Search

The COVID-19 epidemic has had a major impact on people's normal travel. Optimizing the control of the number of passengers boarding and deboarding the customized bus (CB) at CB stops can reduce the contact between passengers in the course of travel, which is meaningful for COVID-19 epidemic prevention and control. In this paper, a dynamic programming model based on nonlinear integer programming (NIP) is established to study the problem of boarding and alighting planning at various CB stops under the influence of COVID-19. Using Gurobi 9.1.1 solver, the optimal plan for passengers boarding and deboarding CB buses could be obtained. Besides, the mathematical model established in this paper can obtain the minimum value of the total number of contacts between passengers during travel under different CB numbers. It is found that the model solution results eventually form a Pareto frontier. When the number of CB buses increases, the total number of contacts between passengers will decrease This study has positive significance for ensuring the normal travel of passengers during the COVID-19 epidemic, and provides useful references for the studies about the planning of the customized bus.

The global spread of COVID-19 has not been effectively controlled, posing a huge threat to public health and the development of the global economy. Currently, a number of vaccines have been approved for use and vaccination campaigns have already started in several countries. This paper designs a mathematical model considering the impact of vaccination to study the spread dynamics of COVID-19. Some basic properties of the model are analyzed. The basic reproductive number ℜ1 of the model is obtained, and the conditions for the existence of endemic equilibria are provided. There exist two endemic equilibria when ℜ1

One approach to understand people's efforts to reduce disease transmission, is to consider the effect of behaviour on case rates. In this paper we present a spatial infection-reducing game model of public behaviour, formally equivalent to a Hopfield neural network coupled to SIRS disease dynamics. Behavioural game parameters can be precisely calibrated to geographical time series of Covid-19 active case numbers, giving an implied spatial history of behaviour. This is used to investigate the effects of government intervention, quantify behaviour area by area, and measure the effect of wealth on behaviour. We also demonstrate how a delay in people's perception of risk levels can induce behavioural instability, and oscillations in infection rates., Comment: The code to generate all the figures is available at https://github.com/gnacikm/BSIRS_model

The global pandemic of the coronavirus disease 2019 (COVID-19) exemplifies the influence of human mobility on epidemic spreading. A framework called the movement-interaction-return (MIR) model is a model to study the impact of human mobility on epidemic spreading. In this paper, we investigate epidemic spreading in interconnected metapopulation networks. Specifically, we incorporate the human mobility pattern called the radiation model into the MIR model. As a result, the proposed model is more realistic in comparison to the original MIR model. We use the tensorial framework to develop Markovian equations that describe the dynamics of the proposed model on interconnected metapopulation networks. Then we derive the corresponding epidemic thresholds by converting tensors into matrices. Comprehensive numerical simulations confirm our analysis.

This paper examines how COVID-19 pandemic has affected volatility persistence in the G7’s stock markets. Based on daily data we divided the whole sample into two sub-samples according to its breakpoints and found that they occurred right after the declaration of COVID-19 pandemic by the World Health Organization — WHO (2020). This approach allows us to assess the main differences between these two distinct phases. Thus, while the first sub-period is relatively calm, the second one, which coincides with the pandemic outbreak, shows higher levels of volatility. Considering this, we rely on GARCH-type models to assess the degree of persistence of volatility and to evaluate how it has evolved across sub-samples. Our results show that the FIGARCH(1,d,1) is the best model to describe the data and that the degree of persistence is very different from the first to the second sub-sample. Thus, while the pre-pandemic period exhibits lower levels of persistence it has greatly increased with the COVID-19 outbreak. In particular, S&P 500 and FTSE/MIB became the most persistent indices in contrast to NIKKEI 225 and FTSE 100, which were amongst the least persistent.

