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.

Traveling Wavefronts of a Diffusive Hematopoiesis Model with Time Delay

In this paper, a reaction-diffusion equation with discrete time delay that describes the dynamics of the blood cell production is analyzed. The existence of the traveling wave front solutions is demonstrated using the technique of upper and lower solutions and the associated monotone iteration.

Traveling wave for a time-periodic Lotka-Volterra model with bistable nonlinearity

This paper studies bistable wavefronts of a diffusive time-periodic Lotka-Volterra system.We obtain a new condition for the existence,uniqueness and stability of bistable timeperiodic traveling waves.This condition is sharp and greatly improves the result established in the reference(X.Bao and Z.Wang,Journal of Differential Equations,255(2013)2402-2435).An example is given to demonstrate our consequence.

An empirical study on travel demand management modeling based on discrete choice method

In view of the problem that the requirements of travel demand management and traffic policy-sensitivity are ignored during the establishment process of the travel demand forecasting model, a discrete-choice-based travel demand forecasting model is proposed to demonstrate its applicability to travel demand management. A car-bus discrete choice model is established, including three variables, i. e,, individual socioeconomic characteristics, time, and cost, and the traffic policy-sensitivity is evaluated through two kinds of traffic policies： parking charges and bus priorities. The empirical results show that travel choice is insensitive to the policy of parking charges as 88. 41% of the travelers are insensitive to parking charges; travel choice is, however, sensitive to the policy of bus priorities as 67.70% of the car travelers and 77.02% of the bus travelers are sensitive to bus priorities. The discrete-choice-based travel demand forecasting model is quite policy-sensitive and also has a good adaptability for travel demand management when meeting the basic functions of the demand forecasting model.

Improved ant colony optimization algorithm for the traveling salesman problems

Ant colony optimization （ACO） is a new heuristic algo- rithm which has been proven a successful technique and applied to a number of combinatorial optimization problems. The traveling salesman problem （TSP） is among the most important combinato- rial problems. An ACO algorithm based on scout characteristic is proposed for solving the stagnation behavior and premature con- vergence problem of the basic ACO algorithm on TSP. The main idea is to partition artificial ants into two groups： scout ants and common ants. The common ants work according to the search manner of basic ant colony algorithm, but scout ants have some differences from common ants, they calculate each route＇s muta- tion probability of the current optimal solution using path evaluation model and search around the optimal solution according to the mutation probability. Simulation on TSP shows that the improved algorithm has high efficiency and robustness.

Collision-free Scheduling of Multi-bridge Machining Systems： A Colored Traveling Salesman Problem-based Approach

Multi-bridge machining systems(MBMS) have gained wide applications in industry due to their high production capacity and efficiency. They contain multiple bridge machines working in parallel within their partially overlapping workspaces.Their scheduling problems can be abstracted into a serial-colored travelling salesman problem in which each salesman has some exclusive cities and some cities shared with its neighbor(s). To solve it, we develop a greedy algorithm that selects a neighboring city satisfying proximity. The algorithm allows a salesman to select randomly its shared cities and runs accordingly many times. It can thus be used to solve job scheduling problems for MBMS. Subsequently, a collision-free scheduling method is proposed to address both job scheduling and collision resolution issues of MBMS. It is an extension of the greedy algorithm by introducing time window constraints and a collision resolution mechanism. Thus, the augmented greedy algorithm can try its best to select stepwise a job for an individual machine such that no time overlaps exist between it and the job sequence of the neighboring machine dealt in the corresponding overlapping workspace; and remove such a time overlap only when it is inevitable. Finally, we conduct a case study of a large triplebridge waterjet cutting system by applying the proposed method.

