Epidemic spreading on spatial higher-order network.

Higher-order interactions exist widely in mobile populations and are extremely important in spreading epidemics, such as influenza. However, research on high-order interaction modeling of mobile crowds and the propagation dynamics above is still insufficient. Therefore, this study attempts to model and simulate higher-order interactions among mobile populations and explore their impact on epidemic transmission. This study simulated the spread of the epidemic in a spatial high-order network based on agent-based model modeling. It explored its propagation dynamics and the impact of spatial characteristics on it. Meanwhile, we construct state-specific rate equations based on the uniform mixing assumption for further analysis. We found that hysteresis loops are an inherent feature of high-order networks in this space under specific scenarios. The evolution curve roughly presents three different states with the initial value change, showing different levels of the endemic balance of low, medium, and high, respectively. Similarly, network snapshots and parameter diagrams also indicate these three types of equilibrium states. Populations in space naturally form components of different sizes and isolations, and higher initial seeds generate higher-order interactions in this spatial network, leading to higher infection densities. This phenomenon emphasizes the impact of high-order interactions and high-order infection rates in propagation. In addition, crowd density and movement speed act as protective and inhibitory factors for epidemic transmission, respectively, and depending on the degree of movement weaken or enhance the effect of hysteresis loops.

Forecasting and mapping dengue fever epidemics in China: a spatiotemporal analysis.

BACKGROUND: Dengue fever (DF) has emerged as a significant public health concern in China. The spatiotemporal patterns and underlying influencing its spread, however, remain elusive. This study aims to identify the factors driving these variations and to assess the city-level risk of DF epidemics in China. METHODS: We analyzed the frequency, intensity, and distribution of DF cases in China from 2003 to 2022 and evaluated 11 natural and socioeconomic factors as potential drivers. Using the random forest (RF) model, we assessed the contributions of these factors to local DF epidemics and predicted the corresponding city-level risk. RESULTS: Between 2003 and 2022, there was a notable correlation between local and imported DF epidemics in case numbers (r = 0.41, P < 0.01) and affected cities (r = 0.79, P < 0.01). With the increase in the frequency and intensity of imported epidemics, local epidemics have become more severe. Their occurrence has increased from five to eight months per year, with case numbers spanning from 14 to 6641 per month. The spatial distribution of city-level DF epidemics aligns with the geographical divisions defined by the Huhuanyong Line (Hu Line) and Qin Mountain-Huai River Line (Q-H Line) and matched well with the city-level time windows for either mosquito vector activity (83.59%) or DF transmission (95.74%). The RF models achieved a high performance (AUC = 0.92) when considering the time windows. Importantly, they identified imported cases as the primary influencing factor, contributing significantly (24.82%) to local DF epidemics at the city level in the eastern region of the Hu Line (E-H region). Moreover, imported cases were found to have a linear promoting impact on local epidemics, while five climatic and six socioeconomic factors exhibited nonlinear effects (promoting or inhibiting) with varying inflection values. Additionally, this model demonstrated outstanding accuracy (hitting ratio = 95.56%) in predicting the city-level risks of local epidemics in China. CONCLUSIONS: China is experiencing an increasing occurrence of sporadic local DF epidemics driven by an unavoidably higher frequency and intensity of imported DF epidemics. This research offers valuable insights for health authorities to strengthen their intervention capabilities against this disease.

Estimating the potential value of MSM-focused evidence-based implementation interventions in three Ending the HIV Epidemic jurisdictions in the United States: a model-based analysis.

