Spread Estimation Research Articles

Spread Estimation With Non-Duplicate Sampling in High-Speed Networks

Per-flow spread measurement in high-speed networks has many practical applications. It is a more difficult problem than the traditional per-flow size measurement. Most prior work is based on sketches, focusing on reducing their space requirements in order to fit in on-chip cache memory. This design allows the measurement to be performed at the line rate, but it suffers from expensive computation for spread queries (unsuitable for online operations) and large errors in spread estimation for small flows. This paper complements the prior art with a new spread estimator design based on an on-chip/off-chip model. By storing traffic statistics in off-chip memory, our new design faces a key technical challenge to design an efficient online module of non-duplicate sampling that cuts down the off-chip memory access. We first propose a two-stage solution for non-duplicate sampling, which is efficient but cannot handle well a sampling probability that is either too small or too big. We then address this limitation through a three-stage solution that is more space-efficient. Our analysis shows that the proposed spread estimator is highly configurable for a variety of probabilistic performance guarantees. We implement our spread estimator in hardware using FPGA. The experiment results based on real Internet traffic traces show that our estimator produces spread estimation with much better accuracy than the prior art, reducing the mean relative (absolute) error by about one order of magnitude. Moreover, it increases the query throughput by around three orders of magnitude, making it suitable for supporting online queries in real time.

Region-wise analysis of dairy cow movements in Japan

BackgroundAnimal movement is considered the most significant factor in the transmission of infectious diseases in livestock. A better understanding of its effects would help provide a more reliable estimation of the disease spread and help develop effective control measures. If the movement pattern is heterogeneous, its characteristics should be considered in epidemiological analyses, such as when using simulation models to obtain reliable outputs. In Japan, following the bovine spongiform encephalopathy epidemic, a traceability system for cattle was established in 2003, and the registration of all cattle movements in the national database began. This study is the first to analyze cattle movements in Japan. We examined regional and seasonal heterogeneity in dairy cow movements, which accounted for most Japanese breeding cattle.ResultsIn the 14 years from April 2005 to March 2018, 4,577,709 between-farm movements of dairy cows were recorded, and the number of movements was counted by month and age for both inter- and intra-regional movements. As a result, two characteristic round-trip movements were observed: one was non-seasonal and inter-regional movements related to cattle-breeding ranches in Hokkaido (the northern region of Japan), which consists of the movement of cows around ages 6 to 8 and 21 to 23 months old. In addition, the seasonal movement of heifers for summer grazing within Hokkaido occurred in May and October at the peak ages of 13 to 14 and 19 to 20 months old, respectively. The observed heterogeneity seemed to reflect the suitability of raising the Holstein breed in Hokkaido and the shortage of supply of replacement heifers and available farming areas outside Hokkaido.ConclusionsUnderstanding the patterns of dairy cow movements will help develop reliable infectious disease models and be beneficial for developing effective control measures against these diseases.

Does high COVID-19 spread impact neighbouring countries? Quasi-experimental evidence from the first year of the pandemic in Ireland.

Background : Coronavirus disease 2019 (COVID-19) has necessitated public health responses on an unprecedented scale. Controlling infectious diseases requires understanding of the conditions that increase spread. Prior studies have identified sociodemographic, epidemiological and geographic associations. Ireland offers an unusual opportunity to quantify how high infection rates in one country impacted cases in a neighbouring country. Methods : We analysed official statistics on confirmed COVID-19 cases on the island of Ireland for 52 weeks from March 2020. Our main research question was: Did higher cases in Northern Ireland (NI) impact the number of cases in the Republic of Ireland (ROI)? We used least squares regression to compare confirmed cases in ROI counties that border NI with the rest of the state. We included in our model sociodemographic, epidemiological and geographic factors. We employed the latitude of each county town as an instrumental variable to isolate a quasi-experimental estimate of the cross-border spread. Results : In the quasi-experimental framework, and controlling for population density, age distribution and circulatory disease prevalence, border counties had an extra 21.0 (95%CI: 8.4-33.6) confirmed COVID-19 cases per 1000 people. This equates to an estimated 9,611 additional cases in ROI, or 4% of the national total in the first year of the pandemic. Our results were substantively similar in non-experimental frameworks, with alternative additional predictors, and in sensitivity analyses. Additionally, population density in ROI counties was positively associated with confirmed cases and higher proportions of residents in the professional classes was negatively associated. Conclusion : On the island of Ireland during the first year of the COVID-19 pandemic, high infection rates in NI increased cases in the neighbouring ROI. Maximising co-ordination of pandemic responses among neighbouring countries is essential to minimising disease spread, and its associated disruptions to society and the economy. Socioeconomic disadvantage appeared to confer significant additional risk of spread.

