Semi-2DCAE: a semi-supervision 2D-CNN AutoEncoder model for feature representation and classification of encrypted traffic.

Traffic classification is essential in network-related areas such as network management, monitoring, and security. As the proportion of encrypted internet traffic rises, the accuracy of port-based and DPI-based traffic classification methods has declined. The methods based on machine learning and deep learning have effectively improved the accuracy of traffic classification, but they still suffer from inadequate extraction of traffic structure features and poor feature representativeness. This article proposes a model called Semi-supervision 2-Dimensional Convolution AutoEncoder (Semi-2DCAE). The model extracts the spatial structure features in the original network traffic by 2-dimensional convolution neural network (2D-CNN) and uses the autoencoder structure to downscale the data so that different traffic features are represented as spectral lines in different intervals of a one-dimensional standard coordinate system, which we call FlowSpectrum. In this article, the PRuLe activation function is added to the model to ensure the stability of the training process. We use the ISCX-VPN2016 dataset to test the classification effect of FlowSpectrum model. The experimental results show that the proposed model can characterize the encrypted traffic features in a one-dimensional coordinate system and classify Non-VPN encrypted traffic with an accuracy of up to 99.2%, which is about 7% better than the state-of-the-art solution, and VPN encrypted traffic with an accuracy of 98.3%, which is about 2% better than the state-of-the-art solution.

Modelling the transmission and control of COVID-19 in Yangzhou city with the implementation of Zero-COVID policy.

In the fight against the COVID-19 pandemic, China has long adhered to the "Dynamic Zero COVID-19" strategy till the end of 2022. To understand the mechanism of this strategy, we used the case of the Yangzhou summer outbreak in 2021 and a multi-stage dynamical model incorporating city-wide and key area testing-trace-isolation (TTI) strategies. We defined two time-varying indexes for measuring the disease transmission risk and the public health prevention and control force, respectively, which allowed us to explore the mechanisms of TTI policies. Integrating with the historical data and literature parameter values, we first estimated the parameters and then quantified the relevant indexes over time. The findings showed that multiple rounds of rapid testing were one of the critical measures to overcome the outbreak in Yangzhou within one month. In addition, we compared the impact of the duration of the free transmission stage, tracking rate, testing interval and precise division of key areas on the epidemiological indicators, including the final sizes of infections and isolations, peak value, peak arrival time and epidemic duration and the minimum round of testing. Our results suggest that the early detection of the epidemic, an improved efficiency of tracking, and a reduced duration of each test play a positive role in restraining COVID-19; however, a considerable investment of resources was essential to achieve a significant effect quickly.

A West Nile virus nonlocal model with free boundaries and seasonal succession.

The paper deals with a West Nile virus (WNv) model, in which the nonlocal diffusion characterizes the long-range movement of birds and mosquitoes, the free boundaries describe their spreading fronts, and the seasonal succession accounts for the effect of the warm and cold seasons. The well-posedness of the mathematical model is established, and its long-term dynamical behaviours, which depend upon the generalized eigenvalues of the corresponding linearized differential operator, are investigated. For both spatially independent and nonlocal WNv models with seasonal successions, the generalized eigenvalues are studied and applied to determine whether the spreading or vanishing occurs. Our results extend those for the case with nonlocal diffusion but no free boundary and those for the case with free boundary but local diffusion, respectively. The generalized eigenvalues reveal that there exists positive correlation between the duration of the warm season and the risk of infection. Moreover, the initial infection length, the initial infection scale and the spreading ability to new areas all play important roles for the long time behaviors of the time dependent solutions.

Assessing the mechanism of citywide test-trace-isolate Zero-COVID policy and exit strategy of COVID-19 pandemic.