INTRODUCTION: Improving the delivery of existing evidence-based interventions to prevent and diagnose HIV is key to Ending the HIV Epidemic in the United States. Structural barriers in the access and delivery of related health services require municipal or state-level policy changes; however, suboptimal implementation can be addressed directly through interventions designed to improve the reach, effectiveness, adoption or maintenance of available interventions. Our objective was to estimate the cost-effectiveness and potential epidemiological impact of six real-world implementation interventions designed to address these barriers and increase the scale of delivery of interventions for HIV testing and pre-exposure prophylaxis (PrEP) in three US metropolitan areas. METHODS: We used a dynamic HIV transmission model calibrated to replicate HIV microepidemics in Atlanta, Los Angeles (LA) and Miami. We identified six implementation interventions designed to improve HIV testing uptake ("Academic detailing for HIV testing," "CyBER/testing," "All About Me") and PrEP uptake/persistence ("Project SLIP," "PrEPmate," "PrEP patient navigation"). Our comparator scenario reflected a scale-up of interventions with no additional efforts to mitigate implementation and structural barriers. We accounted for potential heterogeneity in population-level effectiveness across jurisdictions. We sustained implementation interventions over a 10-year period and evaluated HIV acquisitions averted, costs, quality-adjusted life years and incremental cost-effectiveness ratios over a 20-year time horizon (2023-2042). RESULTS: Across jurisdictions, implementation interventions to improve the scale of HIV testing were most cost-effective in Atlanta and LA (CyBER/testing cost-saving and All About Me cost-effective), while interventions for PrEP were most cost-effective in Miami (two of three were cost-saving). We estimated that the most impactful HIV testing intervention, CyBER/testing, was projected to avert 111 (95% credible interval: 110-111), 230 (228-233) and 101 (101-103) acquisitions over 20 years in Atlanta, LA and Miami, respectively. The most impactful implementation intervention to improve PrEP engagement, PrEPmate, averted an estimated 936 (929-943), 860 (853-867) and 2152 (2127-2178) acquisitions over 20 years, in Atlanta, LA and Miami, respectively. CONCLUSIONS: Our results highlight the potential impact of interventions to enhance the implementation of existing evidence-based interventions for the prevention and diagnosis of HIV.

Exploring the seasonality and optimal control strategy of HIV/AIDS epidemic in China: The impact of seasonal testing.

In this work, we investigate how the seasonal variation in the number of individuals who are tested for an HIV antibody in outpatient clinics affects the HIV transmission patterns in China, which has not been well studied. Based on the characteristics of outpatient testing data and reported cases, we establish a periodic infectious disease model to study the impact of seasonal testing on HIV transmission. The results indicate that the seasonal testing is a driving factor for the seasonality of new cases. We demonstrate the feasibility of ending the HIV/AIDS epidemic. We find that the diagnostic rates related to testing play a crucial role in controlling the size of the epidemic. Specifically, when considering minimizing both infected individuals and diagnostic rates, the level of attention paid to undiagnosed infected individuals is always positively correlated with the optimal diagnostic rates, while the optimal diagnostic rates are negatively correlated with the size of the epidemic at the terminal time.

Innovative use of Australian cancer registry data for early detection of the effects of epidemics and other mass disruptions on cancer incidence.

BACKGROUND: Predictive modelling using pre-epidemic data have long been used to guide public health responses to communicable disease outbreaks and other health disruptions. In this study, cancer registry and related health data available 2-3 months from diagnosis were used to predict changes in cancer detection that otherwise would not have been identified until full registry processing was completed about 18-24 months later. A key question was whether these earlier data could be used to predict cancer incidence ahead of full processing by the cancer registry as a guide to more timely health responses. The setting was the Australian State of New South Wales, covering 31 % of the Australian population. The study year was 2020, the year of emergence of the COVID-19 pandemic. METHODS: Cancer detection in 2020 was modelled using data available 2-3 months after diagnosis. This was compared with data from full registry processing available from 2022. Data from pre-pandemic 2018 were used for exploratory model building. Models were tested using pre-pandemic 2019 data. Candidate predictor variables included pathology, surgery and radiation therapy reports, numbers of breast screens, colonoscopies, PSA tests, and melanoma excisions recorded by the universal Medical Benefits Schedule (MBS). Data were analysed for all cancers collectively and 5 leading types. RESULTS: Compared with full registry processing, modelled data for 2020 had a >95 % accuracy overall, indicating key points of inflexion of cancer detection over the COVID-disrupted 2020 period. These findings highlight the potential of predictive modelling of cancer-related data soon after diagnosis to reveal changes in cancer detection during epidemics and other health disruptions. CONCLUSIONS: Data available 2-3 months from diagnosis in the pandemic year indicated changes in cancer detection that were ultimately confirmed by fully-processed cancer registry data about 24 months later. This indicates the potential utility of using these early data in an early-warning system.

The origin and spread of HIV-1 CRF59_01B epidemic in China: A molecular network and phylogeographic analysis.