Sewage Systems Surveillance for SARS-CoV-2: Identification of Knowledge Gaps, Emerging Threats, and Future Research Needs.

The etiological agent for novel coronavirus (COVID-19, Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2), not only affects the human respiratory system, but also the gastrointestinal tract resulting in gastrointestinal manifestations. The high rate of asymptomatic infected individuals has challenged the estimation of infection spread based on patients’ surveillance, and thus alternative approaches such as wastewater-based epidemiology (WBE) have been proposed. Accordingly, the number of publications on this topic has increased substantially. The present systematic review thus aimed at providing state-of-the-knowledge on the occurrence and existing methods for sampling procedures, detection/quantification of SARS-CoV-2 in sewage samples, as well as anticipating challenges and providing future research direction to improve the current scientific knowledge. Articles were collected from three scientific databases. Only studies reporting measurements of virus in stool, urine, and wastewater samples were included. Results showed that improving the scientific community’s understanding in these avenues is essential if we are to develop appropriate policy and management tools to address this pandemic pointing particularly towards WBE as a new paradigm in public health. It was also evident that standardized protocols are needed to ensure reproducibility and comparability of outcomes. Areas that require the most improvements are sampling procedures, concentration/enrichment, detection, and quantification of virus in wastewater, as well as positive controls. Results also showed that selecting the most accurate population estimation method for WBE studies is still a challenge. While the number of people infected in an area could be approximately estimated based on quantities of virus found in wastewater, these estimates should be cross-checked by other sources of information to draw a more comprehensive conclusion. Finally, wastewater surveillance can be useful as an early warning tool, a management tool, and/or a way for investigating vaccination efficacy and spread of new variants.

Comprehensive Survey of Using Machine Learning in the COVID-19 Pandemic.

Since December 2019, the global health population has faced the rapid spreading of coronavirus disease (COVID-19). With the incremental acceleration of the number of infected cases, the World Health Organization (WHO) has reported COVID-19 as an epidemic that puts a heavy burden on healthcare sectors in almost every country. The potential of artificial intelligence (AI) in this context is difficult to ignore. AI companies have been racing to develop innovative tools that contribute to arm the world against this pandemic and minimize the disruption that it may cause. The main objective of this study is to survey the decisive role of AI as a technology used to fight against the COVID-19 pandemic. Five significant applications of AI for COVID-19 were found, including (1) COVID-19 diagnosis using various data types (e.g., images, sound, and text); (2) estimation of the possible future spread of the disease based on the current confirmed cases; (3) association between COVID-19 infection and patient characteristics; (4) vaccine development and drug interaction; and (5) development of supporting applications. This study also introduces a comparison between current COVID-19 datasets. Based on the limitations of the current literature, this review highlights the open research challenges that could inspire the future application of AI in COVID-19.

Fractional Model with Social Distancing Parameter for Early Estimation of COVID-19 Spread.