Travel time prediction with viscoelastic traffic model

Travel time through a ring road with a total length of 80 km has been predicted by a viscoelastic traffic model(VEM), which is developed in analogous to the non-Newtonian fluid flow. The VEM expresses a traffic pressure for the unfree flow case by space headway, ensuring that the pressure can be determined by the assumption that the relevant second critical sound speed is exactly equal to the disturbance propagation speed determined by the free flow speed and the braking distance measured by the average vehicular length. The VEM assumes that the sound speed for the free flow case depends on the traffic density in some specific aspects, which ensures that it is exactly identical to the free flow speed on an empty road. To make a comparison, the open Navier-Stokes type model developed by Zhang(ZHANG, H. M. Driver memory, traffic viscosity and a viscous vehicular traffic flow model. Transp. Res. Part B, 37, 27–41(2003)) is adopted to predict the travel time through the ring road for providing the counterpart results.When the traffic free flow speed is 80 km/h, the braking distance is supposed to be 45 m,with the jam density uniquely determined by the average length of vehicles l ≈ 5.8 m. To avoid possible singular points in travel time prediction, a distinguishing period for time averaging is pre-assigned to be 7.5 minutes. It is found that the travel time increases monotonically with the initial traffic density on the ring road. Without ramp effects, for the ring road with the initial density less than the second critical density, the travel time can be simply predicted by using the equilibrium speed. However, this simpler approach is unavailable for scenarios over the second critical.

A mixed stochastic user equilibrium model considering influence of advanced traveller information systems in degradable transport network

Advanced traveler information systems （ATIS） can not only improve drivers＇ accessibility to the more accurate route travel time information, but also can improve drivers＇ adaptability to the stochastic network capacity degradations. In this paper, a mixed stochastic user equilibrium model was proposed to describe the interactive route choice behaviors between ATIS equipped and unequipped drivers on a degradable transport network. In the proposed model the information accessibility of equipped drivers was reflected by lower degree of uncertainty in their stochastic equilibrium flow distributions, and their behavioral adaptability was captured by multiple equilibrium behaviors over the stochastic network state set. The mixed equilibrium model was formulated as a fixed point problem defined in the mixed route flows, and its solution was achieved by executing an iterative algorithm. Numerical experiments were provided to verify the properties of the mixed network equilibrium model and the efficiency of the iterative algorithm.

Determination of Scheduled Travel Time for a Fixed Transit Route Based on Multistate Model

In order to provide the guideline for bus drivers to adjust speed to minimize scheduled deviation,the method for setting bus scheduled travel time is proposed. Firstly,multistate model is introduced to fit historical travel time data and identify different service states. Based on the calibrated travel time distribution parameters,an optimization model is proposed,followed by a Monte Carlo( MC) simulation based genetic algorithm( GA)procedure to obtain the optimal scheduled time. A case study from a fixed bus route from Shenzhen is used to demonstrate the model applicability. The sensitivity analysis is conducted to study the effects of parameters setting on optimal slack time for each segment. The results show that multistate model fits travel time under peak hours better than Lognormal distribution,and the length of scheduled travel time basically reflects travel time reliability.

Analysis of travel time, sources of water and well protection zones with groundwater models

This study compares numerical models with analytical solutions in computing travel times and radius of protection zones for a pumping well located in an unconfined aquifer with uniform recharge and in a semi-confined aquifer. Numerical models were capable of delineating protection zones using particle tracking method in both cases. However, protection zones defined by travel time criterion can only protect small percent of source water to the well; large percent of source water is not protected which may pose a risk of pollution of source water to the well. The case study of Leggeloo well field in the Netherlands indicates that although a well field protection area was enforced in 1980 s, elevated nitrate concentration has been monitored in the abstracted water since 1990 s. The analysis of protection areas shows that the current protection area only protects 37.4% of recharge water to the well field. A large protection area must be adopted in order to safeguard the sustainable water supply for the local community.

Travelling Wave in the Generalized Kuramoto Model with Inertia

We study the dynamics of the generalized Kuramoto model with inertia, in which oscillators with positive cou- pling strength are conformists and oscillators with negative coupling strength are contrarians. By numerically simulating the model, we find that the model supports a modulated travelling wave state except for already displayed travelling wave states and π state in previous be characterized by the phase distributions of oscillators. travelling wave state of the model in the parameter space literature. The modulated travelling wave state may Finally, the modulated travelling wave state and the are presented.

Day-to-day traffic user equilibrium model considering influence of intelligent highways and advanced traveler information systems

To explore the influence of intelligent highways and advanced traveler information systems(ATIS)on path choice behavior,a day-to-day(DTD)traffic flow evolution model with information from intelligent highways and ATIS is proposed,whereby the network reliability and experiential learning theory are introduced into the decision process for the travelers’route choice.The intelligent highway serves all the travelers who drive on it,whereas ATIS serves vehicles equipped with information systems.Travelers who drive on intelligent highways or vehicles equipped with ATIS determine their trip routes based on real-time traffic information,whereas other travelers use both the road network conditions from the previous day and historical travel experience to choose a route.Both roadway capacity degradation and travel demand fluctuations are considered to demonstrate the uncertainties in the network.The theory of traffic network flow is developed to build a DTD model considering information from intelligent highway and ATIS.The fixed point theorem is adopted to investigate the equivalence,existence and stability of the proposed DTD model.Numerical examples illustrate that using a high confidence level and weight parameter for the traffic flow reduces the stability of the proposed model.The traffic flow reaches a steady state as travelers’routes shift with repetitive learning of road conditions.The proposed model can be used to formulate scientific traffic organization and diversion schemes during road expansion or reconstruction.