Human immunodeficiency virus type 1 CRF59_01B, identified in China in 2013, has been detected nationwide, exhibiting notably high prevalence in Guangzhou and its vicinity. This study aimed to unravel its origin and migration. A data set was established, incorporating all available CRF59_01B pol gene sequences and their metadata from Guangzhou and the public database. Bayesian phylogeographic analysis demonstrated that CRF59_01B originated in Shenzhen, the neighboring city of Guangzhou, around 1998 with posterior probability of 0.937. Molecular network analysis detected 1131 transmission links and showed a remarkably high clustering rate (78.9%). Substantial inter-city transmissions (26.5%, 300/1131) were observed between Shenzhen and Guangzhou while inter-region transmissions linked Guangzhou with South (46) and Southwest (64) China. The centre of Guangzhou was the hub of CRF59_01B transmission, including the inflow from Shenzhen (3.57 events/year) and outflow to the outskirts of Guangzhou (>2 events/year). The large-scale analysis revealed significant migration from Shenzhen to Guangzhou (5.08 events/year) and North China (0.59 events/year), and spread from Guangzhou to Central (0.47 events/year), East (0.42 events/year), South (0.76 events/year), Southwest China (0.76 events/year) and Shenzhen (1.89 events/year). Shenzhen and Guangzhou served as the origin and the hub of CRF59_01B circulation, emphasizing inter-city cooperation and data sharing to confine its nationwide diffusion.

Dynamical analysis of a stochastic maize streak virus epidemic model with logarithmic Ornstein-Uhlenbeck process.

To describe the transmission dynamics of maize streak virus infection, in the paper, we first formulate a stochastic maize streak virus infection model, in which the stochastic fluctuations are depicted by a logarithmic Ornstein-Uhlenbeck process. This approach is reasonable to simulate the random impacts of main parameters both from the biological significance and the mathematical perspective. Then we investigate the detailed dynamics of the stochastic system, including the existence and uniqueness of the global solution, the existence of a stationary distribution, the exponential extinction of the infected maize and infected leafhopper vector. Especially, by solving the five-dimensional algebraic equations corresponding to the stochastic system, we obtain the specific expression of the probability density function near the quasi-endemic equilibrium of the stochastic system, which provides valuable insights into the stationary distribution. Finally, the model is discretized using the Milstein higher-order numerical method to illustrate our theoretical results numerically. Our findings provide a groundwork for better methods of preventing the spread of this type of virus.

Modeling epidemic dynamics using Graph Attention based Spatial Temporal networks.

The COVID-19 pandemic and influenza outbreaks have underscored the critical need for predictive models that can effectively integrate spatial and temporal dynamics to enable accurate epidemic forecasting. Traditional time-series analysis approaches have fallen short in capturing the intricate interplay between these factors. Recent advancements have witnessed the incorporation of graph neural networks and machine learning techniques to bridge this gap, enhancing predictive accuracy and providing novel insights into disease spread mechanisms. Notable endeavors include leveraging human mobility data, employing transfer learning, and integrating advanced models such as Transformers and Graph Convolutional Networks (GCNs) to improve forecasting performance across diverse geographies for both influenza and COVID-19. However, these models often face challenges related to data quality, model transferability, and potential overfitting, highlighting the necessity for more adaptable and robust approaches. This paper introduces the Graph Attention-based Spatial Temporal (GAST) model, which employs graph attention networks (GATs) to overcome these limitations by providing a nuanced understanding of epidemic dynamics through a sophisticated spatio-temporal analysis framework. Our contributions include the development and validation of the GAST model, demonstrating its superior forecasting capabilities for influenza and COVID-19 spread, with a particular focus on short-term, daily predictions. The model's application to both influenza and COVID-19 datasets showcases its versatility and potential to inform public health interventions across a range of infectious diseases.

Enteroviruses: epidemic potential, challenges and opportunities with vaccines.