COVID-19 disease has come up as a life-threatening outbreak at end of 2019. It has impacted almost all countries in the world. The major source of COVID-19 is a novel beta coronavirus. COVID-19 had a great impact on world throughout the year 2020. Now, the situation is becoming normal due to the invention of the vaccine. All major countries started large vaccination drives. Mathematical models are used to study the impact of different measures used to decrease pandemics. Mathematical models such as susceptible–infected–removed model and susceptible–exposed–infected–removed are used to predict the spread of diseases. But these models are not suitable to predict COVID-19 spread due to various preventive measures (social distancing and quarantine) applied to reduce spread. Hence, in the present manuscript, a novel fractional mathematical model with a social distancing parameter has been proposed to provide early COVID-19 spread estimation. Fractional calculus provides flexibility in choosing arbitrary order of derivative which controls data sensitivity. The model has been validated with real data set. It has been observed that the proposed model is highly accurate in spread estimation.

Estimating the COVID-19 Spread Through Real-time Population Mobility Patterns: Surveillance in Low- and Middle-Income Countries.

BackgroundOn January 21, 2020, the World Health Organization reported the first case of severe acute respiratory syndrome coronavirus 2, which rapidly evolved to the COVID-19 pandemic. Since then, the virus has also rapidly spread among Latin American, Caribbean, and African countries.ObjectiveThe first aim of this study is to identify new emerging COVID-19 clusters over time and space (from January 21 to mid-May 2020) in Latin American, Caribbean, and African regions, using a prospective space–time scan measurement approach. The second aim is to assess the impact of real-time population mobility patterns between January 21 and May 18, 2020, under the implemented government interventions, measurements, and policy restrictions on COVID-19 spread among those regions and worldwide.MethodsWe created a global COVID-19 database, of 218 countries and territories, merging the World Health Organization daily case reports with other measures such as population density and country income levels for January 21 to May 18, 2020. A score of government policy interventions was created for low, intermediate, high, and very high interventions. The population’s mobility patterns at the country level were obtained from Google community mobility reports. The prospective space–time scan statistic method was applied in five time periods between January and May 2020, and a regression mixed model analysis was used.ResultsWe found that COVID-19 emerging clusters within these five periods of time increased from 7 emerging clusters to 28 by mid-May 2020. We also detected various increasing and decreasing relative risk estimates of COVID-19 spread among Latin American, Caribbean, and African countries within the period of analysis. Globally, population mobility to parks and similar leisure areas during at least a minimum of implemented intermediate-level control policies (when compared to low-level control policies) was related to accelerated COVID-19 spread. Results were almost consistent when regional stratified analysis was applied. In addition, worldwide population mobility due to working during high implemented control policies and very high implemented control policies, when compared to low-level control policies, was related to positive COVID-19 spread.ConclusionsThe prospective space–time scan is an approach that low-income and middle-income countries could use to detect emerging clusters in a timely manner and implement specific control policies and interventions to slow down COVID-19 transmission. In addition, real-time population mobility obtained from crowdsourced digital data could be useful for current and future targeted public health and mitigation policies at a global and regional level.

Estimation, control and forecast of COVID-19 disease spread in Central Visayas, Philippines

The current trend of infections from COVID-19 outbreak in Central Visayas (CV) is posing higher risk of continued spreading. When uncontrolled, swarming of infected individuals to hospitals puts a greater challenge to the health care systems in the region and may breakdown. It is imperative in this situation that data-driven decisions and policies are required the most. In response, this study provided estimates of the epidemiologically important parameters namely, reproduction metric (R0) and infection (α), recovery (β) and mortality (γ) rates, by using a modified Susceptible Infected-Recovered-Dead (SIRD) model. This modified model incorporated control parameters, 𝜎 and 𝜔, associated with enhanced community quarantine (ECQ) implementation and observance of social distancing (SD), respectively. For the covered months from 27 March 2020–10 May 2020, results of the simulation estimated these parameters at: R0=3.12, α=0.18, β= 0.029, and γ=0.029 with 90% confidence. Moreover, the reproduction metric can be effectively reduced with the combined effect of the control parameters at 𝜎, 𝜔 ≥ 0.5 resulting to an effective R0 below unity. Similarly, this lowered the peak value of infection to 23% (or 7% of the total number of susceptible population) compared to when these measures are not observed and moved the peak time farther as well. While these estimates reflected the timely implementation of ECQ keeping its current level comparable with the country’s estimates and the world, reducing the reproduction metric effectively requires strict observance to both ECQ and SD control measures. Lastly, the temporal dynamics of this metric may not be necessarily true in any given area, and hence geographically induced.

