Time-varying Transmission Rate Research Articles

Estimating Unreported COVID-19 Cases in the United States Based on Time-Varying SIR Model

Background The potential unreported infection may impair and mislead policymaking，and the contemporary spread of COVID-19 varies in different counties of the United States. It is necessary to estimate the cases that may be underestimated based on county-level data to take better countermeasures against COVID-19. We suggested taking time-varying SIR models with unreported infection rates (UIR)to estimate the factual COVID-19 cases in the United States.Methods SIR integrated with unreported infection rates (SIRu) of fixed time effect and SIR with time-varying parameters (tvSIRu)were applied to estimate and compare the value of transmission rate(TR), UIR, and infection fatality rate (IFR) based on US county-level COVID-19 data. Results Based on US county-level COVID-19 data from January 22 (T1) to August 20 (T212) in 2020, SIRu was first tested and verified by a general OLS regression. The further regression of SIRu at the country-level showed that the average values of TR, UIR, and IFR were 0.034,19.5, 0.51% respectively. The range of IR, UIR, IFR of all states ranged were 0.007-0.157 (mean=0.048) ,7.31-185.6 (mean=38.89), and 0.04%-2.22% (mean=0.22%). Among time-varying transmission rate equations, the power function showed better fitness, which indicated a decline in TR decreasing from 227.58 (T1) to 0.022 (T212). The general equation of tvSIRu showed that both the UIR and IFR were gradually increasing, wherein, the UIR has an estimate of 9.1(95%CI = 5.7-14.0), and IFR was 0.70% (0.52%-0.95%) at T212.Interpretation Despite the decline in TR and IFR, the UIR of the United States is still on the rise, which had been supposed to decrease with sufficient tests or improved countersues. The US medical system may be largely affected by severe cases in the rapid spread of COVDI-19.

Epidemic spreading phenomena on a scale-free network with time-varying transmission rate due to social responses

In this paper, we study and simulate the effect of individual social responses, as a collective factor, on the epidemic spreading processes. We formally define the problem based on the traditional [Formula: see text] and [Formula: see text] compartmental models considering the time-varying infection probability dependent on the social responses. In this study, models of generic and special case scenarios are developed. While in the generic case the effective parameter of behavioral response is demonstrated as one collective factor, in the special case the behavioral response is assumed as the combination of two collective factors: social cost and transfer rate of social awareness. With social cost, we refer to the costs incurred by a certain population to prevent or mitigate an epidemic. With transfer rate of social awareness, we describe the averaged rate of received information and knowledge regarding a disease that individuals hold and make use to avoid negative consequences. We show that, while in both [Formula: see text] and [Formula: see text] models the density of infected agents grows exponentially during the initial time steps, the inclusion of our models of social responses, either generic or special one, leads to mitigation of the spreading. As a result of both generic and special cases, the density of infected agents in the stationary state and the maximum number of infected agents decrease according to power-law functions for different values of collective factors. In the special case results, we also witnessed significant changes in the slope of decreasing trends of stationary density of states happening for a critical value of transfer rate of social awareness, approximately at about the inverse of the time interval of transmission rate update. With this result, we point out that increasing the transfer rate of social awareness to about this critical point outperforms any slight increase in social cost in reducing the number of infected agents.

COVID-19 in the US: Estimates of Scenarios with Possibility of Reinfection

Epidemiological models of COVID-19 transmission assume that recovered individuals have a fully protected immunity. To date, there is no definite answer about whether people who recover from COVID-19 can be reinfected with the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). In the absence of a clear answer about the risk of reinfection, it is instructive to consider the possible scenarios. To study the epidemiological dynamics with the possibility of reinfection, I use a Susceptible-Exposed-Infectious-Resistant-Susceptible model with the time-varying transmission rate. I consider three different ways of modeling reinfection. The crucial feature of this study is that I explore both the difference between the reinfection and no-reinfection scenarios and how the mitigation measures affect this difference. The principal results are the following. First, the dynamics of the reinfection and no-reinfection scenarios are indistinguishable before the infection peak. Second, the mitigation measures delay not only the infection peak, but also the moment when the difference between the reinfection and no-reinfection scenarios becomes prominent. These results are robust to various modeling assumptions.