Enteroviruses (EVs) are the most prevalent viruses in humans. EVs can cause a range of acute symptoms, from mild common colds to severe systemic infections such as meningitis, myocarditis, and flaccid paralysis. They can also lead to chronic diseases such as cardiomyopathy. Although more than 280 human EV serotypes exist, only four serotypes have licenced vaccines. No antiviral drugs are available to treat EV infections, and global surveillance of EVs has not been effectively coordinated. Therefore, poliovirus still circulates, and there have been alarming epidemics of non-polio enteroviruses. Thus, there is a pressing need for coordinated preparedness efforts against EVs.This review provides a perspective on recent enterovirus outbreaks and global poliovirus eradication efforts with continuous vaccine development initiatives. It also provides insights into the challenges and opportunities in EV vaccine development. Given that traditional whole-virus vaccine technologies are not suitable for many clinically relevant EVs and considering the ongoing risk of enterovirus outbreaks and the potential for new emerging pathogenic strains, the need for new effective and adaptable enterovirus vaccines is emphasized.This review also explores the difficulties in translating promising vaccine candidates for clinical use and summarizes information from published literature and clinical trial databases focusing on existing enterovirus vaccines, ongoing clinical trials, the obstacles faced in vaccine development as well as the emergence of new vaccine technologies. Overall, this review contributes to the understanding of enterovirus vaccines, their role in public health, and their significance as a tool for future preparedness.

[The history of the fight against cholera epidemics in the Krasnodar territory in 1892 and 1910 (based on archival data)].

Epidemics of a wide variety of infectious diseases were constantly recorded in Russia. Asian cholera occupied a special place among epidemic diseases. In 1892, cholera was imported into the Russian Empire through the Black Sea ports, which reached the territory of the Kuban region by the summer of the same year. In 1892, about 300 thousand people died of cholera in Russia. They still did not know how to treat this terrible disease, did not know its mechanism of spread, as well as the peculiarities of its course. The article, prepared on the basis of an analysis of documentary data from the Archive Department of the administration of the municipal formation of the city of Novorossiysk and the archival Department of the Administration of the municipal formation of the Mostovsky district, examines the cholera epidemic that swept the territories of the Kuban region in 1892 and 1910. The authors characterize the main factors that contributed to the rapid spread of infection and assess the measures that were taken to combat the disease: the implementation of anti-cholera measures organized by the authorities was greatly hampered by the lack of education, prejudices and superstitions of the vast majority of the population; representatives of the nonresident population not only did not comply with basic standards of personal hygiene, but also expressed distrust, and sometimes and hostility towards doctors. Using archival data, the authors investigate the impact of infectious diseases on the demographic indicators of these settlements.

Optimizing the location of vaccination sites to stop a zoonotic epidemic.

Mass vaccinations are crucial public health interventions for curbing infectious diseases. Canine rabies control relies on mass dog vaccination campaigns (MDVCs) that are held annually across the globe. Dog owners must bring their pets to fixed vaccination sites, but sometimes target coverage is not achieved due to low participation. Travel distance to vaccination sites is an important barrier to participation. We aimed to increase MDVC participation in silico by optimally placing fixed-point vaccination locations. We quantified participation probability based on walking distance to the nearest vaccination site using regression models fit to participation data collected over 4 years. We used computational recursive interchange techniques to optimally place fixed-point vaccination sites and compared predicted participation with these optimally placed vaccination sites to actual locations used in previous campaigns. Algorithms that minimized average walking distance or maximized expected participation provided the best solutions. Optimal vaccination placement is expected to increase participation by 7% and improve spatial evenness of coverage, resulting in fewer under-vaccinated pockets. However, unevenness in workload across sites remained. Our data-driven algorithm optimally places limited resources to increase overall vaccination participation and equity. Field evaluations are essential to assess effectiveness and evaluate potentially longer waiting queues resulting from increased participation.

Instabilities and self-organization in spatiotemporal epidemic dynamics driven by nonlinearity and noise.

Theoretical analysis of epidemic dynamics has attracted significant attention in the aftermath of the COVID-19 pandemic. In this article, we study dynamic instabilities in a spatiotemporal compartmental epidemic model represented by a stochastic system of coupled partial differential equations (SPDE). Saturation effects in infection spread-anchored in physical considerations-lead to strong nonlinearities in the SPDE. Our goal is to study the onset of dynamic, Turing-type instabilities, and the concomitant emergence of steady-state patterns under the interplay between three critical model parameters-the saturation parameter, the noise intensity, and the transmission rate. Employing a second-order perturbation analysis to investigate stability, we uncover both diffusion-driven and noise-induced instabilities and corresponding self-organized distinct patterns of infection spread in the steady state. We also analyze the effects of the saturation parameter and the transmission rate on the instabilities and the pattern formation. In summary, our results indicate that the nuanced interplay between the three parameters considered has a profound effect on the emergence of dynamical instabilities and therefore on pattern formation in the steady state. Moreover, due to the central role played by the Turing phenomenon in pattern formation in a variety of biological dynamic systems, the results are expected to have broader significance beyond epidemic dynamics.

