporary evolution of vaccination strategies. Our findings suggest that sharing information with the entire population about the negative and positive consequences of infection and vaccination is beneficial as it boosts behaviors that can reduce the final epidemic size. Finally, we validate our transmission mechanism on real data from the COVID-19 pandemic in France.

Epidemic Waves and Exact Solutions of a Sequence of Nonlinear Differential Equations Connected to the SIR Model of Epidemics.

The SIR model of epidemic spreading can be reduced to a nonlinear differential equation with an exponential nonlinearity. This differential equation can be approximated by a sequence of nonlinear differential equations with polynomial nonlinearities. The equations from the obtained sequence are treated by the Simple Equations Method (SEsM). This allows us to obtain exact solutions to some of these equations. We discuss several of these solutions. Some (but not all) of the obtained exact solutions can be used for the description of the evolution of epidemic waves. We discuss this connection. In addition, we use two of the obtained solutions to study the evolution of two of the COVID-19 epidemic waves in Bulgaria by a comparison of the solutions with the available data for the infected individuals.

Influences of obstacle factors on the transmission trends of respiratory infectious diseases in indoor public places

Public facilities are important transmission places for respiratory infectious diseases (e.g., COVID-19), due to the frequent crowd interactions inside. Usually, changes of obstacle factors can affect the movements of human crowds and result in different epidemic transmissions among individuals. However, most related studies only focus on the specific scenarios, but the common rules are usually ignored for the impacts of obstacles' spatial elements on epidemic transmission. To tackle these problems, this study aims to evaluate the impacts of three spatial factors of obstacles (i.e., size, quantity, and placement) on infection spreading trends in two-dimension, which can provide scientific and concise spatial design guidelines for indoor public places. Firstly, we used the obstacle area proportion as the indicator of the size factor, gave the mathematical expression of the quantity factor, and proposed the walkable-space distribution indicator to represent the placement factor by introducing the Space Syntax. Secondly, two spreading epidemic indicators (i.e., daily new cases and people's average exposure risk) were estimated based on the fundamental model named exposure risk with the virion-laden particles, which accurately forecasted the disease spreading between individuals. Thirdly, 120 indoor scenarios were built and simulated, based on which the value of independent and dependent variables can be measured. Besides, structural equation modeling was employed to examine the effects of obstacle factors on epidemic transmissions. Finally, three obstacle-related guidelines were provided for policymakers to mitigate the disease spreading: minimizing the size of obstacles, dividing the obstacle into more sub-ones, and placing obstacles evenly distributed in space. © 2022 Elsevier Ltd

Bifurcation analysis of the Microscopic Markov Chain Approach to contact-based epidemic spreading in networks

The dynamics of many epidemic compartmental models for infectious diseases that spread in a single host population present a second-order phase transition. This transition occurs as a function of the infectivity parameter, from the absence of infected individuals to an endemic state. Here, we study this transition, from the perspective of dynamical systems, for a discrete-time compartmental epidemic model known as Microscopic Markov Chain Approach, whose applicability for forecasting future scenarios of epidemic spreading has been proved very useful during the COVID-19 pandemic. We show that there is an endemic state which is stable and a global attractor and that its existence is a consequence of a transcritical bifurcation. This mathematical analysis grounds the results of the model in practical applications. © 2022 Elsevier Ltd

Effective node vaccination and containing strategies to halt SIR epidemic spreading in real-world face-to-face contact networks

We model the COVID-19 spreading by running SIR Monte-Carlo simulations in four real face-to-face contact networks. We evaluate the effectiveness of the 'facemask use' and 'vaccination policies' to curb epidemic spreading. We model the facemask use policy by assuming a lower individual infection probability β. We found that while this strategy can delay the disease spreading, it does not significantly reduce the total number of infected individuals (TI), as 80% of the total population still is infected at the end of the epidemic. We model vaccination by setting individual's infection probability β=0, which is equivalent to remove nodes/individuals from the network. The vaccination was found to be very effective. Even with a partial vaccination of 30% of the population nodes selected considering their centrality measure ranking, such as degree, betweenness, or PageRank, it was possible to reduce the TI of 14%. Finally, yet importantly, random partial vaccination is not effective at all, meaning that most of the unvaccinated population will be infected. © 2022 IEEE.

Mass Testing and Proactiveness Affect Epidemic Spreading.

