Estimation of ocean primary productivity and its spatio-temporal variation mechanism for East China Sea based on VGPM model

According to calculation results of ocean chlorophyll concentration based on SeaWiFS data by SeaBAM model and synchronous ship-measured data, this research set up an improved model for CaseⅠand CaseⅡwater bodies respectively. The monthly chlorophyll distribution in the East China Sea in 1998 was obtained from this improved model on calculation results of SeaBAM. The euphotic depth distribution in 1998 in the East China Sea is calculated by using remote sensing data of K 490 from SeaWiFS according to the relation between the euphotic depth and the oceanic diffuse attenuation coefficient. With data of ocean chlorophyll concentration, euphotic depth, ocean surface photosynthetic available radiation (PAR), daily photoperiod and optimal rate of daily carbon fixation within a water column, the monthly and annual primary productivity spatio-temporal distributions in the East China Sea in 1998 were obtained based on VGPM model. Based on analysis of those distributions, the conclusion can be drawn that there is a clear bimodality character of primary productivity in the monthly distribution in the East China Sea. In detail, the monthly distribution of primary productivity stays the lowest level in winter and rises rapidly to the peak in spring. It gets down a little in summer, and gets up a little in autumn. The daily average of primary productivity in the whole East China Sea is 560.03 mg/m 2 /d, which is far higher than the average of subtropical ocean areas. The annual average of primary productivity is 236.95 g/m 2 /a. The research on the seasonal variety mechanism of primary productivity shows that several factors that affect the spatio-temporal distribution may include the chlorophyll concentration distribution, temperature condition, the Yangtze River diluted water variety, the euphotic depth, ocean current variety, etc. But the main influencing factors may be different in each local sea area.

Spatio-temporal variation and focal mechanism of the Wenchuan M_S8.0 earthquake sequence

Based on abundant aftershock sequence data of the Wenchuan Ms8.0 earthquake on May 12, 2008, we studied the spatio-temporal variation process and segmentation rupture characteristic. Dense aftershocks distribute along Longmenshan central fault zone of NE direction and form a narrow strip with the length of 325 krn and the depth between several and 40 km. The depth profile （section of NW direction） vertical to the strike of aftershock zone （NE direction） shows anisomerous wedgy distribution characteristic of afiershock concentrated regions; it is related to the force form of the Longmenshan nappe tectonic belt. The stronger aftershocks could be divided into northern segment and southern segment apparently and the focal depths of strong aftershocks in the 50 km area between northern segment and southern segment are shallower. It seems like ＇to be going to rupture＇ segment. We also study focal mechanisms and segmentation of strong aftershocks. The principal compressive stress azimuth of aftershock area is WNW direction and the faulting types of aftershocks at southern and northern segment have the same proportion. Because afiershocks distribute on different secondary faults, their focal mechanisms present complex local tectonic stress field. The faulting of seven strong earthquakes on the Longmenshan central fault is mainly characterized by thrust with the component of right-lateral strike-slip. Meantime six strong aftershocks on the Longmenshan back-range fault and Qingchuan fault present strike-slip faulting. At last we discuss the complex segmentation rupture mechanism of the Wenchuan earthquake.

Spatio-temporal variation and propagation direction of coal fire in Jharia Coalfield,India by satellite-based multi-temporal night-time land surface temperature imaging

In this paper,the spatio-temporal variation and propagation direction of coal fire were studied in the Jharia Coalfield(JCF),India during 2006–2015 through satellite-based night-time land surface temperature(LST)imaging.The LST was retrieved from Advanced Spaceborne Thermal Emission and Reflection Radiometer(ASTER)night-time thermal-infrared data by a robust split-window algorithm based on scene-specific regression coefficients,band-specific hybrid emissivity,and night-time atmospheric transmittance.The LST-profile-based coal fire detection algorithm was formulated through statistical analysis of the LST values along multiple transects across diverse coal fire locations in the JCF in order to compute date-specific threshold temperatures for separating thermally-anomalous and background pixels.This algorithm efficiently separates surface fire,subsurface fire,and thermally-anomalous transitional pixels.During the observation period,it was noticed that the coal fire area increased significantly,which resulted from new coal fire at many places owing to extensive opencast-mining operations.It was observed that the fire propagation occurred primarily along the dip direction of the coal seams.At places,lateral-propagation of limited spatial extent was also observed along the strike direction possibly due to spatial continuity of the coal seams along strike.Moreover,the opencast-mining activities carried out during 2009–2015 and the structurally weak planes facilitated the fire propagation.

