The relationship between clustering and networked Turing patterns.

Networked Turing patterns often manifest as groups of nodes distributed on either side of the homogeneous equilibrium, exhibiting high and low density. These pattern formations are significantly influenced by network topological characteristics, such as the average degree. However, the impact of clustering on them remains inadequately understood. Here, we investigate the relationship between clustering and networked Turing patterns using classical prey-predator models. Our findings reveal that when nodes of high and low density are completely distributed on both sides of the homogeneous equilibrium, there is a linear decay in Turing patterns as global clustering coefficients increase, given a fixed node size and average degree; otherwise, this linear decay may not always hold due to the presence of high-density nodes considered as low-density nodes. This discovery provides a qualitative assessment of how clustering coefficients impact the formation of Turing patterns and may contribute to understanding why using refuges in ecosystems could enhance the stability of prey-predator systems. The results link network topological structures with the stability of prey-predator systems, offering new insights into predicting and controlling pattern formations in real-world systems from a network perspective.

Urban 3D building morphology and energy consumption: empirical evidence from 53 cities in China.

The impact of building morphology on building energy consumption has been extensively studied. However, research on how 3D building morphology affects energy consumption at a macroscopic scale is lacking. In this study, we measured the mean building height (BH), mean building volume (BV), and mean European nearest neighbor distance (MENN) of the city to quantify the 3D building morphology. We then used a spatial regression model to analyze the quantitative impact of urban 3D building morphology on per capita electricity consumption (PCEC). Results indicate that at the macroscopic scale of the city, the BH and the MENN have a significant positive impact on the PCEC, while the BV has a significant negative impact on the PCEC. Moreover, the inclusion of the 3D building morphology greatly improves the model's ability to explain building energy efficiency, surpassing the impact of traditional economic factors. Considering the 3D building morphology indicators together, buildings with a lower height, a larger volume, and a more compact 3D morphology have greater potential for energy savings and are more conducive to electricity conservation. This study offers valuable insights for the energy-efficient arrangement of buildings.

Urban population density and energy conservation: Empirical evidence from 276 cities in China.

Reducing urban energy consumption is a crucial step towards achieving sustainable urban development. Urban energy plays a fundamental role in urban development, and while previous studies have examined the relationship between population size and energy conservation, the impact of increasing population density on per capita energy consumption (PCEC) remains unclear. To achieve urban energy conservation in China, it is vital to comprehend this significant relationship. This study constructs a spatial regression model to examine the relationship between population density and PCEC using 9 years of balanced panel data from 276 cities to fill a gap in the literature. The results of spatial autocorrelation indicate a significant negative relationship and heterogeneity between population density and PCEC. The results of spatial regression show that for every 1% increase in population density, there is a subsequent increase in PCEC of 0.074%. Our findings suggest that lower PCEC correlation is associated with higher urban population density. This study can be a reference for policymakers seeking new energy conservation strategies for urban development.

Final epidemic size of a two-community SIR model with asymmetric coupling.

Communities are commonly not isolated but interact asymmetrically with each other, allowing the propagation of infectious diseases within the same community and between different communities. To reveal the impact of asymmetrical interactions and contact heterogeneity on disease transmission, we formulate a two-community SIR epidemic model, in which each community has its contact structure while communication between communities occurs through temporary commuters. We derive an explicit formula for the basic reproduction number R 0 , give an implicit equation for the final epidemic size z, and analyze the relationship between them. Unlike the typical positive correlation between R 0 and z in the classic SIR model, we find a negatively correlated relationship between counterparts of our model deviating from homogeneous populations. Moreover, we investigate the impact of asymmetric coupling mechanisms on R 0 . The results suggest that, in scenarios with restricted movement of susceptible individuals within a community, R 0 does not follow a simple monotonous relationship, indicating that an unbending decrease in the movement of susceptible individuals may increase R 0 . We further demonstrate that network contacts within communities have a greater effect on R 0 than casual contacts between communities. Finally, we develop an epidemic model without restriction on the movement of susceptible individuals, and the numerical simulations suggest that the increase in human flow between communities leads to a larger R 0 .

Impact of climate change on vegetation patterns in Altay Prefecture, China.