The detection and management of diseases become quite complicated when pathogens contain asymptomatic phenotypes amongst their ranks, as evident during the recent COVID-19 pandemic. Spreading of diseases has been studied extensively under the paradigm of susceptible-infected-recovered-deceased (SIRD) dynamics. Various game-theoretic approaches have also addressed disease spread, many of which consider S , I , R , and D as strategies rather than as states. Remarkably, most studies from the above approaches do not account for the distinction between the symptomatic or asymptomatic aspect of the disease. It is well-known that precautionary measures like washing hands, wearing masks and social distancing significantly mitigate the spread of many contagious diseases. Herein, we consider the adoption of such precautions as strategies and treat S , I , R , and D as states. We also attempt to capture the differences in epidemic spreading arising from symptomatic and asymptomatic diseases on various network topologies. Through extensive computer simulations, we examine that the cost of maintaining precautionary measures as well as the extent of mass testing in a population affects the final fraction of socially responsible individuals. We observe that the lack of mass testing could potentially lead to a pandemic in case of asymptomatic diseases. Network topology also seems to play an important role. We further observe that the final fraction of proactive individuals depends on the initial fraction of both infected as well as proactive individuals. Additionally, edge density can significantly influence the overall outcome. Our findings are in broad agreement with the lessons learnt from the ongoing COVID-19 pandemic.

Optimal curing resource allocation for epidemic spreading processes

The networked Susceptible–Infected–Susceptible (SIS) model is one of the well-developed models for epidemic spreading processes in networked systems. For a network that has an unstable healthy state, and follows the networked SIS model, a problem of interest is to stabilize the healthy state by increasing the curing rates of individuals, while minimizing the total cost associated with the additional curing rates over the network. Here this minimum control budget problem is reformulated as a standard semidefinite programming problem and an iterative algorithm is developed for determining the optimal additional curing rates for each agent in the network. We address arbitrary undirected topologies, with both symmetric and asymmetric infection rates. For a number of topologies, solutions have been provided for the case of uniform curing and infection rates for all possible ranges of the effective infection rate. Moreover, we have investigated the case of discrete-time SIS models and have shown that the algorithm developed based on the continuous-time model can be extended to this case. Based on the daily COVID-19 infections over the USA, the curing and infection rates have been estimated for a simulation scenario. Using these simulations, the algorithm is shown to have lower complexity than the well-known SDPT3 tool, and to have orders of magnitude lower computational and memory requirements.

Leveraging Human Mobility Data for Efficient Parameter Estimation in Epidemic Models of COVID-19

Effectively predicting the evolution of COVID-19 is of great significance to contain the pandemic. Extensive previous studies proposed a great number of SIR variants, which are efficient to capture the transmission characteristics of COVID-19. However, the parameter estimation methods in previous studies are based on data from epidemiological investigations, which inevitably have caused a large delay. The popularity of digital trajectory data world-wide makes it possible to understand epidemic spreading from human mobility perspective. The major advantage of digital trajectory data lies in that the co-location level of a population is reflected at every moment, making it possible to forecast the evolution in advance. We showed that the mobility data contributed by mobile phone users could be exploited to estimate the contact probability between individuals, thus revealing the dynamic transmission of COVID-19. Specifically, we developed an estimation method to obtain human co-location levels and quantified the variations of human mobility during the epidemic. Then, we extended the infection rate with a real-time co-location level to further forecast the transmission of an epidemic, predicting the epidemic size much more accurately than conventional methods. Finally, the proposed method was applied to evaluate the quantitative effect of different non-pharmacological interventions by predicting the epidemic situations with various mobility characteristics. The empirical results and simulations corroborated our theoretical analysis, providing effective guidance to contain the pandemic. IEEE

Analysis of Epidemic Vaccination Dilemma Considering Pathogen Evolution Based on SVIR Model and Evolutionary Game

The global pandemic of COVID-19 warns that pathogens constantly evolve in the epidemic spreading. Therefore, we assume that the pathogens will mutate at a certain probability, the transmission rate of mutant strains increases meanwhile the cost of infection decreases, and the vaccination is only effective for the original strain but ineffective to the mutant strain. Extensive numerical simulations show that in addition to the virus mutation rate, it will lead to more interesting results, with the increase of the transmission rate of the mutant strain and the cost of vaccination, the vaccination rate will gradually decrease. Copyright © World Academic Press, World Academic Union.