Numerical Analysis of Smoke Spreading in a Medium-High Building under Different Ventilation Conditions

Smoke from fires in residential buildings represents the greatest threat to the life and health of inhabitants and firefighters at the scene of an accident. Therefore, the aim of this study was to reconstruct a numerical model for the estimation of smoke spread in a medium-high building under different ventilation conditions. Here, the three-dimensional geometry of a designated medium-high building was reconstructed and an exit door in the basement was specified as a smoke inlet; a window in the upper part was marked as outlet; and an entrance door, which allowed the outside air to enter the building after opening, was designated as an inlet door. The initial simulation, in which no air could enter the building, predicted the time taken for the staircase to become filled with smoke. In a second simulation, the entrance door was a fresh air inlet. The results showed that, for the analyzed building, rapid use of the mechanical ventilation can shorten the time of operations and improve their safety.

Simulations of dispersion through an irregular urban building array

Following the release of a harmful substance within an urban environment, buildings and street canyons create complex flow regimes that affect dispersion and localized effluent concentrations. While some fast-response dispersion models can capture the effects caused by individual buildings, further research is required to refine urban characterizations such as plume channeling and spreading, and initial dispersion, especially within the presence of a nonhomogeneous array of structures. Field, laboratory, and modeling experiments that simulate urban or industrial releases are critical in advancing current dispersion models. This project leverages the configuration of buildings used in a full-scale, mock urban field study to examine the concentrations of a neutrally buoyant tracer in a series of wind tunnel and Embedded Large Eddy Simulation (ELES) experiments. The behavior, propagation, and magnitude of the plumes were examined and compared to identify microscale effects.After demonstrating excellent quantitative and qualitative comparisons between the wind tunnel and ELES via lateral and vertical concentration profiles, we show that a nonlinear least squares fit of the Gaussian plume equation well represents these profiles, even within the array of buildings and network of street canyons. The initial plume dispersion depended strongly on the structures immediately adjacent to the release, and consequently, the near-surface plume spread very rapidly in the first few street canyons downwind of the source. The ELES modeling showed that under slightly oblique incoming wind directions of 5° and 15°, an additional 5° and 14° off-axis channeling of the plume occurred at ground level, respectively. This indicates how building structures can cause considerable plume drift from the otherwise expected centerline axis, especially with greater wind obliquity. Additionally, AERMOD was used to represent the class of fast-running, Gaussian dispersion models to inform where these types of models may be usefully applied within urban areas or groups of buildings. Using an urban wind speed profile and other parameters that may be locally available after a release, AERMOD was shown to qualitatively represent the ground-level plume while somewhat underestimating peak concentrations. It also overestimated the lateral plume spread and was challenged in the very near-field to the source. Adding a turbulence profile from the ELES data into AERMOD's meteorological input improved model estimates of lateral plume spread and centerline concentrations, although peak concentration values were still underestimated in the far field. Finally, we offer some observations and suggestions for Gaussian dispersion modeling based on this mock urban modeling exercise.

Does high COVID-19 spread impact neighbouring countries? Evidence from Ireland.