Spatio-temporal Variation of Soil Respiration and Its Driving Factors in Semi-arid Regions of North China

Soil respiration （SR） is the second-largest flux in ecosystem carbon cycling. Due to the large spatio-temporal variability of environmental factors, SR varied among different vegetation types, thereby impeding accurate estimation of CO2 emissions via SR. However, studies on spatio-temporal variation of SR are still scarce for semi-arid regions of North China. In this study, we conducted 12-month SR measurements in six land-use types, including two secondary forests （Populus tomentosa （PT） and Robinia pseudoacacia （RP））, three artificial plantations （Armeniaca sibirica （AS）, Punica granatum （PG） and Ziziphusjujuba （Z J）） and one natural grassland （GR）, to quantify spatio-temporal variation of SR and distinguish its controlling factors. Results indicated that SR exhibited distinct sea- sonal patterns for the six sites. Soil respiration peaked in August 2012 and bottomed in April 2013. The temporal coefficient of variation （CI0 of SR for the six sites ranged from 76.98% to 94.08%, while the spatial CV of SR ranged from 20.28% to 72.97% across the 12-month measurement. Soil temperature and soil moisture were the major controlling factors of temporal variation of SR in the six sites, while spatial variation in SR was mainly caused by the differences in soil total nitrogen （STN）, soil organic carbon （SOC）, net photosynthesis rate, and fine root biomass. Our results show that the annual average SR and Q10 （temperature sensitivity of soil respira- tion） values tended to decrease from secondary forests and grassland to plantations, indicating that the conversion of natural ecosystems to man-made ecosystems may reduce CO2 emissions and SR temperature sensitivity. Due to the high spatio-temporal variation of SR in our study area, care should be taken when converting secondary forests and grassland to plantations from the point view of accurately quantifying C02 emissions via SR at regional scales.

Spatio-temporal Variations of Temperature and Precipitation During 1951–2019 in Arid and Semiarid Region, China

Understanding the spatio-temporal variations of temperature and precipitation in the arid and semiarid region of China(ASRC)is of great significance for promoting regional eco-environmental protection and policy-making.In this study,the annual and seasonal spatio-temporal patterns of change in average temperature and precipitation and their influencing factors in the ASRC were analyzed using the Mann-Kendall test,linear tendency estimation,accumulative anomaly and the Pearson’s correlation coefficient.The results showed that both annual average temperature and average annual precipitation increased in the ASRC during 1951–2019.The temperature rose by about 1.93℃and precipitation increased by about 24 mm.The seasonal average temperature presented a significant increase trend,and the seasonal precipitation was conspicuous ascension in spring and winter.The spatio-temporal patterns of change in temperature and precipitation differed,with the southwest area showing the most obvious variation in each season.Abrupt changes in annual and seasonal average temperature and precipitation occurred mainly around the 1990 s and after 2000,respectively.Atmospheric circulation had an important effect on the trends and abrupt changes in temperature and precipitation.The East Asian summer monsoon had the largest impact on the trend of average annual temperature,as well as on the abrupt changes of annual average temperature and precipitation.Temperature and precipitation changes in the ASRC were influenced by long-term and short-term as well as direct and indirect anthropogenic and natural factors.This study identifies the characteristics of spatio-temporal variations in temperature and precipitation in the ASRC and provides a scientific reference for the formulation of climate change responses.

SPATIO-TEMPORAL VARIATION OF ACTUAL EVAPOTRANSPIRATION AND ITS RELATION WITH CLIMATE PARAMETERS IN THE PEARL RIVER BASIN,CHINA

Spatio-temporal variation of actual evapotranspiration(ETa) in the Pearl River basin from 1961 to 2010 are analyzed based on daily data from 60 national observed stations. ETa is calculated by the Advection-Aridity model(AA model) in the current study, and Mann-Kendall test(MK) and Inverse Distance Weighted interpolation method(IDW)were applied to detect the trends and spatial variation pattern. The relations of ETa with climate parameters and radiation/dynamic terms are analyzed by Person correlation method. Our findings are shown as follows: 1) Mean annual ETa in the Pearl River basin is about 665.6 mm/a. It has significantly decreased in 1961-2010 at a rate of-24.3mm/10 a. Seasonally, negative trends of summer and autumn ETa are higher than that of spring and winter. 2) The value of ETa is higher in the southeast coastal area than in the northwest region of the Pearl River basin, while the latter has shown the strongest negative trend. 3) Negative trends of ETa in the Pearl River basin are most probably due to decreasing radiation term and increasing dynamic term. The decrease of the radiation term is related with declining diurnal temperature range and sunshine duration, and rising atmospheric pressure as well. The contribution of dynamic term comes from increasing average temperature, maximum and minimum temperatures in the basin. Meanwhile, the decreasing average wind speed weakens dynamic term and finally, to a certain extent, it slows down the negative trend of the ETa.