Altay Prefecture, a typical arid region in northwestern China, has experienced the climate transition from warming-drying to warming-wetting since 1980s and has attracted widespread attention. Nonetheless, it is still unclear how climate change has influenced the distribution of vegetation in this region. In this paper, a reaction-diffusion model of the climate-vegetation system is proposed to study the impact of climate change (precipitation, temperature and carbon dioxide concentration) on vegetation patterns in Altay Prefecture. Our results indicate that the tendency of vegetation growth in Altay Prefecture improved gradually from 1985 to 2010. Under the current climate conditions, the increase of precipitation results in the change of vegetation pattern structures, and eventually vegetation coverage tends to be uniform. Moreover, we found that there exists an optimal temperature where the spot vegetation pattern structure remains stable. Furthermore, the increase in carbon dioxide concentration induces vegetation pattern transition. Based on four climate change scenarios of the Coupled Model Intercomparison Project Phase 6 (CMIP6), we used the power law range (PLR) to predict the optimal scenario for the sustainable development of the vegetation ecosystem in Altay Prefecture.

Forecast of peak infection and estimate of excess deaths in COVID-19 transmission and prevalence in Taiyuan City, 2022 to 2023.

In this paper, with the method of epidemic dynamics, we assess the spread and prevalence of COVID-19 after the policy adjustment of prevention and control measure in December 2022 in Taiyuan City in China, and estimate the excess population deaths caused by COVID-19. Based on the transmission mechanism of COVID-19 among individuals, a dynamic model with heterogeneous contacts is established to describe the change of control measures and the population's social behavior in Taiyuan city. The model is verified and simulated by basing on reported case data from November 8th to December 5th, 2022 in Taiyuan city and the statistical data of the questionnaire survey from December 1st to 23rd, 2022 in Neijiang city. Combining with reported numbers of permanent residents and deaths from 2017 to 2021 in Taiyuan city, we apply the dynamic model to estimate theoretical population of 2022 under the assumption that there is no effect of COVID-19. In addition, we carry out sensitivity analysis to determine the propagation character of the Omicron strain and the effect of the control measures. As a result of the study, it is concluded that after adjusting the epidemic policy on December 6th, 2022, three peaks of infection in Taiyuan are estimated to be from December 22nd to 31st, 2022, from May 10th to June 1st, 2023, and from September 5th to October 13th, 2023, and the corresponding daily peaks of new cases can reach 400 000, 44 000 and 22 000, respectively. By the end of 2022, excess deaths can range from 887 to 4887, and excess mortality rate can range from 3.06% to 14.82%. The threshold of the infectivity of the COVID-19 variant is estimated 0.0353, that is if the strain infectivity is above it, the epidemic cannot be control with the previous normalization measures.

A time independent least squares algorithm for parameter identification of Turing patterns in reaction-diffusion systems.

Turing patterns arising from reaction-diffusion systems such as epidemic, ecology or chemical reaction models are an important dynamic property. Parameter identification of Turing patterns in spatial continuous and networked reaction-diffusion systems is an interesting and challenging inverse problem. The existing algorithms require huge account operations and resources. These drawbacks are amplified when apply them to reaction-diffusion systems on large-scale complex networks. To overcome these shortcomings, we present a new least squares algorithm which is rooted in the fact that Turing patterns are the stationary solutions of reaction-diffusion systems. The new algorithm is time independent, it translates the parameter identification problem into a low dimensional optimization problem even a low order linear algebra equations. The numerical simulations demonstrate that our algorithm has good effectiveness, robustness as well as performance.

Optimal control dynamics of Gonorrhea in a structured population.

Gonorrhea is a serious global health problem due to its high incidence, with approximately 82.4 million new cases in 2020. To evaluate the consequences of targeted dynamic control of gonorrhea infection transmission, a model for gonorrhea with optimal control analysis is proposed for a structured population. The study looked at the model's positively invariant and bounded regions. The gonorrhea secondary infection expression, R0 for the structured population is computed. The maximum principle of Pontryagin is utilised to construct the optimal system for the formulated mathematical model. To reduce the continuous propagation of gonorrhea, we incorporated education, condoms usage, vaccinations, and treatment as control strategies. The numerical simulations show that the number of infections decreases when the controls are implemented. The effectiveness of the controls is shown using the efficacy plots.

Evaluating the impact of test-trace-isolate for COVID-19 management and alternative strategies.

There are many contrasting results concerning the effectiveness of Test-Trace-Isolate (TTI) strategies in mitigating SARS-CoV-2 spread. To shed light on this debate, we developed a novel static-temporal multiplex network characterizing both the regular (static) and random (temporal) contact patterns of individuals and a SARS-CoV-2 transmission model calibrated with historical COVID-19 epidemiological data. We estimated that the TTI strategy alone could not control the disease spread: assuming R0 = 2.5, the infection attack rate would be reduced by 24.5%. Increased test capacity and improved contact trace efficiency only slightly improved the effectiveness of the TTI. We thus investigated the effectiveness of the TTI strategy when coupled with reactive social distancing policies. Limiting contacts on the temporal contact layer would be insufficient to control an epidemic and contacts on both layers would need to be limited simultaneously. For example, the infection attack rate would be reduced by 68.1% when the reactive distancing policy disconnects 30% and 50% of contacts on static and temporal layers, respectively. Our findings highlight that, to reduce the overall transmission, it is important to limit contacts regardless of their types in addition to identifying infected individuals through contact tracing, given the substantial proportion of asymptomatic and pre-symptomatic SARS-CoV-2 transmission.