Influences of obstacle factors on the transmission trends of respiratory infectious diseases in indoor public places

Public facilities are important transmission places for respiratory infectious diseases (e.g., COVID-19), due to the frequent crowd interactions inside. Usually, changes of obstacle factors can affect the movements of human crowds and result in different epidemic transmissions among individuals. However, most related studies only focus on the specific scenarios, but the common rules are usually ignored for the impacts of obstacles' spatial elements on epidemic transmission. To tackle these problems, this study aims to evaluate the impacts of three spatial factors of obstacles (i.e., size, quantity, and placement) on infection spreading trends in two-dimension, which can provide scientific and concise spatial design guidelines for indoor public places. Firstly, we used the obstacle area proportion as the indicator of the size factor, gave the mathematical expression of the quantity factor, and proposed the walkable-space distribution indicator to represent the placement factor by introducing the Space Syntax. Secondly, two spreading epidemic indicators (i.e., daily new cases and people's average exposure risk) were estimated based on the fundamental model named exposure risk with the virion-laden particles, which accurately forecasted the disease spreading between individuals. Thirdly, 120 indoor scenarios were built and simulated, based on which the value of independent and dependent variables can be measured. Besides, structural equation modeling was employed to examine the effects of obstacle factors on epidemic transmissions. Finally, three obstacle-related guidelines were provided for policymakers to mitigate the disease spreading: minimizing the size of obstacles, dividing the obstacle into more sub-ones, and placing obstacles evenly distributed in space.

The effect of information-driven resource allocation on the propagation of epidemic with incubation period.

In the pandemic of COVID-19, there are exposed individuals who are infected but lack distinct clinical symptoms. In addition, the diffusion of related information drives aware individuals to spontaneously seek resources for protection. The special spreading characteristic and coevolution of different processes may induce unexpected spreading phenomena. Thus we construct a three-layered network framework to explore how information-driven resource allocation affects SEIS (susceptible-exposed-infected-susceptible) epidemic spreading. The analyses utilizing microscopic Markov chain approach reveal that the epidemic threshold depends on the topology structure of epidemic network and the processes of information diffusion and resource allocation. Conducting extensive Monte Carlo simulations, we find some crucial phenomena in the coevolution of information diffusion, resource allocation and epidemic spreading. Firstly, when E-state (exposed state, without symptoms) individuals are infectious, long incubation period results in more E-state individuals than I-state (infected state, with obvious symptoms) individuals. Besides, when E-state individuals have strong or weak infectious capacity, increasing incubation period has an opposite effect on epidemic propagation. Secondly, the short incubation period induces the first-order phase transition. But enhancing the efficacy of resources would convert the phase transition to a second-order type. Finally, comparing the coevolution in networks with different topologies, we find setting the epidemic layer as scale-free network can inhibit the spreading of the epidemic.

Simple Equations Method (SEsM): An Effective Algorithm for Obtaining Exact Solutions of Nonlinear Differential Equations.

Exact solutions of nonlinear differential equations are of great importance to the theory and practice of complex systems. The main point of this review article is to discuss a specific methodology for obtaining such exact solutions. The methodology is called the SEsM, or the Simple Equations Method. The article begins with a short overview of the literature connected to the methodology for obtaining exact solutions of nonlinear differential equations. This overview includes research on nonlinear waves, research on the methodology of the Inverse Scattering Transform method, and the method of Hirota, as well as some of the nonlinear equations studied by these methods. The overview continues with articles devoted to the phenomena described by the exact solutions of the nonlinear differential equations and articles about mathematical results connected to the methodology for obtaining such exact solutions. Several articles devoted to the numerical study of nonlinear waves are mentioned. Then, the approach to the SEsM is described starting from the Hopf-Cole transformation, the research of Kudryashov on the Method of the Simplest Equation, the approach to the Modified Method of the Simplest Equation, and the development of this methodology towards the SEsM. The description of the algorithm of the SEsM begins with the transformations that convert the nonlinearity of the solved complicated equation into a treatable kind of nonlinearity. Next, we discuss the use of composite functions in the steps of the algorithms. Special attention is given to the role of the simple equation in the SEsM. The connection of the methodology with other methods for obtaining exact multisoliton solutions of nonlinear differential equations is discussed. These methods are the Inverse Scattering Transform method and the Hirota method. Numerous examples of the application of the SEsM for obtaining exact solutions of nonlinear differential equations are demonstrated. One of the examples is connected to the exact solution of an equation that occurs in the SIR model of epidemic spreading. The solution of this equation can be used for modeling epidemic waves, for example, COVID-19 epidemic waves. Other examples of the application of the SEsM methodology are connected to the use of the differential equation of Bernoulli and Riccati as simple equations for obtaining exact solutions of more complicated nonlinear differential equations. The SEsM leads to a definition of a specific special function through a simple equation containing polynomial nonlinearities. The special function contains specific cases of numerous well-known functions such as the trigonometric and hyperbolic functions and the elliptic functions of Jacobi, Weierstrass, etc. Among the examples are the solutions of the differential equations of Fisher, equation of Burgers-Huxley, generalized equation of Camassa-Holm, generalized equation of Swift-Hohenberg, generalized Rayleigh equation, etc. Finally, we discuss the connection between the SEsM and the other methods for obtaining exact solutions of nonintegrable nonlinear differential equations. We present a conjecture about the relationship of the SEsM with these methods.