SPATIO-TEMPORAL VARIATION CHARACTERISTICS OF EXTREMELY HEAVY PRECIPITATION FREQUENCY OVER SOUTH CHINA IN THE LAST 50 YEARS

This paper comprehensively studies the spatio-temporal characteristics of the frequency of extremely heavy precipitation events over South China by using the daily precipitation data of 110 stations during 1961 to 2008 and the extremely heavy precipitation thresholds determined for different stations by REOF, trend coefficients, linear trend, Mann-Kendall test and variance analysis. The results are shown as follows. The frequency distribution of extremely heavy precipitation is high in the middle of South China and low in the Guangdong coast and western Guangxi. There are three spatial distribution types of extremely heavy precipitation in South China. The consistent anomaly distribution is the main type. Distribution reversed between the east and the west and between the south and the north is also an important type. Extremely heavy precipitation events in South China mainly occurred in the summer-half of the year. Their frequency during this time accounts for 83.7% of the total frequency. In the 1960 s and 1980 s, extremely heavy precipitation events were less frequent while having an increasing trend from the late 1980 s. Their climatological tendency rates decrease in the central and rise in the other areas of South China, and on average the mean series also shows an upward but insignificant trend at all of the stations. South China's frequency of extremely heavy precipitation events can be divided into six major areas and each of them shows a different inter-annual trend and three of the representative stations experience abrupt changes by showing remarkable increases in terms of Mann-Kendall tests.

Spatio-Temporal Variation of HIV Infection in Kenya

Disease mapping is the study of the distribution of disease relative risks or rates in space and time, and normally uses generalized linear mixed models (GLMMs) which includes fixed effects and spatial, temporal, and spatio-temporal random effects. Model fitting and statistical inference are commonly accomplished through the empirical Bayes (EB) and fully Bayes (FB) approaches. The EB approach usually relies on the penalized quasi-likelihood (PQL), while the FB approach, which has increasingly become more popular in the recent past, usually uses Markov chain Monte Carlo (McMC) techniques. However, there are many challenges in conventional use of posterior sampling via McMC for inference. This includes the need to evaluate convergence of posterior samples, which often requires extensive simulation and can be very time consuming. Spatio-temporal models used in disease mapping are often very complex and McMC methods may lead to large Monte Carlo errors if the dimension of the data at hand is large. To address these challenges, a new strategy based on integrated nested Laplace approximations (INLA) has recently been recently developed as a promising alternative to the McMC. This technique is now becoming more popular in disease mapping because of its ability to fit fairly complex space-time models much more quickly than the McMC. In this paper, we show how to fit different spatio-temporal models for disease mapping with INLA using the Leroux CAR prior for the spatial component, and we compare it with McMC using Kenya HIV incidence data during the period 2013-2016.

Wi-Fi Positioning Dataset with Multiusers and Multidevices Considering Spatio-Temporal Variations

Precise information on indoor positioning provides a foundation for position-related customer services.Despite the emergence of several indoor positioning technologies such as ultrawideband,infrared,radio frequency identification,Bluetooth beacons,pedestrian dead reckoning,and magnetic field,Wi-Fi is one of the most widely used technologies.Predominantly,Wi-Fi fingerprinting is the most popular method and has been researched over the past two decades.Wi-Fi positioning faces three core problems:device heterogeneity,robustness to signal changes caused by human mobility,and device attitude,i.e.,varying orientations.The existing methods do not cover these aspects owing to the unavailability of publicly available datasets.This study introduces a dataset that includes the Wi-Fi received signal strength(RSS)gathered using four different devices,namely Samsung Galaxy S8,S9,A8,LG G6,and LG G7,operated by three surveyors,including a female and two males.In addition,three orientations of the smartphones are used for the data collection and include multiple buildings with a multifloor environment.Various levels of human mobility have been considered in dynamic environments.To analyze the time-related impact on Wi-Fi RSS,data over 3 years have been considered.