Reconstruction of the full transmission dynamics of COVID-19 in Wuhan.

As countries in the world review interventions for containing the pandemic of coronavirus disease2019 (COVID-19), important lessons can be drawn from the study of the full transmission dynamics of its causative agent-severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)- in Wuhan (China), where vigorous non-pharmaceutical interventions have suppressed the local outbreak of this disease1. Here we use a modelling approach to reconstruct the full-spectrum dynamics of COVID-19 in Wuhan between 1January and 8March2020 across 5periods defined by events and interventions, on the basis of 32,583laboratory-confirmed cases1. Accounting for presymptomatic infectiousness2, time-varying ascertainment rates, transmission rates and population movements3, we identify two key features of the outbreak: high covertness and high transmissibility. We estimate 87% (lower bound, 53%) of the infections before 8March2020 were unascertained (potentially including asymptomatic and mildly symptomatic individuals); and a basic reproduction number (R0) of 3.54 (95% credible interval 3.40-3.67) in the early outbreak, much higher than that of severe acute respiratory syndrome (SARS) and Middle East respiratory syndrome (MERS)4,5. We observe that multipronged interventions had considerable positive effects on controlling the outbreak, decreasing the reproduction number to 0.28 (95% credible interval 0.23-0.33) and-by projection-reducing the total infections in Wuhan by 96.0% as of 8March2020. We also explore the probability of resurgence following the lifting of all interventions after 14consecutive days of no ascertained infections; we estimate this probability at 0.32 and 0.06 on the basis of models with 87% and 53% unascertained cases, respectively-highlighting the risk posed by substantial covert infections when changing control measures. These results have important implications when considering strategies of continuing surveillance and interventions to eventually contain outbreaks of COVID-19.

Insights into the dynamics and control of COVID-19 infection rates.

This work aims to model, simulate and provide insights into the dynamics and control of COVID-19 infection rates. Using an established epidemiological model augmented with a time-varying disease transmission rate allows daily model calibration using COVID-19 case data from countries around the world. This hybrid model provides predictive forecasts of the cumulative number of infected cases. It also reveals the dynamics associated with disease suppression, demonstrating the time to reduce the effective, time-dependent, reproduction number. Model simulations provide insights into the outcomes of disease suppression measures and the predicted duration of the pandemic. Visualisation of reported data provides up-to-date condition monitoring, while daily model calibration allows for a continued and updated forecast of the current state of the pandemic.

Routing With Intelligent Spectrum Assignment in Full-Duplex Cognitive Networks Under Varying Channel Conditions

Recent developments of self-interference suppression techniques have enabled practical implementations of full-duplex (FD) cognitive-radio (CR) communication systems. Such systems can significantly enhance spectrum utilization by allowing a CR user to simultaneously transmit and receive over the same frequency channel. However, the CR FD-capabilities challenge the effectiveness of existing CR-based routing protocols as joint FD-aware channel-assignment and routing are essential to enhance network performance. In this letter, we propose a joint FD-aware channel-assignment and route selection protocol in FD-based CR networks (CRNs) under time-varying channel conditions and transmission rates. Specifically, for a given set of paths between a CR source-destination pair, our protocol computes the channel-assignment over each path that maximizes the end-to-end network throughput subject to interference constraints. This assignment problem is shown to be an NP-hard binary linear programming (BLP) that can be sub-optimally solved in polynomial-time using the sequential-fixing procedure. Then, our protocol determines the path with the highest end-to-end network throughput. Simulation results reveal that our proposed routing protocol significantly improves the end-to-end throughput compared to previous FD-aware routing protocols.

Effect of time varying transmission rates on the coupled dynamics of epidemic and awareness over a multiplex network.