Near-surface model reconstruction using pseudo well-surface simultaneous travel time tomographic inversion

The static correction of a near-surface model may be improved by using travel time tomographic inversion.We discuss unfavorable factors in the inversion of surface seismic waves that have been analyzed by the first break.These factors show that sources and geophones arranged on the surface,or close to the surface,give a first break that only includes the direct wave and the up going wave from the down going to up going transition.These up going waves have weak directivity when they arrive at a geophone and so the rays passing through the grids have small directional differences and a narrow azimuth.Drawing lessons from the advantages of Vertical Seismic Profiling(VSP) acquisition mode we describe a pseudo well-surface simultaneous travel time tomographic inversion of a near-surface model.The well depth should be increased in the surface seismic study to produce a pure up going wave,to enhance the verticality of the rays and to increase the azimuth and shorten path length of the rays.Simulations of the effect of well depth on a pseudo well-surface simultaneous travel time tomographic inversion model are reported.The results show that the static corrections are improved significantly when the well depth extends below the weathered or sub-weathered layers.The root mean square error of the statics is 1.14 or 0.93 ms for these two situations,respectively.

Existence of Travelling Waves with Strong Generic Kernel in a Vector-Disease Model

In this paper, traveling wave solutions for a vector-disease model incorporating time delay and diffusion have been studied. The existence of traveling wave solutions for the sufficiently small delays has been proved. In order to solve these problems, we are able to deal with travelling wave solutions using dynamical systems techniques, invariant manifold theory, together with linear chain techniques and the geometric singular perturbation theory. For the strong generic delay kernel, traveling wave solutions exist while the delay is sufficiently small, using the methods above.

Observations and modelling of the travel time delay and leading negative phase of the 16 September 2015 Illapel,Chile tsunami

The systematic discrepancies in both tsunami arrival time and leading negative phase(LNP)were identified for the recent transoceanic tsunami on 16 September 2015 in Illapel,Chile by examining the wave characteristics from the tsunami records at 21 Deep-ocean Assessment and Reporting of Tsunami(DART)sites and 29 coastal tide gauge stations.The results revealed systematic travel time delay of as much as 22 min(approximately 1.7%of the total travel time)relative to the simulated long waves from the 2015 Chilean tsunami.The delay discrepancy was found to increase with travel time.It was difficult to identify the LNP from the near-shore observation system due to the strong background noise,but the initial negative phase feature became more obvious as the tsunami propagated away from the source area in the deep ocean.We determined that the LNP for the Chilean tsunami had an average duration of 33 min,which was close to the dominant period of the tsunami source.Most of the amplitude ratios to the first elevation phase were approximately 40%,with the largest equivalent to the first positive phase amplitude.We performed numerical analyses by applying the corrected long wave model,which accounted for the effects of seawater density stratification due to compressibility,self-attraction and loading(SAL)of the earth,and wave dispersion compared with observed tsunami waveforms.We attempted to accurately calculate the arrival time and LNP,and to understand how much of a role the physical mechanism played in the discrepancies for the moderate transoceanic tsunami event.The mainly focus of the study is to quantitatively evaluate the contribution of each secondary physical effect to the systematic discrepancies using the corrected shallow water model.Taking all of these effects into consideration,our results demonstrated good agreement between the observed and simulated waveforms.We can conclude that the corrected shallow water model can reduce the tsunami propagation speed and reproduce the LNP,which is observed for tsunamis that have propagated over long distances frequently.The travel time delay between the observed and corrected simulated waveforms is reduced to<8 min and the amplitude discrepancy between them was also markedly diminished.The incorporated effects amounted to approximately 78%of the travel time delay correction,with seawater density stratification,SAL,and Boussinesq dispersion contributing approximately 39%,21%,and 18%,respectively.The simulated results showed that the elastic loading and Boussinesq dispersion not only affected travel time but also changed the simulated waveforms for this event.In contrast,the seawater stratification only reduced the tsunami speed,whereas the earth’s elasticity loading was responsible for LNP due to the depression of the seafloor surrounding additional tsunami loading at far-field stations.This study revealed that the traditional shallow water model has inherent defects in estimating tsunami arrival,and the leading negative phase of a tsunami is a typical recognizable feature of a moderately strong transoceanic tsunami.These results also support previous theory and can help to explain the observed discrepancies.