Source-Sink Dynamics in a Two-Patch SI Epidemic Model with Life Stages and No Recovery from Infection.

This study presents a comprehensive analysis of a two-patch, two-life stage SI model without recovery from infection, focusing on the dynamics of disease spread and host population viability in natural populations. The model, inspired by real-world ecological crises like the decline of amphibian populations due to chytridiomycosis and sea star populations due to Sea Star Wasting Disease, aims to understand the conditions under which a sink host population can present ecological rescue from a healthier, source population. Mathematical and numerical analyses reveal the critical roles of the basic reproductive numbers of the source and sink populations, the maturation rate, and the dispersal rate of juveniles in determining population outcomes. The study identifies basic reproduction numbers R 0 for each of the patches, and conditions for the basic reproduction numbers to produce a receiving patch under which its population. These findings provide insights into managing natural populations affected by disease, with implications for conservation strategies, such as the importance of maintaining reproductively viable refuge populations and considering the effects of dispersal and maturation rates on population recovery. The research underscores the complexity of host-pathogen dynamics in spatially structured environments and highlights the need for multi-faceted approaches to biodiversity conservation in the face of emerging diseases.

From morphology of human body to reshaping a morphology of the society: heritage in the field of pathology of infectious diseases of Wilhelm Ebstein and work of councilman Sigismund Asch. A story how to counteract epidemics and to transform feudal system into civil democracy.

Collected, primary resources enabled us to extract data that are scarcely present in medical literature of the two Breslauer morphologists of both the human body and - metaphorically - the society: Wilhelm Ebstein (1836-1912) and Sigismund Asch (1825-1901), particularly the latter, who described morphology of melanosis in his doctoral dissertation in 1846, to switch on reshaping social morphology of Wroclaw (Breslau) in Virchow-like manner. In contrast to the main perspective of Ebstein's anomaly that has been finely described in past biographical papers, a primary aspect of infectious diseases is highlighted here in Ebstein's heritage. In 1869, his habilitation on recurrent typhus provided professional support for Asch. As Ebstein cared for the poor in shelters of Wroclaw, Asch admitted poor patients from early morning hours to gain such a great esteem to be elected alderman. Asch's mentality corresponded to Ferdinand Lassalle's philosophy of the social democratic movement. In front of cholera epidemics, Asch contributed to medical control of meat, development of city canalization, establishment of green areas as well he deeply got involved in charity institutions for widows and orphans and was a model medical doctor to follow for much more famous Janusz Korczak who perished together with children from his orphanage in Nazi Concentration Camp in Treblinka. Asch was immortalized as "Doctor Klaus" in the popular play by Adolf L'Arronge and united people in progress from feudal discrimination to democracy and in fight for civil rights in industrial society to gradually replace aristocracy with meritocracy in the mainstream of development of modern society.

Impact of community structure on the spread of epidemics on time-varying multiplex networks.

Community structure plays a crucial role in realistic networks and different communities can be created by groups of interest and activity events, and exploring the impact of community properties on collective dynamics is an active topic in the field of network science. Here, we propose a new coupled model with different time scales for online social networks and offline epidemic spreading networks, in which community structure is added into online social networks to investigate its role in the interacting dynamics between information diffusion and epidemic spreading. We obtain the analytical equations of epidemic threshold by MMC (Microscopic Markov Chain) method and conduct a large quantities of numerical simulations using Monte Carlo simulations in order to verify the accuracy of the MMC method, and more valuable insights are also obtained. The results indicate that an increase in the probability of the mobility of an individual can delay the spread of epidemic-related information in the network, as well as delaying the time of the peak of the infection density in the network. However, an increase in the contact ability of mobile individuals produces a facilitating effect on the spread of epidemics. Finally, it is also found that the stronger the acceptance of an individual to information coming from a different community, the lower the infection density in the network, which suggests that it has an inhibitory effect on the disease spreading.

Surveillance of respiratory viruses by aerosol screening in indoor air as an early warning system for epidemics.