Background : Coronavirus disease 2019 (COVID-19) has necessitated public health responses on an unprecedented scale. Controlling infectious diseases requires understanding of the conditions that increase spread. Prior studies have identified sociodemographic, epidemiological and geographic associations. Ireland offers an unusual opportunity to quantify how high infection rates in one country impacted cases in a neighbouring country. Methods : We analysed official statistics on confirmed COVID-19 cases on the island of Ireland for 52 weeks from March 2020. Our main research question was: Did higher cases in Northern Ireland (NI) impact the number of cases in the Republic of Ireland (ROI)? We used least squares regression to compare confirmed cases in ROI counties that border NI with the rest of the state. We included in our model sociodemographic, epidemiological and geographic factors. We employed the latitude of each county town as an instrumental variable to isolate a quasi-experimental estimate of the cross-border spread. Results : In the quasi-experimental framework, and controlling for population density, age distribution and circulatory disease prevalence, border counties had an extra 21.0 (95%CI: 8.4-33.6) confirmed COVID-19 cases per 1000 people. This equates to an estimated 9,611 additional cases in ROI, or 4% of the national total in the first year of the pandemic. Our results were substantively similar in non-experimental frameworks, with alternative additional predictors, and in sensitivity analyses. Additionally, population density in ROI counties was positively associated with confirmed cases and higher proportions of residents in the professional classes was negatively associated. Conclusion : On the island of Ireland during the first year of the COVID-19 pandemic, high infection rates in NI increased cases in the neighbouring ROI. Maximising co-ordination of pandemic responses among neighbouring countries is essential to minimising disease spread, and its associated disruptions to society and the economy. Socioeconomic disadvantage appeared to confer significant additional risk of spread.

A discrete genetic learning enabled PSO for targeted positive influence maximization in consumer review networks

A consumer review network (CRN) is a social network among the members of a consumer review website where the relationships are formed based on the mutual ratings of the existing reviews of the participating members. The relationship is positive (negative) i.e. trust-based (distrust-based) when most of the reviews are given high (low) ratings. In a CRN, the consumers may not be interested in all product categories. The influence maximization in such a network demands seed set selection in such a way that the number of influenced consumers (with interest in the advertised product category) will be maximum. Formally, this is referred to as the targeted influence maximization (TIM) problem. Moreover, as the CRN is treated as a signed social network, the polarity of the social relationships impacts the influence propagation. As per the present state of the art, none of the existing solutions for TIM have considered the network as a signed one and are thus not suitable for CRN. In this paper, a metaheuristic discrete genetic-learning-enabled particle swarm optimization algorithm combined with a trustworthiness-heuristic-based local search strategy has been proposed for targeted positive influence maximization in CRNs. The existing spread estimation function has been replaced by a computationally efficient positive influence spread estimation function. The experiment has been conducted on two real-life CRNs and compared with the existing notable algorithm for necessary validation of the proposed solution.

Boldness Personality Traits Are Associated With Reduced Risk Perceptions and Adoption of Protective Behaviors During the First COVID-19 Outbreak.

The containment measures imposed during the first COVID-19 outbreak required economic, social, and behavioral changes to minimize the spread of the coronavirus. Some studies have focused on how personality predicts distinct patterns of adherence to protective measures with psychopathic and antisocial traits predicting reduced engagement in such measures. In this study we extended previous findings by analyzing how boldness, meanness, and disinhibition psychopathic traits relate with both risk perceptions and protective behaviors during the first COVID-19 outbreak. A sample of 194 individuals (24% male) engaged in the survey, were assessed for psychopathic traits with the Triarchic Psychopathy Measure, and completed a COVID-19 survey targeting risk perceptions (spread, risk of becoming infected, state anxiety toward the COVID-19, and perceived risk of specific behaviors) and frequency of protective behaviors (e.g., not engaging in social distancing). Overall results show that boldness predicts reduced estimate of COVID-19 spread, reduced perceived risk of becoming infected, reduced state anxiety toward COVID-19, and reduced frequency of protective behaviors. Exploratory mediation models suggest that risk perceptions are not significant mediators of the association between psychopathic traits and reduced engagement in protective behaviors. Our results unveil that psychopathic traits affect risk perceptions and the propensity to engage in protective measures, emphasizing the need to accommodate these personality features in the public health strategy to control the COVID-19 spread.