Dynamic analysis of rabies transmission and elimination in mainland China.

Rabies is an acute zoonotic infectious disease caused by rabies virus. In 2015, the World Health Organization proposed the goal of eliminating dog-induced human rabies by 2030. In response to this goal positively, China has been dedicated to the control and elimination of rabies mainly caused by dogs, for nearly 10 years. By applying infectious disease dynamics, in this paper, we establish a dog-human rabies transmission model to forecast future epidemic trends of rabies, assess whether the goal of eliminating dog-induced human rabies cases in China can be achieved in 2030, and further evaluate and suggest the follow-up sustained preventive measures after the elimination of human rabies. By analyzing and simulating above dynamic model, it is concluded that rabies has been well controlled in China in recent years, but dog-induced human rabies cannot be eliminated by 2030 according to current situation. In addition, we propose to improve rabies control efforts by increasing the immunization coverage rate of rural domestic dogs, controlling the number of stray dogs and preventing the import of rabies virus in wild animals. Immunization coverage rate of rural domestic dogs which is currently less than 10% is far from requirement, and it needs to reach 50%-60% to meet the goal of 2030. Since it is difficult to immunize stray dogs, we suggest to control the number of stray dogs below 15.27 million to achieve the goal. If the goal of eliminating human rabies is reached in 2030, the essential immunization coverage needs to be maintained for 18 years to reduce the number of canine rabies cases to zero. Lastly, to prevent transmission of rabies virus from wild animals to dogs, the thresholds of the number of dogs and the immunization coverage rate of dogs after eliminating canine rabies cases are also discussed.

A hierarchical intervention scheme based on epidemic severity in a community network.

As there are no targeted medicines or vaccines for newly emerging infectious diseases, isolation among communities (villages, cities, or countries) is one of the most effective intervention measures. As such, the number of intercommunity edges ([Formula: see text]) becomes one of the most important factor in isolating a place since it is closely related to normal life. Unfortunately, how [Formula: see text] affects epidemic spread is still poorly understood. In this paper, we quantitatively analyzed the impact of [Formula: see text] on infectious disease transmission by establishing a four-dimensional [Formula: see text] edge-based compartmental model with two communities. The basic reproduction number [Formula: see text] is explicitly obtained subject to [Formula: see text] [Formula: see text]. Furthermore, according to [Formula: see text] with zero [Formula: see text], epidemics spread could be classified into two cases. When [Formula: see text] for the case 2, epidemics occur with at least one of the reproduction numbers within communities greater than one, and otherwise when [Formula: see text] for case 1, both reproduction numbers within communities are less than one. Remarkably, in case 1, whether epidemics break out strongly depends on intercommunity edges. Then, the outbreak threshold in regard to [Formula: see text] is also explicitly obtained, below which epidemics vanish, and otherwise break out. The above two cases form a severity-based hierarchical intervention scheme for epidemics. It is then applied to the SARS outbreak in Singapore, verifying the validity of our scheme. In addition, the final size of the system is gained by demonstrating the existence of positive equilibrium in a four-dimensional coupled system. Theoretical results are also validated through numerical simulation in networks with the Poisson and Power law distributions, respectively. Our results provide a new insight into controlling epidemics.

Forecast for peak infections in the second wave of the Omicron after the adjustment of zero-COVID policy in the mainland of China.

On December 7, 2022, the Chinese government optimized the current epidemic prevention and control policy, and no longer adopted the zero-COVID policy and mandatory quarantine measures. Based on the above policy changes, this paper establishes a compartment dynamics model considering age distribution, home isolation and vaccinations. Parameter estimation was performed using improved least squares and Nelder-Mead simplex algorithms combined with modified case data. Then, using the estimated parameter values to predict a second wave of the outbreak, the peak of severe cases will reach on 8 May 2023, the number of severe cases will reach 206,000. Next, it is proposed that with the extension of the effective time of antibodies obtained after infection, the peak of severe cases in the second wave of the epidemic will be delayed, and the final scale of the disease will be reduced. When the effectiveness of antibodies is 6 months, the severe cases of the second wave will peak on July 5, 2023, the number of severe cases is 194,000. Finally, the importance of vaccination rates is demonstrated, when the vaccination rate of susceptible people under 60 years old reaches 98%, and the vaccination rate of susceptible people over 60 years old reaches 96%, the peak of severe cases in the second wave of the epidemic will be reached on 13 July 2023, when the number of severe cases is 166,000.