Urban Growth Management through Travel Demand Modeling in Washington and Oregon

Among the fast growing states in the USA,the States of Washington and Oregon have enacted legislative land use and transportation concurrency/balancing planning policies for orderly urban growth management since 1990 and 1991,respectively.Regional or urban travel demand forecasting models play an instrumental role in implementing the Washington GMA(Growth Management Act)and the Oregon TPR(Transportation Planning Rule).Both program-and project-level modeling approaches to urban land use/transportation system management are evaluated through the selected cities in Washington and Oregon.

Travel path selection based on Nested Logit model And time value calculation

This paper introduces the theory of utility maximization ofNested Logit model,the establishment of selective limbs and its probability expressions;the basic calculation formula of time value. Investigate the travel routes and travel mode choices of residents from Suzhou to Shanghai,consider different impact variables in the survey,and divide their travel lines into two travel days on weekdays due to commuting to Shanghai, and free travel to Shanghai on weekdays.The data of the survey were analyzed and analyzed,and the parameters of the established Nested Logit model were calibrated by ST AT A software.The selection model and time value of the travel route and travel mode of residents under different scenarios and different influence variables were obtained Analyze.

Modeling Interstation Travel Speed of Hybrid Bus Rapid Transit within A Bayesian Framework

Interstation travel speed is an important indicator of the running state of hybrid Bus Rapid Transit and passenger experience. Due to the influence of road traffic, traffic lights and other factors, the interstation travel speeds are often some kind of multi-peak and it is difficult to use a single distribution to model them. In this paper, a Gaussian mixture model charactizing the interstation travel speed of hybrid BRT under a Bayesian framework is established. The parameters of the model are inferred using the Reversible-Jump Markov Chain Monte Carlo approach (RJMCMC), including the number of model components and the weight, mean and variance of each component. Then the model is applied to Guangzhou BRT, a kind of hybrid BRT. From the results, it can be observed that the model can very effectively describe the heterogeneous speed data among different inter-stations, and provide richer information usually not available from the traditional models, and the model also produces an excellent fit to each multimodal speed distribution curve of the interstations. The causes of different speed distribution can be identified through investigating the Internet map of GBRT, they are big road traffic and long traffic lights respectively, which always contribute to a main road crossing. So, the BRT lane should be elevated through the main road to decrease the complexity of the running state.

Modeling the Infection Disease (Covid-19) and the Effect of Vaccination

In this paper we provide different types of approach in mathematical biology about infection disease and understanding the dynamic of epidemic mathematical models specially in COVID-19 disease which first outbroke in China and fast spread around the world. We work in the connection between the mathematical models and the solution analytically and numerically. At first, we emphasize the Susceptible-Infectious-Recovered (SIR) models’ extension for policy significance. Then, we found the improved SIER model done by research. In third section, we examine the improved model when an appropriate vaccine has been found, we introduce the model of SIR with vaccine term which ends up with discussion and conclusion about the effect of vaccinate. The comprehension of COVID-19 transmission methods, structures, and characteristics is greatly aided by these mathematical models analytically and numerically.

Dynamical Analysis of an SIS Epidemic Integrodifference Model

In order to analyze the impact of dispersal on disease transmission, we establish an SIS epidemic integrodifference model with a nonlinear incidence function. Firstly, the discrete-time SIS epidemic model is established and studied, including the existence and stability of equilibria, the existence of a flip bifurcation, and chaos. Secondly, the SIS epidemic integrodifference model is built based on the discrete-time SIS epidemic model with dispersal. The dynamic analysis of the model includes the existence and stability of equilibria, the existence of a traveling wave solution, and a minus-one bifurcation. Finally, the results suggest that dispersal causes the system to become more unstable and accelerates the spread of the disease when the equilibrium is unstable. Numerical examples are provided to demonstrate the theoretical results.