Navigation on graphs is the problem how an agent walking on the graph can get from a source to a target with limited information about the graph. The information and the way to exploit it can vary. In this paper, we study navigation on temporal networks -- networks where we have explicit information about the time of the interaction, not only who interacts with whom. We contrast a type of greedy navigation -- where agents follow paths that would have worked well in the past -- with two strategies that do not exploit the additional information. We test these on empirical temporal network data sets. The greedy navigation is indeed more efficient than the reference strategies, meaning that there are correlations in the real temporal networks that can be exploited. We find that the navigability for individual nodes is most strongly correlated with degree and burstiness, i.e., both topological and temporal structures affect the navigation efficiency.

Infectious diseases, such as the current COVID-19, have a huge economic and societal impact. The ability to model its transmission characteristics is critical to minimize its impact. In fact, predicting how fast an infection is spreading could be a major factor in deciding on the severity, extent and strictness of the applied mitigation measures, such as the recent lockdowns. Even though modelling epidemics is a well studied subject, usually models do not include quarantine or other social measures, such as those imposed in the recent pandemic. The current work builds upon a recent paper by Maier and Brockmann (2020), where a compartmental SIRX model was implemented. That model included social or individual behavioural changes during quarantine, by introducing state X, in which symptomatic quarantined individuals are not transmitting the infection anymore, and described well the transmission in the initial stages of the infection. The results of the model were applied to real data from several provinces in China, quite successfully. In our approach we use a Monte-Carlo simulation model on networks. Individuals are network nodes and the links are their contacts. We use a spreading mechanism from the initially infected nodes to their nearest neighbours, as has been done previously. Initially, we find the values of the rate constants (parameters) the same way as in Maier and Brockmann (2020) for the confirmed cases of a country, on a daily basis, as given by the Johns Hopkins University. We then use different types of networks (random Erdős–Rényi, Small World, and Barabási–Albert Scale-Free) with various characteristics in an effort to find the best fit with the real data for the same geographical regions as reported in Maier and Brockmann (2020). Our simulations show that the best fit comes with the Erdős–Rényi random networks. We then apply this method to several other countries, both for large-size countries, and small size ones. In all cases investigated we find the same result, i.e. best agreement for the evolution of the pandemic with time is for the Erdős–Rényi networks. Furthermore, our results indicate that the best fit occurs for a random network with an average degree of the order of 〈k〉≈ 10–25, for all countries tested. Scale Free and Small World networks fail to fit the real data convincingly.

In this paper, we propose and analyze from a stability viewpoint a deterministic, ODE-based class of rumor spreading models with two distinct inhibiting and adjusting mechanisms, together with its corresponding stochastic counterpart. For the deterministic model, a threshold parameter R 0 defined ad hoc, called the basic influence number, is used to ascertain whether the rumors are prevailing or not. If R 0 1 , the rumor-free equilibrium is found to be locally asymptotically stable, while if R 0 > 1 it is shown that there is at least one additional rumor-prevailing equilibrium, which is necessarily locally asymptotically stable. For the stochastic model, we first show that there exists a unique global solution. Subsequently, we investigate the asymptotic behavior of the stochastic system around the equilibria of the deterministic system by constructing suitable Lyapunov functionals. Furthermore, numerical simulations are given to illustrate, support and enhance our theoretical analysis.

In this paper, we explore an evolutionary vaccination game in the modified activity driven network by considering the closeness. We set a closeness parameter p which is used to describe the way of connection between two individuals. The simulation results show that the closeness p may have an active role in weakening both the spreading of epidemic and the vaccination. Besides, when vaccination is not allowed, the final recovered density increases with the value of the ratio of the infection rate to the recovery rate λ/μ. However, when vaccination is allowed the final density of recovered individual first increases and then decreases with the value of λ/μ. Two variables are designed to identify the relation between the individuals’ activities and their states. The results draw that both recovered and vaccinated frequency increase with the increase of the individuals’ activities. Meanwhile, the immune fee has less impact on the individuals’ vaccination than the closeness. While the λ/μ is in a certain range, with the increase of the value of λ/μ, the recovered frequency of the whole crowds reduces. Our results, therefore, reveal the fact that the best of intentions may lead to backfire., Highlights • The evolutionary vaccination game is considered in a modified activity driven network. • A closeness parameter p which is used to describe the connection between individuals is presented. • The closeness p may have an active role in weakening both the spreading of epidemic and the vaccination. • Infected frequency increases with the increase of the individuals’ activity. • Results indicate some better hope (such as reducing the connection) may lead to backfire.