Exploring the effect of ecological land structure on PM2.5: A panel data study based on 277 prefecture-level cities in China.

In the context of serious urban air pollution and limited land resources, it is important to understand the environmental value of ecological land. Previous studies focused mostly on the effectiveness of a particular type of green space or the total amount of ecological land on PM2.5 and have rarely analyzed the association between ecological land structure and PM2.5 systematically and quantitatively. Therefore, we took 277 cities in China as an example, comprehensively compared the results of different models, and selected a spatial Durbin model using time-fixed effects to dissect the degree of influence of ecological land and different land types within it on PM2.5. The urban ecological land use structure was closely related to PM2.5, and the higher the proportion of ecological land use was, the lower the PM2.5. The degree and direction of influence of different types of land functions within ecological land on PM2.5 differed, with forests, shrubs, and grasslands causing a weakening impact on PM2.5, while wetlands and waters did not have a weakening role. The degree of reduction of PM2.5 by a single type of ecological land was significantly smaller than that by a composite type of ecological land. Green space should be comprehensively considered, designed and adjusted in urban planning to continuously optimize the ecological spatial structure, increase landscape diversity and maximize ecological benefits. The findings of this study help with exploring the effects of land use structure under the goal-oriented control of air pollution and provide theoretical reference and decision-making support for formulating precise air pollution control policies and optimizing the spatial development of national land.

Quantitative evaluation of the role of Fangcang shelter hospitals in the control of Omicron transmission: A case study of the outbreak in Shanghai, China in 2022.

Since Omicron began to spread in China, Shanghai has become one of the cities with more severe outbreaks. Under the comprehensive consideration of the vaccine coverage rate, the number of Fangcang shelter hospital beds and the number of designated hospital beds in Shanghai, this paper established a deterministic compartmental model and used the Nelder-Mead Simplex Direct Search Algorithm and chi-square values to estimate the model parameters. we calculate ℛ0 = 3.6429 when the number of beds in the Fangcang shelter hospital is relatively tight in the second stage and ℛ0 = 0.4974 in the fifth stage when there are enough beds in both Fangcang shelter hospital and designated hospital. Then we perform a sensitivity analysis on ℛ0 by using perturbation of fixed point estimation of model parameters in the fifth stage, and obtain three parameters that are more sensitive to ℛ0, which are transmission rate (ß 1d ), proportion of the infectious (η) and the hospitalization rate of asymptomatic infected cases (δ 1). Through simulation, we obtain that if the hospitalization rate of asymptomatic infections δ 2 > 0.9373 or the transmission rate ß 1b  < 0.0467, the second stage of Omicron transmission in Shanghai can be well controlled. Finally, we find the measure that converting the National Convention and Exhibition Center (NECC) into a Fangcang shelter hospital has played an important role in curbing the epidemic. Whether this temporary Fangcang shelter hospital is not built or delayed, the cumulative number of confirmed cases will both exceed 100,000, and the cumulative asymptomatic infections will both exceed 1 million. In addition, for a city of 10 million people, we obtain that if a permanent Fangcang shelter hospital with 17,784 beds is built ahead of epidemic, there will be no shortage of beds during the outbreak of Omicron. Our findings enrich the content of the impact of Fangcang shelter hospital beds on the spread of Omicron and confirm the correct policy adopted by the Chinese government.

Mathematical modeling the dynamics of SARS-CoV-2 infection with antibody-dependent enhancement.

The advent and swift global spread of the novel coronavirus (COVID-19) transmitted by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) have caused massive deaths and economic devastation worldwide. Antibody-dependent enhancement (ADE) is a common phenomenon in virology that directly affects the effectiveness of the vaccine, and there is no fully effective vaccine for diseases. In order to study the potential role of ADE on SARS-CoV-2 infection, we establish the SARS-CoV-2 infection dynamics model with ADE. The basic reproduction number is computed. We prove that when R 0 < 1 , the infection-free equilibrium is globally asymptotically stable, and the system is uniformly persistent when R 0 > 1 . We carry out the sensitivity analysis by the partial rank correlation coefficients and the extended version of the Fourier amplitude sensitivity test. Numerical simulations are implemented to illustrate the theoretical results. The potential impact of ADE on SARS-CoV-2 infection is also assessed. Our results show that ADE may accelerate SARS-CoV-2 infection. Furthermore, our findings suggest that increasing antibody titers can have the ability to control SARS-CoV-2 infection with ADE, but enhancing the neutralizing power of antibodies may be ineffective to control SARS-CoV-2 infection with ADE. Our study presumably contributes to a better understanding of the dynamics of SARS-CoV-2 infection with ADE.