BACKGROUND: Countries that aimed for eliminating the cases of COVID-19 with test-trace-isolate policy are found to have lower infections, deaths, and better economic performance, compared with those that opted for other mitigation strategies. However, the continuous evolution of new strains has raised the question of whether COVID-19 eradication is still possible given the limited public health response capacity and fatigue of the epidemic. We aim to investigate the mechanism of the Zero-COVID policy on outbreak containment, and to explore the possibility of eradication of Omicron transmission using the citywide test-trace-isolate (CTTI) strategy. METHODS: We develop a compartmental model incorporating the CTTI Zero-COVID policy to understand how it contributes to the SARS-CoV-2 elimination. We employ our model to mimic the Delta outbreak in Fujian Province, China, from September 10 to October 9, 2021, and the Omicron outbreak in Jilin Province, China for the period from March 1 to April 1, 2022. Projections and sensitivity analyses were conducted using dynamical system and Latin Hypercube Sampling/ Partial Rank Correlation Coefficient (PRCC). RESULTS: Calibration results of the model estimate the Fujian Delta outbreak can end in 30 (95% confidence interval CI: 28-33) days, after 10 (95% CI: 9-11) rounds of citywide testing. The emerging Jilin Omicron outbreak may achieve zero COVID cases in 50 (95% CI: 41-57) days if supported with sufficient public health resources and population compliance, which shows the effectiveness of the CTTI Zero-COVID policy. CONCLUSIONS: The CTTI policy shows the capacity for the eradication of the Delta outbreaks and also the Omicron outbreaks. Nonetheless, the implementation of radical CTTI is challenging, which requires routine monitoring for early detection, adequate testing capacity, efficient contact tracing, and high isolation compliance, which constrain its benefits in regions with limited resources. Moreover, these challenges become even more acute in the face of more contagious variants with a high proportion of asymptomatic cases. Hence, in regions where CTTI is not possible, personal protection, public health control measures, and vaccination are indispensable for mitigating and exiting the COVID-19 pandemic.

The impact factors of the risk index and diffusive dynamics of a SIS free boundary model.

To discuss the impact factors on the spread of infectious diseases, we study a free boundary problem describing a SIS (susceptible-infected-susceptible) model in a heterogeneous environment. Firstly, the existence and uniqueness of the global solution are given. Then the basic reproduction number related to time is defined, and a spreading-vanishing dichotomy of infectious diseases is obtained. The impacts of the diffusion rate of infected individuals, expanding capability, and the scope and scale of initial infection on the spreading and vanishing of infectious disease are analyzed. Numerical simulations are given to show that the large expanding capability is unfavorable to the prevention and control of the disease.

Four-tier response system and spatial propagation of COVID-19 in China by a network model.

In order to investigate the effectiveness of lockdown and social distancing restrictions, which have been widely carried out as policy choice to curb the ongoing COVID-19 pandemic around the world, we formulate and discuss a staged and weighted network system based on a classical SEAIR epidemiological model. Five stages have been taken into consideration according to four-tier response to Public Health Crisis, which comes from the National Contingency Plan in China. Staggered basic reproduction number has been derived and we evaluate the effectiveness of lockdown and social distancing policies under different scenarios among 19 cities/regions in mainland China. Further, we estimate the infection risk associated with the sequential release based on population mobility between cities and the intensity of some non-pharmaceutical interventions. Our results reveal that Level I public health emergency response is necessary for high-risk cities, which can flatten the COVID-19 curve effectively and quickly. Moreover, properly designed staggered-release policies are extremely significant for the prevention and control of COVID-19, furthermore, beneficial to economic activities and social stability and development.

Coexistence of a cross-diffusive West Nile virus model in a heterogenous environment.

This paper is concerned with a strongly-coupled elliptic system, which describes a West Nile virus (WNv) model with cross-diffusion in a heterogeneous environment. The basic reproduction number is introduced through the next generation infection operator and some related eigenvalue problems. The existence of coexistence states is presented by using a method of upper and lower solutions. The true positive solutions are obtained by monotone iterative schemes. Our results show that a cross-diffusive WNv model possesses at least one coexistence solution if the basic reproduction number is greater than one and the cross-diffusion rates are small enough, while if the basic reproduction number is less than or equal to one, the model has no positive solution. To illustrate the impact of cross-diffusion and environmental heterogeneity on the transmission of WNv, some numerical simulations are given.