Immunizing important nodes has been shown to be an effective solution to suppress the epidemic spreading. Most studies focus on the globally important nodes in a network, but neglect the locally important nodes in different communities. We claim that given the temporal community feature of opportunistic social networks (OSN), this strategy has a biased understanding of the epidemic dynamics, leading us to conjecture that it is not “the more central, the better” for the implementation of control strategy. In this paper, we track the evolution of community structure and study the effect of community-based immunization strategy on epidemic spreading. We first break the OSN traces down into different communities, and find that the community structure helps to delay the outbreak of epidemic. We then evaluate the local importance of nodes in communities, and show that immunizing nodes with high local importance can remarkably suppress the epidemic. More interestingly, we find that high local importance but non-central nodes play a big role in epidemic spreading process, removing them improves the immunization efficiency by 25% to 150% at different scenarios., Highlights • The community structure helps to delay the outbreak of epidemic. • Nodes with high local importance can remarkably suppress the epidemic. • It is not “the more central, the better” for the implementation of control strategy.

In this paper, we study epidemic spreading in metapopulation networks wherein each node represents a subpopulation symbolizing a city or an urban area and links connecting nodes correspond to the human traveling routes among cities. Differently from previous studies, we introduce a heterogeneous infection rate to characterize the effect of nodes’ local properties, such as population density, individual health habits, and social conditions, on epidemic infectivity. By means of a mean-field approach and Monte Carlo simulations, we explore how the heterogeneity of the infection rate affects the epidemic dynamics, and find that large fluctuations of the infection rate have a profound impact on the epidemic threshold as well as the temporal behavior of the prevalence above the epidemic threshold. This work can refine our understanding of epidemic spreading in metapopulation networks with the effect of nodes’ local properties., Highlights • SIS epidemic dynamics is studied in metapopulation networks. • NIR and PIR heterogeneous infection regimes are proposed. • The two regimes both increase the threshold when only infected individuals move. • NIR increases and PIR decreases the threshold if two types of individuals both move. • We also explore the impact of the two regimes on the temporal behavior of epidemic.

This paper aims to study an SIS epidemic model with media coverage from a general deterministic model to a stochastic differential equation with environment fluctuation. Mathematically, we use the Markov semigroup theory to prove that the basic reproduction number R0s can be used to control the dynamics of stochastic system. Epidemiologically, we show that environment fluctuation can inhibit the occurrence of the disease, namely, in the case of disease persistence for the deterministic model, the disease still dies out with probability one for the stochastic model. So to a great extent the stochastic perturbation under media coverage affects the outbreak of the disease., Highlights • A stochastic epidemic model with media coverage is developed. • The global dynamics of the deterministic model is shown. • The stochastic dynamics of the SDE model is given. • The existence of a unique stationary distribution of the SDE model is displayed.

In this paper, we investigate the dynamical behavior for a stochastic SIS epidemic model with isolation which is as an important strategy for the elimination of infectious diseases. It is assumed that the stochastic effects manifest themselves mainly as fluctuation in the transmission coefficient, the death rate and the proportional coefficient of the isolation of infective. It is shown that the extinction and persistence in the mean of the model are determined by a threshold value R0S. That is, if R0S1, then the disease is stochastic persistent in the means with probability one. Furthermore, the existence of a unique stationary distribution is discussed, and the sufficient conditions are established by using the Lyapunov function method. Finally, some numerical examples are carried out to confirm the analytical results., Highlights • A stochastic SIS epidemic model with isolation and multiple noises perturbation is proposed. • The criteria on the extinction and persistence in the mean with probability one are obtained. • The sufficient conditions for the existence of unique stationary distribution are established.