The development of effective methods for the surveillance of seasonal respiratory viruses is required for the timely management of outbreaks. We aimed to survey Influenza-A, Influenza-B, RSV-A, Rhinovirus and SARS-CoV-2 surveillance in a tertiary hospital and a campus over 5 months. The effectiveness of air screening as an early warning system for respiratory viruses was evaluated in correlation with respiratory tract panel test results. The overall viral positivity was higher on the campus than in the hospital (55.0% vs. 38.0%). Influenza A was the most prevalent pathogen in both locations. There were two influenza peaks (42nd and 49th weeks) in the hospital air, and a delayed peak was detected on campus in the 1st-week of January. Panel tests indicated a high rate of Influenza A in late December. RSV-A-positivity was higher on the campus than the hospital (21.6% vs. 7.4%). Moreover, we detected two RSV-A peaks in the campus air (48th and 51st weeks) but only one peak in the hospital and panel tests (week 49). Although rhinovirus was the most common pathogen in panel tests, rhinovirus positivity was low in air samples. The air screening for Influenza-B and SARS-Cov-2 revealed comparable positivity rates with panel tests. Air screening can be integrated into surveillance programs to support infection control programs for potential epidemics of respiratory virus infections except for rhinoviruses.

A sub-national HIV epidemic appraisal in Kenya: a new approach for identifying priority geographies, populations and programmes for optimizing coverage for HIV prevention.

INTRODUCTION: The HIV Prevention 2025 Roadmap, developed by UNAIDS, recommends the adoption of a precision prevention approach focused on priority populations and geographies. With reduction in new HIV acquisitions in many countries, designing a differentiated HIV prevention response, using a Programme Science approach, based on the understanding of the epidemic and transmission dynamics at a sub-national level, is critical. METHODS: To support strategic planning, an epidemic appraisal at the sub-national level across 47 counties, with the 2019 population ranging from 0.14 million in Lamu to 4.40 million in Nairobi City, was conducted in Kenya using several existing data sources. Using 2021 Spectrum/EPP/Naomi model estimates of national and sub-national HIV incidence and prevalence, counties with high HIV incidence and prevalence were identified for geographic prioritization. The size of local key population (KP) networks and HIV prevalence in key and general populations were used to define epidemic typology and prioritize populations for HIV prevention programmes. Analysis of routine programme monitoring data for 2021 was used to assess coverage gaps in HIV prevention programmes, including prevention of vertical transmission, anti-retroviral therapy, KP programmes, adolescent girls and young women programme, and voluntary male medical circumcision programme. RESULTS: Ten counties with more than 1000 incident acquisitions in 2021 accounted for 57% of new acquisitions. Twenty-four counties were grouped into the concentrated epidemic type-due to their low prevalence in the general population, high prevalence in KPs and relatively higher density of female sex workers and men who have sex with men populations. Four counties reflected a generalized epidemic, where HIV prevalence was more than 10% and 30%, respectively, among the general and key populations. The remaining 19 counties were classified as having mixed epidemics. Gaps in programmes were identified and counties where these gaps need to be addressed were also prioritized. CONCLUSIONS: The HIV burden in Kenya is unevenly distributed and hence the mix of prevention strategies may vary according to the epidemic typology of the county. Prioritization of programmes based not only on disease burden and epidemic typology, but also on the prevailing gaps in coverage for reducing inequities is a key aspect of this appraisal.

Prevention and control of Ebola virus transmission: mathematical modelling and data fitting.

The Ebola virus disease (EVD) has been endemic since 1976, and the case fatality rate is extremely high. EVD is spread by infected animals, symptomatic individuals, dead bodies, and contaminated environment. In this paper, we formulate an EVD model with four transmission modes and a time delay describing the incubation period. Through dynamical analysis, we verify the importance of blocking the infection source of infected animals. We get the basic reproduction number without considering the infection source of infected animals. And, it is proven that the model has a globally attractive disease-free equilibrium when the basic reproduction number is less than unity; the disease eventually becomes endemic when the basic reproduction number is greater than unity. Taking the EVD epidemic in Sierra Leone in 2014-2016 as an example, we complete the data fitting by combining the effect of the media to obtain the unknown parameters, the basic reproduction number and its time-varying reproduction number. It is shown by parameter sensitivity analysis that the contact rate and the removal rate of infected group have the greatest influence on the prevalence of the disease. And, the disease-controlling thresholds of these two parameters are obtained. In addition, according to the existing vaccination strategy, only the inoculation ratio in high-risk areas is greater than 0.4, the effective reproduction number can be less than unity. And, the earlier the vaccination time, the greater the inoculation ratio, and the faster the disease can be controlled.