Free boundary models for mosquito range movement driven by climate warming.

As vectors, mosquitoes transmit numerous mosquito-borne diseases. Among the many factors affecting the distribution and density of mosquitoes, climate change and warming have been increasingly recognized as major ones. In this paper, we make use of three diffusive logistic models with free boundary in one space dimension to explore the impact of climate warming on the movement of mosquito range. First, a general model incorporating temperature change with location and time is introduced. In order to gain insights of the model, a simplified version of the model with the change of temperature depending only on location is analyzed theoretically, for which the dynamical behavior is completely determined and presented. The general model can be modified into a more realistic one of seasonal succession type, to take into account of the seasonal changes of mosquito movements during each year, where the general model applies only for the time period of the warm seasons of the year, and during the cold season, the mosquito range is fixed and the population is assumed to be in a hibernating status. For both the general model and the seasonal succession model, our numerical simulations indicate that the long-time dynamical behavior is qualitatively similar to the simplified model, and the effect of climate warming on the movement of mosquitoes can be easily captured. Moreover, our analysis reveals that hibernating enhances the chances of survival and successful spreading of the mosquitoes, but it slows down the spreading speed.

The risk index for an SIR epidemic model and spatial spreading of the infectious disease.

In this paper, a reaction-diffusion-advection SIR model for the transmission of the infectious disease is proposed and analyzed. The free boundaries are introduced to describe the spreading fronts of the disease. By exhibiting the basic reproduction number RDA0 for an associated model with Dirichlet boundary condition, we introduce the risk index RF0(t) for the free boundary problem, which depends on the advection coefficient and time. Sufficient conditions for the disease to prevail or not are obtained. Our results suggest that the disease must spread if RF0(t0) ≤ 1 for some t0 and the disease is vanishing if RF0(∞) < 1, while if RF0 (0) < 1, the spreading or vanishing of the disease depends on the initial state of infected individuals as well as the expanding capability of the free boundary. We also illustrate the impacts of the expanding capability on the spreading fronts via the numerical simulations.

Spatial spreading model and dynamics of West Nile virus in birds and mosquitoes with free boundary.

In this paper, a reaction-diffusion system is proposed to model the spatial spreading of West Nile virus in vector mosquitoes and host birds in North America. Transmission dynamics are based on a simplified model involving mosquitoes and birds, and the free boundary is introduced to model and explore the expanding front of the infected region. The spatial-temporal risk index [Formula: see text], which involves regional characteristic and time, is defined for the simplified reaction-diffusion model with the free boundary to compare with other related threshold values, including the usual basic reproduction number [Formula: see text]. Sufficient conditions for the virus to vanish or to spread are given. Our results suggest that the virus will be in a scenario of vanishing if [Formula: see text], and will spread to the whole region if [Formula: see text] for some [Formula: see text], while if [Formula: see text], the spreading or vanishing of the virus depends on the initial number of infected individuals, the area of the infected region, the diffusion rate and other factors. Moreover, some remarks on the basic reproduction numbers and the spreading speeds are presented and compared.

Seasonality of Influenza A(H7N9) Virus in China-Fitting Simple Epidemic Models to Human Cases.