A non-linear stochastic model is presented to study the effect of time variation of transmission rates on the co-evolution of epidemics and its corresponding awareness over a two layered multiplex network. In the model, the infection transmission rate of a given node in the epidemic layer depends upon its awareness probability in the awareness layer. Similarly, the infection information transmission rate of a node in the awareness layer depends upon its infection probability in the epidemic layer. The spread of disease resulting from physical contacts is described in terms of a Susceptible Infected Susceptible process over the epidemic layer and the spread of information about the disease outbreak is described in terms of an Unaware Aware Unaware process over the virtual interaction mediated awareness layer. The time variation of the transmission rates and the resulting co-evolution of these mutually competing processes are studied in terms of a network topology dependent parameter ( ). Using a second order linear theory, it is shown that in the continuous time limit, the co-evolution of these processes can be described in terms of damped and driven harmonic oscillator equations. From the results of a Monte-Carlo simulation, it is shown that for a suitable choice of the parameter , the two processes can either exhibit sustained oscillatory or damped dynamics. The damped dynamics corresponds to the endemic state. Furthermore, for the case of an endemic state, it is shown that the inclusion of the awareness layer significantly lowers the disease transmission rate and reduces the size of the epidemic. The infection probability of the nodes in the endemic state is found to have a dependence on both the transmission rates and on their absolute degrees in each of the network layers and on the relative differences between their degrees in the respective layers.

Delay constrained throughput optimisation with imperfect CSI using discrete adaptive power

ABSTRACTLink adaptation is an effective tool to overcome fading effects in wireless links. However, time-varying adaptive transmission rate leads to queueing delay, and moreover, in practise, imperfect channel state information (CSI) is available for the transmitter to adapt its transmission rate and power. This article aims to consider practical constraints to enhance the link adaptation scheme. We reformulate and optimise buffer delay constrained throughput of a wireless link based on outdated noisy CSI. Discrete power adaptation is proposed, in which a limited number of feedback bits (just the index of transmission power level) is required, while the performance is improved compared to the constant power and is close to continuous adaptive power. A unified scheme is set-up, where constant, discrete or continuous adaptive power transmission is utilised considering average or instantaneous bit error rate constraints based on imperfect CSI. The effectiveness of our designs is evaluated by numerical evaluations.

Impact of stochastically generated heterogeneity in hazard rates on individually randomized vaccine efficacy trials.

Background/aims Network structure and individuals' level of exposure to a pathogen can impact results from efficacy evaluation studies of interventions against infectious diseases. Heterogeneity in infection risk can cause randomized groups to increasingly differ as a trial progresses and as more high-risk individuals become infected (described in prior work as the "frailty" phenomenon). Here, we show the impact this phenomenon can have on an individually randomized trial of a leaky vaccine in which all participants are exchangeable a priori. Methods We model a vaccine trial by generating a network of individuals grouped into communities, which are connected to a larger main population. We then simulate an epidemic, deterministically and with time-varying transmission rates in the main population and stochastically in the communities. The disease natural history follows a susceptible-exposed-infectious-recovered model. Simulation results are used to estimate vaccine efficacy [Formula: see text] with a Cox proportional hazards model. Results We find downward bias in [Formula: see text] associated with low connectivity between communities in the study population and high force of infection, even when all participants in the trial are exchangeable at the time of randomization. This phenomenon arises because the stochastic dynamics in such a setting randomly lead to community-level variation in the force of infection. Stratifying a Cox model by community alleviates this bias with no loss of power. Conclusion Understanding and accounting for the impact of heterogeneous hazard rates can allow for more accurate estimates of [Formula: see text] in epidemic settings.

Bayesian inference in an extended SEIR model with nonparametric disease transmission rate: an application to the Ebola epidemic in Sierra Leone.

The 2014 Ebola outbreak in Sierra Leone is analyzed using a susceptible-exposed-infectious-removed (SEIR) epidemic compartmental model. The discrete time-stochastic model for the epidemic evolution is coupled to a set of ordinary differential equations describing the dynamics of the expected proportions of subjects in each epidemic state. The unknown parameters are estimated in a Bayesian framework by combining data on the number of new (laboratory confirmed) Ebola cases reported by the Ministry of Health and prior distributions for the transition rates elicited using information collected by the WHO during the follow-up of specific Ebola cases. The time-varying disease transmission rate is modeled in a flexible way using penalized B-splines. Our framework represents a valuable stochastic tool for the study of an epidemic dynamic even when only irregularly observed and possibly aggregated data are available. Simulations and the analysis of the 2014 Sierra Leone Ebola data highlight the merits of the proposed methodology. In particular, the flexible modeling of the disease transmission rate makes the estimation of the effective reproduction number robust to the misspecification of the initial epidemic states and to underreporting of the infectious cases.