Impacts of climate change on vegetation pattern: Mathematical modeling and data analysis.

Climate change has become increasingly severe, threatening ecosystem stability and, in particular, biodiversity. As a typical indicator of ecosystem evolution, vegetation growth is inevitably affected by climate change, and therefore has a great potential to provide valuable information for addressing such ecosystem problems. However, the impacts of climate change on vegetation growth, especially the spatial and temporal distribution of vegetation, are still lacking of comprehensive exposition. To this end, this review systematically reveals the influences of climate change on vegetation dynamics in both time and space by dynamical modeling the interactions of meteorological elements and vegetation growth. Moreover, we characterize the long-term evolution trend of vegetation growth under climate change in some typical regions based on data analysis. This work is expected to lay a necessary foundation for systematically revealing the coupling effect of climate change on the ecosystem.

What is the role of aerosol transmission in SARS-Cov-2 Omicron spread in Shanghai?

The Omicron transmission has infected nearly 600,000 people in Shanghai from March 26 to May 31, 2022. Combined with different control measures taken by the government in different periods, a dynamic model was constructed to investigate the impact of medical resources, shelter hospitals and aerosol transmission generated by clustered nucleic acid testing on the spread of Omicron. The parameters of the model were estimated by least square method and MCMC method, and the accuracy of the model was verified by the cumulative number of asymptomatic infected persons and confirmed cases in Shanghai from March 26 to May 31, 2022. The result of numerical simulation demonstrated that the aerosol transmission figured prominently in the transmission of Omicron in Shanghai from March 28 to April 30. Without aerosol transmission, the number of asymptomatic subjects and symptomatic cases would be reduced to 130,000 and 11,730 by May 31, respectively. Without the expansion of shelter hospitals in the second phase, the final size of asymptomatic subjects and symptomatic cases might reach 23.2 million and 4.88 million by May 31, respectively. Our results also revealed that expanded vaccination played a vital role in controlling the spread of Omicron. However, even if the vaccination rate were 100%, the transmission of Omicron should not be completely blocked. Therefore, other control measures should be taken to curb the spread of Omicron, such as widespread antiviral therapies, enhanced testing and strict tracking quarantine measures. This perspective could be utilized as a reference for the transmission and prevention of Omicron in other large cities with a population of 10 million like Shanghai.

Spatial dynamics of a vegetation model with uptake-diffusion feedback in an arid environment.

Vegetation patterns with a variety of structures is amazing phenomena in arid or semi-arid areas, which can identify the evolution law of vegetation and are typical signals of ecosystem functions. Many achievements have been made in this respect, yet the mechanisms of uptake-diffusion feedback on the pattern structures of vegetation is not fully understood. To well reveal the influences of parameters perturbation on the pattern formation of vegetation, we give a comprehensive analysis on a vegetation-water model in the forms of reaction-diffusion equation which is posed by Zelnik et al. (Proc Natl Acad Sci 112:12,327-12,331, 2015). We obtain the exact parameters range for stationary patterns and show the dynamical behaviors near the bifurcation point based on nonlinear analysis. It is found that the model has the properties of spot, labyrinth and gap patterns. Moreover, water diffusion rate prohibits the growth of vegetation while shading parameter promotes the increase of vegetation biomass. Our results show that gradual transitions from uniform state to gap pattern can occur for suitable value of parameters which may induce the emergence of desertification.

Transmission characteristic and dynamic analysis of COVID-19 on contact network with Tianjin city in China.

The outbreak of 2019 novel coronavirus pneumonia (COVID-19) has had a profound impact on people's lives around the world, and the spread of COVID-19 between individuals were mainly caused by contact transmission of the social networks. In order to analyze the network transmission of COVID-19, we constructed a case contact network using available contact data of 136 early diagnosed cases in Tianjin. Based on the constructed case contact network, the structural characteristics of the network were first analyzed, and then the centrality of the nodes was analyzed to find the key nodes. In addition, since the constructed network may contain missing edges and false edges, link prediction algorithms were used to reconstruct the network. Finally, to understand the spread of COVID-19 in the network, an individual-based susceptible-latent-exposed-infected-recover (SLEIR) model is established and simulated in the network. The results showed that the disease peak scale caused by the node with the highest centrality is larger, and reducing the contact infection rate of the infected person during the incubation period has a greater impact on the peak disease scale.