In this paper, we propose the daily computed weighted averaging basic reproduction number R0,k,ωn for Middle East respiratory syndrome coronavirus (MERS-CoV) outbreak in South Korea, May to July 2015. We use an SIR model with piecewise constant parameters β (contact rate) and γ (removed rate). We use the explicit Euler’s method for the solution of the SIR model and a nonlinear least-square fitting procedure for finding the best parameters. In R0,k,ωn, the parameters n, k, and w denote days from a reference date, the number of days in averaging, and a weighting factor, respectively. We perform a series of numerical experiments and compare the results with the real-world data. In particular, using the predicted reproduction number based on the previous two consecutive reproduction numbers, we can predict the future behavior of the reproduction number., Highlights • We propose the daily basic reproduction number for MERS-CoV in South Korea. • We use an SIR model with piecewise constant contact and removed rates. • We apply the explicit Euler’s method for the solution of the SIR model. • We use nonlinear least-square fitting procedure for finding the best parameters.

We present a dynamical model for the spread of HIV in a finite discrete population of size n represented by the set V. The model takes into account the structure of the sexual network, the density of infected population in each individual’s sexual partners, and a reasonable amount of the influence of noninfectious HIV positive individuals on HIV infectious partners which may occur in communities. In our analytic results, we give a precise epidemic threshold which, together with certain network properties, is then used to analyse and investigate the existence of epidemic and stability in the HIV spreading dynamics. Our results reproduce common observed patterns in the dynamics of HIV spreading in communities., Highlights ► This paper presents a new dynamical model for the spread of HIV in communities. ► The non-static model considers, among other factors, structure of the sexual network. ► The analytic results from this model are obtained through rigorous mathematical proof.

The paper mainly applies the information categorization method to analyze the financial time series. The method is used to examine the similarity of different sequences by calculating the distances between them. We apply this method to quantify the similarity of different stock markets. And we report the results of similarity in US and Chinese stock markets in periods 1991–1998 (before the Asian currency crisis), 1999–2006 (after the Asian currency crisis and before the global financial crisis), and 2007–2013 (during and after global financial crisis) by using this method. The results show the difference of similarity between different stock markets in different time periods and the similarity of the two stock markets become larger after these two crises. Also we acquire the results of similarity of 10 stock indices in three areas; it means the method can distinguish different areas’ markets from the phylogenetic trees. The results show that we can get satisfactory information from financial markets by this method. The information categorization method can not only be used in physiologic time series, but also in financial time series., Highlights • We apply the information categorization method and succeed to classify the financial markets. • We investigate the similarity among US and Chinese stock indices for the Asian currency crisis and the global financial crisis. • The phylogenetic trees of different stock indices are presented and provide obvious phenomenon.

In this paper, explicitly considering the influences of an epidemic outbreak on human travel, a time-varying human mobility pattern is introduced to model the time variation of global human travel. The impacts of the pattern on epidemic dynamics in heterogeneous metapopulation networks, wherein each node represents a subpopulation with any number of individuals, are investigated by using a mean-field approach. The results show that the pattern does not alter the epidemic threshold, but can slightly lower the final average density of infected individuals as a whole. More importantly, we also find that the pattern produces different impacts on nodes with different degree, and that there exists a critical degree kc. For nodes with degree smaller than kc, the pattern produces a positive impact on epidemic mitigation; conversely, for nodes with degree larger than kc, the pattern produces a negative impact on epidemic mitigation., Highlights • We propose a time-varying human mobility pattern. • The pattern does not alter the epidemic threshold. • The pattern can lower the final density of infected individuals as a whole. • We derive a critical node degree leading to the presence of a transition.

By mapping nucleotide sequences onto a "DNA walk", we uncovered remarkably long-range power law correlations [Nature 356 (1992) 168] that imply a new scale invariant property of DNA. We found such long-range correlations in intron-containing genes and in non-transcribed regulatory DNA sequences, but not in cDNA sequences or intron-less genes. In this paper, we present more explicit evidences to support our findings.