BACKGROUND: Three epidemic waves of influenza A(H7N9) (hereafter 'H7N9') human cases have occurred between March 2013 and July 2015 in China. However, the underlying transmission mechanism remains unclear. Our main objective is to use mathematical models to study how seasonality, secular changes and environmental transmission play a role in the spread of H7N9 in China. METHODS: Data on human cases and chicken cases of H7N9 infection were downloaded from the EMPRES-i Global Animal Disease Information System. We modelled on chicken-to-chicken transmission, assuming a constant ratio of 10-6 human case per chicken case, and compared the model fit with the observed human cases. We developed three different modified Susceptible-Exposed-Infectious-Recovered-Susceptible models: (i) a non-periodic transmission rate model with an environmental class, (ii) a non-periodic transmission rate model without an environmental class, and (iii) a periodic transmission rate model with an environmental class. We then estimated the key epidemiological parameters and compared the model fit using Akaike Information Criterion and Bayesian Information Criterion. RESULTS: Our results showed that a non-periodic transmission rate model with an environmental class provided the best model fit to the observed human cases in China during the study period. The estimated parameter values were within biologically plausible ranges. CONCLUSIONS: This study highlighted the importance of considering secular changes and environmental transmission in the modelling of human H7N9 cases. Secular changes were most likely due to control measures such as Live Poultry Markets closures that were implemented during the initial phase of the outbreaks in China. Our results suggested that environmental transmission via viral shedding of infected chickens had contributed to the spread of H7N9 human cases in China.

Stability patterns for a size-structured population model and its stage-structured counterpart.

In this paper we compare a general size-structured population model, where a size-structured consumer feeds upon an unstructured resource, to its simplified stage-structured counterpart in terms of equilibrium stability. Stability of the size-structured model is understood in terms of an equivalent delayed system consisting of a renewal equation for the consumer population birth rate and a delayed differential equation for the resource. Results show that the size- and stage-structured models differ considerably with respect to equilibrium stability, although the two models have completely identical equilibrium solutions. First, when adult consumers are superior foragers to juveniles, the size-structured model is more stable than the stage-structured model while the opposite occurs when juveniles are the superior foragers. Second, relatively large juvenile (adult) mortality tends to stabilise (destabilise) the size-structured model but destabilise (stabilise) the stage-structured model. Third, the stability pattern is sensitive to the adult-offspring size ratio in the size-structured model but much less sensitive in the stage-structured model. Finally, unless the adult-offspring size ratio is sufficiently small, the stage-structured model cannot satisfactorily capture the dynamics of the size-structured model. We conclude that caution must be taken when the stage-structured population model is applied, although it can consistently translate individual life history and stage-specific differences to the population level.

The spreading frontiers of avian-human influenza described by the free boundary.

In this paper, a reaction-diffusion system is proposed to investigate avian-human influenza. Two free boundaries are introduced to describe the spreading frontiers of the avian influenza. The basic reproduction numbers r 0 F (t) and R 0 F (t) are defined for the bird with the avian influenza and for the human with the mutant avian influenza of the free boundary problem, respectively. Properties of these two time-dependent basic reproduction numbers are obtained. Sufficient conditions both for spreading and for vanishing of the avian influenza are given. It is shown that if r 0 F (0) < 1 and the initial number of the infected birds is small, the avian influenza vanishes in the bird world. Furthermore, if r 0 F (0) < 1 and R 0 F (0) < 1, the avian influenza vanishes in the bird and human worlds. In the case that r 0 F (0) < 1 and R 0 F (0) > 1, spreading of the mutant avian influenza in the human world is possible. It is also shown that if r 0 F (t 0) ⩾ 1 for any t 0 ⩾ 0, the avian influenza spreads in the bird world.

Effects of growth curve plasticity on size-structured population dynamics.

The physiological-structured population models assume that a fixed fraction of energy intake is utilized for individual growth and maintenance while the remaining for adult fertility. The assumption results in two concerns: energy loss for juveniles and a reproduction dilemma for adults. The dilemma results from the possibility that adults have to breed even if metabolic costs fail to be covered. We consider a size-structured population model, where standard metabolism is given top priority for utilizing energy intake and the surplus energy, if there is any, is distributed to individual growth and reproduction. Moreover, the portion of surplus energy for reproduction is size-dependent and increases monotonically with size. Using the newly developed parameter continuation, we demonstrate their disparate effects on population dynamics. Results show that the size-dependent mechanism of energy allocation primarily exerts destabilizing effects on the system but considerably promotes species coexistence, in comparison with the size-independent mechanism. We conclude that the size-dependent mechanism is, to a large extent, a dispensable component of model ingredients when ontogeny is explicitly taken into consideration.