Nearly-optimal scheduling of users with Markovian time-varying transmission rates

We address the problem of developing a well-performing and implementable scheduler of users with wireless connections to the central controller, which arise in areas such as mobile data networks, heterogeneous networks, or vehicular communications systems. The main feature of such systems is that the quality of each user’s channel is time-varying due to fading. The evolution of the channel over its quality states thus causes a time-varying transmission rate of each user. We consider Markovian channel dynamics, relaxing the common but unrealistic assumption of i.i.d. channels. We first focus on three-state channels and show that threshold policies (of giving higher priority to users with higher transmission rate) are not necessarily optimal. For the general case we design a scheduler which generalizes the recently proposed Potential Improvement (PI) scheduler, which gives priority to the users who are unlikely to improve their actual transmission rate soon by much. We propose two practical approximations of PI, whose performance is analyzed and compared to existing alternative schedulers in a variety of simulation scenarios. Our computational experiments indicate that the variant of PI, which only relies on the steady-state distribution of the channel, is robust and performs extremely well, and therefore we recommend its use for practical implementation.

The Inverse Method for a Childhood Infectious Disease Model with Its Application to Pre-vaccination and Post-vaccination Measles Data.

In this paper, we improve the classic SEIR model by separating the juvenile group and the adult group to better describe the dynamics of childhood infectious diseases. We perform stability analysis to study the asymptotic dynamics of the new model, and perform sensitivity analysis to uncover the relative importance of the parameters on infection. The transmission rate is a key parameter in controlling the spread of an infectious disease as it directly determines the disease incidence. However, it is essentially impossible to measure the transmission rate for certain infectious diseases. We introduce an inverse method for our new model, which can extract the time-dependent transmission rate from either prevalence data or incidence data in existing open databases. Pre- and post-vaccination measles data sets from Liverpool and London are applied to estimate the time-varying transmission rate. From the Fourier transform of the transmission rate of Liverpool and London, we observe two spectral peaks with frequencies 1/year and 3/year. These dominant frequencies are robust with respect to different initial values. The dominant 1/year frequency is consistent with common belief that measles is driven by seasonal factors such as environmental changes and immune system changes and the 3/year frequency indicates the superiority of school contacts in driving measles transmission over other seasonal factors. Our results show that in coastal cities, the main modulator of the transmission of measles virus, paramyxovirus, is school seasons. On the other hand, in landlocked cities, both weather and school seasons have almost the same influence on paramyxovirus transmission.

Optimal Control Strategies for Virus Spreading in Inhomogeneous Epidemic Dynamics

Abstract.In this paper, we study the spread of virus/worm in computer networks with a view to addressing cyber security problems. Epidemic models have been applied extensively to model the propagation of computer viruses, which characterize the fact that infected machines may spread malware to other hosts connected to the network. In our framework, the dynamics of hosts evolves according to a modified inhomogeneous Susceptible-Infectious-Susceptible (SIS) epidemic model with time-varying transmission rate and recovery rate. The infection of computers is subject to direct attack as well as propagation among hosts. Based on optimal control theory, optimal attack strategies are provided by minimizing the cost (equivalently maximizing the profit) of the attacker. We present a threshold function of the fraction of infectious hosts, which captures the dynamically evolving strategies of the attacker and reflects the persistence of virus spreading. Moreover, our results indicate that if the infectivity of a computer worm is low and the computers are installed with antivirus software with high reliability, the intensity of attacks incurred will likely be low. This agrees with our intuition.

Scheduling of users with markovian time-varying transmission rates

We address the problem of developing a well-performing and implementable scheduler of users with wireless connection to the base station. The main feature of such real-life systems is that the quality conditions of the user channels are time-varying, which turn into the time-varying transmission rate due to different modulation and coding schemes. We assume that this phenomenon follows a Markovian law and most of the discussion is dedicated to the case of three quality conditions of each user, for which we characterize an optimal index policy and show that threshold policies (of giving higher priority to users with higher transmission rate) are not necessarily optimal. For the general case of arbitrary number of quality conditions we design a scheduler and propose its two practical approximations, and illustrate the performance of the proposed index-based schedulers and existing alternatives in a variety of simulation scenarios.