Bandwidth Selection of Normal Information Spread Estimation Method for Geotechnical Parameter Probability Distribution

Normal information spread estimation method (NISEM) is an effective method to infer the geotechnical parameter probability density function. However, it is found that the optimal bandwidth calculated by the existing method is not consistent with the actual situation in engineering application. In order to determine the matching bandwidth of NISEM, the histogram grouping number and group distance according to the sample quantity and range are first determined in this paper. Then the bandwidth h of NISEM is calculated, taking h as the benchmark, 0.1h as the step to change bandwidth. And combining with judgment coefficient, the optimal matching bandwidth of NISEM is finally obtained. The validity and rationality of the proposed method are verified by geotechnical test data of two groups of large samples and four groups of small samples in practical engineering. The results show that: under the condition of limited geotechnical samples, the best matching bandwidth is related to the number of histogram groups, which is relative. And the bandwidth of each group of test samples is different. The research work in this paper perfects the application of NISEM in inferring geotechnical parameter probability density function.

Directional spreading resolution from point measurements for mixed seas and sea states with frequency dependent spreading

Recently (Adcock and Taylor, 2009) devised a method to estimate the underlying directional spreading from a single point measurement. Subsequently, this method has been successfully applied to sea states with frequency independent directional spreading. In contrast, the present work has applied this method to synthetic sea states generated with an underlying frequency dependent spreading. However, in the application of the method, it was assumed that the underlying sea states have a frequency independent spreading. It was found that applying this method in this manner predicts directional spreading that is close to the spectrally averaged spreading. Re–computing the widely used Velocity Reduction Factor (vrf) based on the predictions from the new method showed that it agreed within ±1.5% with the actual value, showing that a reasonable estimate of the directional spreading can be obtained by the new method even under the restrictive assumption of frequency independent spreading. The major implication of these findings is that, a reasonable estimate of the directional spreading function can be obtained for sea states with complex spreading from a single point measurement even with the assumption of frequency dependent spreading.

Reconciling estimates of global spread and infection fatality rates of COVID-19: An overview of systematic evaluations.

BackgroundEstimates of community spread and infection fatality rate (IFR) of COVID‐19 have varied across studies. Efforts to synthesize the evidence reach seemingly discrepant conclusions.MethodsSystematic evaluations of seroprevalence studies that had no restrictions based on country and which estimated either total number of people infected and/or aggregate IFRs were identified. Information was extracted and compared on eligibility criteria, searches, amount of evidence included, corrections/adjustments of seroprevalence and death counts, quantitative syntheses and handling of heterogeneity, main estimates and global representativeness.ResultsSix systematic evaluations were eligible. Each combined data from 10 to 338 studies (9‐50 countries), because of different eligibility criteria. Two evaluations had some overt flaws in data, violations of stated eligibility criteria and biased eligibility criteria (eg excluding studies with few deaths) that consistently inflated IFR estimates. Perusal of quantitative synthesis methods also exhibited several challenges and biases. Global representativeness was low with 78%‐100% of the evidence coming from Europe or the Americas; the two most problematic evaluations considered only one study from other continents. Allowing for these caveats, four evaluations largely agreed in their main final estimates for global spread of the pandemic and the other two evaluations would also agree after correcting overt flaws and biases.ConclusionsAll systematic evaluations of seroprevalence data converge that SARS‐CoV‐2 infection is widely spread globally. Acknowledging residual uncertainties, the available evidence suggests average global IFR of ~0.15% and ~1.5‐2.0 billion infections by February 2021 with substantial differences in IFR and in infection spread across continents, countries and locations.

Maximum likelihood-based extended Kalman filter for COVID-19 prediction.