Improved spatio-temporal alignment measurement method for hull deformation

In this paper,an improved spatio-temporal alignment measurement method is presented to address the inertial matching measurement of hull deformation under the coexistence of time delay and large misalignment angle.Large misalignment angle and time delay often occur simultaneously and bring great challenges to the accurate measurement of hull deformation in space and time.The proposed method utilizes coarse alignment with large misalignment angle and time delay estimation of inertial measurement unit modeling to establish a brand-new spatiotemporal aligned hull deformation measurement model.In addition,two-step loop control is designed to ensure the accurate description of dynamic deformation angle and static deformation angle by the time-space alignment method of hull deformation.The experiments illustrate that the proposed method can effectively measure the hull deformation angle when time delay and large misalignment angle coexist.

Epidemic Characteristics and Spatio-Temporal Patterns of HFRS in Qingdao City,China,2010-2022

Objective This study investigated the epidemic characteristics and spatio-temporal dynamics of hemorrhagic fever with renal syndrome(HFRS)in Qingdao City,China.Methods Information was collected on HFRS cases in Qingdao City from 2010 to 2022.Descriptive epidemiologic,seasonal decomposition,spatial autocorrelation,and spatio-temporal cluster analyses were performed.Results A total of 2,220 patients with HFRS were reported over the study period,with an average annual incidence of 1.89/100,000 and a case fatality rate of 2.52%.The male:female ratio was 2.8:1.75.3%of patients were aged between 16 and 60 years old,75.3%of patients were farmers,and 11.6%had both“three red”and“three pain”symptoms.The HFRS epidemic showed two-peak seasonality:the primary fall-winter peak and the minor spring peak.The HFRS epidemic presented highly spatially heterogeneous,street/township-level hot spots that were mostly distributed in Huangdao,Pingdu,and Jiaozhou.The spatio-temporal cluster analysis revealed three cluster areas in Qingdao City that were located in the south of Huangdao District during the fall-winter peak.Conclusion The distribution of HFRS in Qingdao exhibited periodic,seasonal,and regional characteristics,with high spatial clustering heterogeneity.The typical symptoms of“three red”and“three pain”in patients with HFRS were not obvious.

Dynamic adaptive spatio-temporal graph network for COVID-19 forecasting

Appropriately characterising the mixed space-time relations of the contagion process caused by hybrid space and time factors remains the primary challenge in COVID-19 forecasting.However,in previous deep learning models for epidemic forecasting,spatial and temporal variations are captured separately.A unified model is developed to cover all spatio-temporal relations.However,this measure is insufficient for modelling the complex spatio-temporal relations of infectious disease transmission.A dynamic adaptive spatio-temporal graph network(DASTGN)is proposed based on attention mechanisms to improve prediction accuracy.In DASTGN,complex spatio-temporal relations are depicted by adaptively fusing the mixed space-time effects and dynamic space-time dependency structure.This dual-scale model considers the time-specific,space-specific,and direct effects of the propagation process at the fine-grained level.Furthermore,the model characterises impacts from various space-time neighbour blocks under time-varying interventions at the coarse-grained level.The performance comparisons on the three COVID-19 datasets reveal that DASTGN achieves state-of-the-art results with a maximum improvement of 17.092%in the root mean-square error and 11.563%in the mean absolute error.Experimental results indicate that the mechanisms of designing DASTGN can effectively detect some spreading characteristics of COVID-19.The spatio-temporal weight matrices learned in each proposed module reveal diffusion patterns in various scenarios.In conclusion,DASTGN has successfully captured the dynamic spatio-temporal variations of COVID-19,and considering multiple dynamic space-time relationships is essential in epidemic forecasting.

An Intelligent Framework for Resilience Recovery of FANETs with Spatio-Temporal Aggregation and Multi-Head Attention Mechanism

Due to the time-varying topology and possible disturbances in a conflict environment,it is still challenging to maintain the mission performance of flying Ad hoc networks(FANET),which limits the application of Unmanned Aerial Vehicle(UAV)swarms in harsh environments.This paper proposes an intelligent framework to quickly recover the cooperative coveragemission by aggregating the historical spatio-temporal network with the attention mechanism.The mission resilience metric is introduced in conjunction with connectivity and coverage status information to simplify the optimization model.A spatio-temporal node pooling method is proposed to ensure all node location features can be updated after destruction by capturing the temporal network structure.Combined with the corresponding Laplacian matrix as the hyperparameter,a recovery algorithm based on the multi-head attention graph network is designed to achieve rapid recovery.Simulation results showed that the proposed framework can facilitate rapid recovery of the connectivity and coverage more effectively compared to the existing studies.The results demonstrate that the average connectivity and coverage results is improved by 17.92%and 16.96%,respectively compared with the state-of-the-art model.Furthermore,by the ablation study,the contributions of each different improvement are compared.The proposed model can be used to support resilient network design for real-time mission execution.