Understanding the Interplay Between Herd Behaviors and Epidemic Spreading Using Federated Evolutionary Games

The recent COVID-19 pandemic has led to an increasing interest in the modeling and analysis of infectious diseases. Our social behaviors in the daily lives have been significantly affected by the pandemic. In this paper, we propose a federated evolutionary game-theoretic framework to study the coupling of herd behaviors changes and epidemics spreading. Our framework extends the classical degree-based mean-field epidemic model over complex networks by integrating it with the evolutionary game dynamics. The statistically equivalent individuals in a population choose their social activity intensities based on the fitness or the payoffs that depend on the state of the epidemics. Meanwhile, the spread of infectious diseases over the complex network is reciprocally influenced by the players' social activities. We address the challenge of federated dynamics by breaking the analysis into the studies of the stationary properties of the epidemic for given herd behavior and the structural properties of the game for a given epidemic process. We use numerical experiments to show that our framework enables the prediction of the historical COVID-19 statistics. © 2022 American Automatic Control Council.

Safe Policy Design for Controlling Epidemic Spreading under Heterogeneous Testing Capabilities

This paper studies a model that captures epidemic spreading in a population with heterogeneous testing capabilities. The detection of the disease is faster in a subpopulation because of access to better testing capabilities, whereas another subpopulation relies on standard testing to confirm positive cases once individual have manifested symptoms. This model is a particular case of a recently proposed vectorized SIR model, for which we characterize various invariance properties and the stability properties of its set of equilibria. We leverage these analytical results to design social distancing policies that guarantee that the impact of the pandemic satisfies certain specifications, namely, that the total capacity of the healthcare system does not get overburdened and that the total number of infections throughout the pandemic remains below a thresh-old. Simulations illustrate the extent to which higher testing capabilities allow for more lenient social distancing policies. © 2022 American Automatic Control Council.

Competitive epidemic spreading over networks

In this letter, we consider an epidemic model for two competitive viruses spreading over a metapopulation network, termed the ‘bivirus model’for convenience. The dynamics are described by a networked continuous-time dynamical system, with each node representing a population and edges representing infection pathways for the viruses. We survey existing results on the bivirus model beginning with the nature of the equilibria, including whether they are isolated, and where they exist within the state space with the corresponding interpretation in the context of epidemics. We identify key convergence results, including the conclusion that for generic system parameters, global convergence occurs for almost all initial conditions. Conditions relating to the stability properties of various equilibria are also presented. In presenting these results, we also recall some of the key tools and theories used to secure them. We conclude by discussing the various open problems, ranging from control and network optimization, to further characterization of equilibria, and finally extensions such as modeling three or more viruses. IEEE

Epidemic dynamics on higher-dimensional small world networks.

Dimension governs dynamical processes on networks. The social and technological networks which we encounter in everyday life span a wide range of dimensions, but studies of spreading on finite-dimensional networks are usually restricted to one or two dimensions. To facilitate investigation of the impact of dimension on spreading processes, we define a flexible higher-dimensional small world network model and characterize the dependence of its structural properties on dimension. Subsequently, we derive mean field, pair approximation, intertwined continuous Markov chain and probabilistic discrete Markov chain models of a COVID-19-inspired susceptible-exposed-infected-removed (SEIR) epidemic process with quarantine and isolation strategies, and for each model identify the basic reproduction number R 0 , which determines whether an introduced infinitesimal level of infection in an initially susceptible population will shrink or grow. We apply these four continuous state models, together with discrete state Monte Carlo simulations, to analyse how spreading varies with model parameters. Both network properties and the outcome of Monte Carlo simulations vary substantially with dimension or rewiring rate, but predictions of continuous state models change only slightly. A different trend appears for epidemic model parameters: as these vary, the outcomes of Monte Carlo change less than those of continuous state methods. Furthermore, under a wide range of conditions, the four continuous state approximations present similar deviations from the outcome of Monte Carlo simulations. This bias is usually least when using the pair approximation model, varies only slightly with network size, and decreases with dimension or rewiring rate. Finally, we characterize the discrepancies between Monte Carlo and continuous state models by simultaneously considering network efficiency and network size.