Prediction of COVID-19 spread plays a significant role in the epidemiology study and government battles against the epidemic. However, the existing studies on COVID-19 prediction are dominated by constant model parameters, unable to reflect the actual situation of COVID-19 spread. This paper presents a new method for dynamic prediction of COVID-19 spread by considering time-dependent model parameters. This method discretises the susceptible-exposed-infected-recovered-dead (SEIRD) epidemiological model in time domain to construct the nonlinear state-space equation for dynamic estimation of COVID-19 spread. A maximum likelihood estimation theory is established to online estimate time-dependent model parameters. Subsequently, an extended Kalman filter is developed to estimate dynamic COVID-19 spread based on the online estimated model parameters. The proposed method is applied to simulate and analyse the COVID-19 pandemics in China and the United States based on daily reported cases, demonstrating its efficacy in modelling and prediction of COVID-19 spread.

NUMERICAL SIMULATION OF MUDFLOW WITH A TWO-DIMENSIONAL DEPTH-AVERAGED MODEL

This study is motivated by the need to mitigate damages caused by mudflow disaster, which is occurring frequently due to intensive forest clearing and uncontrolled land use at highland. Numerical modelling of mudflow is challenging as the propagation speed and rheological behavior of the flow relies on the accuracy of the numerical scheme and choice of rheological model. In this study, a two-dimensional depth-averaged model was developed to simulate a simplified mudflow event. In order to capture shock in mudflow, the finite volume method (FVM) with third order accurate Monotonic Upstream-centered Scheme of Conservation Laws (MUSCL) scheme was adopted in the numerical model and the model was verified against a benchmark partial dam-break problem. By assuming that the mudflow has high amount of fine mud suspension. the rheological model was represented by a simplified Herschel-Bulkley model. Numerical results showed that the Herschel-Bulkley model could reproduce the viscoplastic behavior of mudflow well, especially in the estimation of final longitudinal flow spreading (2% difference compared to experimental value) and depth of peak wave (8.8% maximum difference). The robustness and stability of the model was demonstrated by simulating a simplified mudflow event with obstacles.

Spatio-temporal predictive modeling framework for infectious disease spread

A novel predictive modeling framework for the spread of infectious diseases using high-dimensional partial differential equations is developed and implemented. A scalar function representing the infected population is defined on a high-dimensional space and its evolution over all the directions is described by a population balance equation (PBE). New infections are introduced among the susceptible population from a non-quarantined infected population based on their interaction, adherence to distancing norms, hygiene levels and any other societal interventions. Moreover, recovery, death, immunity and all aforementioned parameters are modeled on the high-dimensional space. To epitomize the capabilities and features of the above framework, prognostic estimates of Covid-19 spread using a six-dimensional (time, 2D space, infection severity, duration of infection, and population age) PBE is presented. Further, scenario analysis for different policy interventions and population behavior is presented, throwing more insights into the spatio-temporal spread of infections across duration of disease, infection severity and age of the population. These insights could be used for science-informed policy planning.

Spreading–Vanishing Scenarios in a Time-Periodic Parasitic–Mutualistic Model of Mistletoes and Birds in Heterogeneous Environment with Free Boundary

In this paper, we investigate the asymptotic dynamics of a time-periodic parasitic–mutualistic model of mistletoes and birds in heterogeneous environment with the especial concerns over the spreading–vanishing scenarios, in which the Stefan class free boundary is introduced as the spreading frontier. By defining the ecological reproduction number and generalizing it as the spatial-temporal risk index, a considerably universal spreading–vanishing dichotomy and the sharp criteria are first established in birds world in the absence of mistletoes, and some estimates of the asymptotic spreading speed of the free boundary provided that spreading occurs are also obtained. Furthermore, the comprehensive considerations containing the spreading frontiers, asymptotic profiles and estimates of the asymptotic spreading speed are exhibited in mistletoes-birds world by the monotone iteration technique with the proper upper and lower solutions. The results suggest that even for the spreading case, the mistletoes population will eventually persist in long term provided that its own risk index is larger than 1, otherwise it may be eradicated.