Warhead fragments motion trajectories tracking and spatio-temporal distribution reconstruction method based on high-speed stereo photography

High speed photography technique is potentially the most effective way to measure the motion parameter of warhead fragment benefiting from its advantages of high accuracy,high resolution and high efficiency.However,it faces challenge in dense objects tracking and 3D trajectories reconstruction due to the characteristics of small size and dense distribution of fragment swarm.To address these challenges,this work presents a warhead fragments motion trajectories tracking and spatio-temporal distribution reconstruction method based on high-speed stereo photography.Firstly,background difference algorithm is utilized to extract the center and area of each fragment in the image sequence.Subsequently,a multi-object tracking(MOT)algorithm using Kalman filtering and Hungarian optimal assignment is developed to realize real-time and robust trajectories tracking of fragment swarm.To reconstruct 3D motion trajectories,a global stereo trajectories matching strategy is presented,which takes advantages of epipolar constraint and continuity constraint to correctly retrieve stereo correspondence followed by 3D trajectories refinement using polynomial fitting.Finally,the simulation and experimental results demonstrate that the proposed method can accurately track the motion trajectories and reconstruct the spatio-temporal distribution of 1.0×10^(3)fragments in a field of view(FOV)of 3.2 m×2.5 m,and the accuracy of the velocity estimation can achieve 98.6%.

A cloud model target damage effectiveness assessment algorithm based on spatio-temporal sequence finite multilayer fragments dispersion

To solve the problem of target damage assessment when fragments attack target under uncertain projectile and target intersection in an air defense intercept,this paper proposes a method for calculating target damage probability leveraging spatio-temporal finite multilayer fragments distribution and the target damage assessment algorithm based on cloud model theory.Drawing on the spatial dispersion characteristics of fragments of projectile proximity explosion,we divide into a finite number of fragments distribution planes based on the time series in space,set up a fragment layer dispersion model grounded in the time series and intersection criterion for determining the effective penetration of each layer of fragments into the target.Building on the precondition that the multilayer fragments of the time series effectively assail the target,we also establish the damage criterion of the perforation and penetration damage and deduce the damage probability calculation model.Taking the damage probability of the fragment layer in the spatio-temporal sequence to the target as the input state variable,we introduce cloud model theory to research the target damage assessment method.Combining the equivalent simulation experiment,the scientific and rational nature of the proposed method were validated through quantitative calculations and comparative analysis.

Self-Attention Spatio-Temporal Deep Collaborative Network for Robust FDIA Detection in Smart Grids

False data injection attack(FDIA)can affect the state estimation of the power grid by tampering with the measured value of the power grid data,and then destroying the stable operation of the smart grid.Existing work usually trains a detection model by fusing the data-driven features from diverse power data streams.Data-driven features,however,cannot effectively capture the differences between noisy data and attack samples.As a result,slight noise disturbances in the power grid may cause a large number of false detections for FDIA attacks.To address this problem,this paper designs a deep collaborative self-attention network to achieve robust FDIA detection,in which the spatio-temporal features of cascaded FDIA attacks are fully integrated.Firstly,a high-order Chebyshev polynomials-based graph convolution module is designed to effectively aggregate the spatio information between grid nodes,and the spatial self-attention mechanism is involved to dynamically assign attention weights to each node,which guides the network to pay more attention to the node information that is conducive to FDIA detection.Furthermore,the bi-directional Long Short-Term Memory(LSTM)network is introduced to conduct time series modeling and long-term dependence analysis for power grid data and utilizes the temporal selfattention mechanism to describe the time correlation of data and assign different weights to different time steps.Our designed deep collaborative network can effectively mine subtle perturbations from spatiotemporal feature information,efficiently distinguish power grid noise from FDIA attacks,and adapt to diverse attack intensities.Extensive experiments demonstrate that our method can obtain an efficient detection performance over actual load data from New York Independent System Operator(NYISO)in IEEE 14,IEEE 39,and IEEE 118 bus systems,and outperforms state-of-the-art FDIA detection schemes in terms of detection accuracy and robustness.