Epidemic-Based Information Dissemination in Wireless Mobile Sensor Networks

In this paper, we consider wireless mobile sensor networks under extreme environments where nodes: 1) have local knowledge; 2) have limited computational power; 3) make distributed decisions; and 4) move rapidly over time. Information dissemination in these networks (or gossip) can be modeled via epidemic models that analyze behavior of the system mimicking the way diseases spread (or even gossip for that matter). However, the limitation on computational power and energy of nodes forces us to consider explicit stopping criteria that are seldom done in the literature. Furthermore, harsh environments considered in this paper prevent nodes from transmitting sensed information at specified time slots and hence might cause a large variation in intertransmission time distribution. The objective of this paper is to characterize the dynamics of the information spread and obtain performance measures based on stochastic modeling. We start with modeling information flow using a Markov chain and obtain performance measures such as time to transfer information and fraction of nodes receiving information. Then, we provide a method to obtain those performance measures when the assumption on intertransmission time distribution is relaxed, e.g., time-varying transmission rates and nonexponential intertransmission time distributions, which makes our model more realistic. We make a curious finding in that, for our proposed model, the average fraction of nodes receiving information is a parameter-free constant. We also show that our model is scalable and effective.

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.

Rate-regulated power control for supporting flexible transmission in future CDMA mobile networks

In code division multiple access (CDMA) mobile networks, transmitted power is controlled to provide each user an acceptable connection by limiting the interference seen by other users. Previous work has focused on finding a power assignment that maximizes the minimum carrier-to-interference ratio where the transmission rate of each user is known and fixed. In future mobile networks, however, fluctuations in mobiles' transmission rate should be considered in designing power control algorithms. In this work, we present an algorithm for controlling mobiles' transmitter power levels while explicitly handling their time-varying transmission rates. During the whole power control process, the required signal quality is always maintained. The traffic-carrying performance of the algorithm is evaluated by simulation where different types of users are sending burst data.

Itakura-Saito clustering and rate distortion functions for a composite source model of speech

Composite source (CS) models for speech signals consist of a finite number of subsources describing specific spectral characteristics and a switch process representing the variation of these characteristics. They allow the computation of rate distortion functions (RDFs) which are significantly below those for simple stochastic models. In this paper, it is discussed how to estimate a switch state sequence such that it is optimal in the computation of an RDF. Using a maximum-likelihood approach, a new relationship between Itakura-Saito clustering and rate distortion theory for composite sources is derived. The performance bounds are based on the mean squared error distortion measure. It will be shown that for a given number of subsources the resulting composite source model has the lowest possible RDF in the range of small values of distortion. In addition, a lower bound for the RDF for a composite source having an arbitrarily high number of subsources is derived. Finally, it is shown that rate distortion theory for composite sources provides explicit bit-allocation rules for a class of blockwise adaptive (switched) waveform coding schemes with time-varying transmission rate.

Shortage of junior staff

<h3>Abstract</h3> The implementation of non-pharmaceutical public health interventions can have simultaneous impacts on pathogen transmission rates as well as host mobility rates. For instance, with SARS-CoV-2, masking can influence host-to-host transmission, while stay-at-home orders can influence mobility. Importantly, transmission rates and mobility patterns can influence pathogen-induced hospitalization rates. This poses a significant challenge for the use of mathematical models of disease dynamics in forecasting the spread of a pathogen; to create accurate forecasts in spatial models of disease spread, we must simultaneously account for time-varying rates of transmission and host movement. In this study, we develop a statistical model-fitting algorithm to estimate dynamic rates of SARS-CoV-2 transmission and host movement from geo-referenced hospitalization data. Using simulated data sets, we then test whether our method can accurately estimate these time-varying rates simultaneously, and how this accuracy is influenced by the spatial population structure. Our model-fitting method relies on a highly parallelized process of grid search and a sliding window technique that allows us to estimate time-varying transmission rates with high accuracy and precision, as well as movement rates with somewhat lower precision. Estimated parameters also had lower precision in more rural data sets, due to lower hospitalization rates (i.e., these areas are less data-rich). This model-fitting routine could easily be generalized to any stochastic, spatially-explicit modeling framework, offering a flexible and efficient method to estimate time-varying parameters from geo-referenced data sets.