Multi-Scale Location Attention Model for Spatio-Temporal Prediction of Disease Incidence

Due to the increasingly severe challenges brought by various epidemic diseases,people urgently need intelligent outbreak trend prediction.Predicting disease onset is very important to assist decision-making.Most of the exist-ing work fails to make full use of the temporal and spatial characteristics of epidemics,and also relies on multi-variate data for prediction.In this paper,we propose a Multi-Scale Location Attention Graph Neural Networks(MSLAGNN)based on a large number of Centers for Disease Control and Prevention(CDC)patient electronic medical records research sequence source data sets.In order to understand the geography and timeliness of infec-tious diseases,specific neural networks are used to extract the geography and timeliness of infectious diseases.In the model framework,the features of different periods are extracted by a multi-scale convolution module.At the same time,the propagation effects between regions are simulated by graph convolution and attention mechan-isms.We compare the proposed method with the most advanced statistical methods and deep learning models.Meanwhile,we conduct comparative experiments on data sets with different time lengths to observe the predic-tion performance of the model in the face of different degrees of data collection.We conduct extensive experi-ments on real-world epidemic-related data sets.The method has strong prediction performance and can be readily used for epidemic prediction.

Spatio-Temporal Change of Dispersal Areas of Greater Kudu (Tragelaphus strepsiceros) in Lake Bogoria Landscape, Kenya

Decline in wildlife populations is manifest globally, regionally and locally. A wildlife decline of 68% has been reported in Kenya’s rangelands with Baringo County experiencing more than 85% wildlife loss in the last four decades. Greater Kudu (Tragelaphus strepsiceros) is endemic to Lake Bogoria landscape in Baringo County and constitutes a major tourist attraction for the region necessitating use of its photo on the County’s logo and thus a flagship species. Tourism plays a central role in Baringo County’s economy and is a major source of potential growth and employment creation. The study was carried out to assess spatio-temporal change of dispersal areas of Greater Kudu (GK) in Lake Bogoria landscape in the last four years for enhanced adaptive management and improved livelihoods. GK population distribution primary data collected in December 2022 and secondary data acquired from Lake Bogoria National Game Reserve (LBNGR) for 2019 and 2020 were digitized using in a Geographic Information System (GIS). Measures of dispersion and point pattern analysis (PPA) were used to analyze dispersal of GK population using GIS. Spatio-temporal change of GK dispersal in LBNR was evident thus the null hypothesis was rejected. It is recommended that anthropogenic activities contributing to GK’s habitat degradation be curbed by providing alternative livelihood sources and promoting community adoption of sustainable technologies for improved livelihoods.

Research on the Spatio-Temporal Evolution and Driving Forces of Green Spaces in the Central Urban Area of Zunyi City

Green space,as a medium for carrying out urban functions and guiding urban development,is becoming a scarce resource along with the urbanization process and the intensification of environmental problems.In the face of the spatial mismatch between high demand and low supply,it is of great significance to clarify the evolution mechanism of green space to undertake national spatial planning,protect the natural strategic resources in the urban fringe area,and promote the sustainable development of the“three living spaces.”The study focuses on the Zunyi City Center,selecting the 20 years of rapid development following its establishment as a city as the study period.It explores the dynamic evolution of green space and the main driving forces during different periods using remote-sensing image data.The study shows that from 2003 to 2023,the total scale of green space has an obvious decreasing trend along with the expansion of the urban built-up area.A large amount of arable land is being converted to construction land,resulting in a sudden decrease in arable land area.In the past 10 years,the comprehensive land use dynamics have accelerated.Still,the spatial difference has gradually narrowed,indicating that the overall development intensity of Zunyi City’s central urban area has increased.There is a gradual spread of the trend to the hilly areas.The limiting effect of the mountainous natural environment on the city’s development has gradually diminished under the superposition of external factors,such as economic development,industrial technological upgrading,and policy orientation so the importance of the effective protection and rational utilization of urban green space has become more prominent.

Traveling Wave Solutions of a SIR Epidemic Model with Spatio-Temporal Delay

In this paper, we studied the traveling wave solutions of a SIR epidemic model with spatial-temporal delay. We proved that this result is determined by the basic reproduction number R0and the minimum wave speed c*of the corresponding ordinary differential equations. The methods used in this paper are primarily the Schauder fixed point theorem and comparison principle. We have proved that when R0>1and c>c*, the model has a non-negative and non-trivial traveling wave solution. However, for R01and c≥0or R0>1and 0cc*, the model does not have a traveling wave solution.