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The prevention and control of the spread of Cystic Echinococcosis is an important public health issue. Health education has been supported by many governments because it can increase public awareness of echinococcosis, promote the development of personal hygiene habits, and subsequently reduce the transmission of echinococcosis. In this paper, a dynamic model of echinococcosis is used to integrate all aspects of health education. Theoretical analysis and numerical model fitting were used to quantitatively analysed by the impact of health education on the spread of echinococcosis. Theoretical findings indicate that the basic reproduction number is crucial in determining the prevalence of echinococcosis within a given geographical area. The parameters of the model were estimated and fitted by using data from the Ningxia Hui Autonomous Region in China, and the sensitivity of the basic reproduction number was analysed by using the partial rank correlation coefficient method. These findings illustrate that all aspects of health education demonstrate a negative correlation with the basic reproduction number, suggesting the effectiveness of health education in reducing the basic reproduction number and mitigating the transmission of echinococcosis, which is consistent with reality. Particularly, the basic reproduction number showed a strong negative correlation with the burial rate of infected livestock (b) and the incidence of infected livestock viscera that is not fed to dogs (q). This paper further analyzes the implementation plan for canine deworming rates and sheep immunity rates, as well as the transmission of infected hosts over time under different parameters b and q. According to the findings, emphasizing the management of infected livestock in health education has the potential to significantly reduce the risk of echinococcosis transmission. This study will provide scientific support for the creation of higher quality health education initiatives. [ABSTRACT FROM AUTHOR]

The efficacy of vaccination, incomplete treatment and disease relapse are critical challenges that must be faced to prevent and control the spread of infectious diseases. Age heterogeneity is also a crucial factor for this study. In this paper, we investigate a new age-structured SVEIR epidemic model with the nonlinear incidence rate, waning immunity, incomplete treatment and relapse. Next, the asymptotic smoothness, the uniform persistence and the existence of interior global attractor of the solution semi-flow generated by the system are given. We define the basic reproduction number R 0 and prove the existence of the equilibria of the model. And we study the global asymptotic stability of the equilibria. Then the parameters of the model are estimated using tuberculosis data in China. The sensitivity analysis of R 0 is derived by the Partial Rank Correlation Coefficient method. These main theoretical results are applied to analyze and predict the trend of tuberculosis prevalence in China. Finally, the optimal control problem of the model is discussed. We choose to take strengthening treatment and controlling relapse as the control parameters. The necessary condition for optimal control is established., (© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

In this paper, we propose a reaction-advection-diffusion dengue fever model with seasonal developmental durations and intrinsic incubation periods. Firstly, we establish the well-posedness of the model. Secondly, we define the basic reproduction number ℜ 0 for this model and show that ℜ 0 is a threshold parameter: if ℜ 0 < 1 , then the disease-free periodic solution is globally attractive; if ℜ 0 > 1 , the system is uniformly persistent. Thirdly, we study the global attractivity of the positive steady state when the spatial environment is homogeneous and the advection of mosquitoes is ignored. As an example, we use the model to investigate the dengue fever transmission case in Guangdong Province, China, and explore the impact of model parameters on ℜ 0 . Our findings indicate that ignoring seasonality may underestimate ℜ 0 . Additionally, the spatial heterogeneity of transmission may increase the risk of disease transmission, while the increase of seasonal developmental durations, intrinsic incubation periods and advection rates can all reduce the risk of disease transmission., (© 2024. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

Since the global outbreak of COVID-19, the virus has continuously mutated and can survive in the air for long periods of time. This paper establishes and analyzes a model of COVID-19 with self-protection and quarantine measures affected by viruses in the environment to investigate the influence of viruses in the environment on the spread of the outbreak, as well as to develop a rational prevention and control measure to control the spread of the outbreak. The basic reproduction number was calculated and Lyapunov functions were constructed to discuss the stability of the model equilibrium points. The disease-free equilibrium point was proven to be globally asymptotically stable when $ R&#95;0 < 1 $, and the endemic equilibrium point was globally asymptotically stable when $ R&#95;0 > 1 $. The model was fitted using data from COVID-19 cases in Chongqing between November 1 to November 25, 2022. Based on the numerical analysis, the following conclusion was obtained: clearing the virus in the environment and strengthening the isolation measures for infected people can control the epidemic to a certain extent, but enhancing the self-protection of individuals can be more effective in reducing the risk of being infected and controlling the transmission of the epidemic, which is more conducive to the practical application.

Background: To control resurging infectious diseases like mumps, it is necessary to resort to effective control and preventive measures. These measures include increasing vaccine coverage, providing the community with advice on how to reduce exposure, and closing schools. To justify such intervention, it is important to understand how well each of these measures helps to limit transmission. Methods: In this paper, we propose a simple SEILR (susceptible-exposed-symptomatically infectious-asymptomatically infectious-recovered) model by using a novel transmission rate function to incorporate temperature, humidity, and closing school factors. This new transmission rate function allows us to verify the impact of each factor either separately or combined. Using reported mumps cases from 2004 to 2018 in the mainland of China, we perform data fitting and parameter estimation to evaluate the basic reproduction number R 0 . As a wide range of one-dose measles, mumps, and rubella (MMR) vaccine programs in China started only in 2008, we use different vaccination proportions for the first Stage I period (from 2004 to 2008) and the second Stage II period (from 2009 to 2018). This allows us to verify the importance of higher vaccine coverage with a possible second dose of MMR vaccine. Results: We find that the basic reproduction number R 0 is generally between 1 and 3. We then use the Akaike Information Criteria to assess the extent to which each of the three factors contributed to the spread of mumps. The findings suggest that the impact of all three factors is substantial, with temperature having the most significant impact, followed by school opening and closing, and finally humidity. Conclusion: We conclude that the strategy of increasing vaccine coverage, changing micro-climate (temperature and humidity), and closing schools can greatly reduce mumps transmission. [ABSTRACT FROM AUTHOR]

In this paper, based on the transmission mechanism of echinococcosis in China, we propose a discrete-time dynamical model for the transmission of echinococcosis. The research results indicate that transmission dynamics of this discrete-time model are determined by basic reproduction number R0. It is shown that when R0 ≤ 1 then the disease-free equilibrium is globally asymptotically stable and when R0 > 1 then the model is permanent while the disease-free equilibrium is unstable. Finally, on the basis of the theoretical results established in this paper, we come up with some specific measures to control the transmission of echinococcosis. [ABSTRACT FROM AUTHOR]

In this paper, the author proposes and studies a mathematical model for the spread of coronavirus 2019. The effect of preventive programs on the control of disease is also considered. The basic reproduction number R0$$ {R}_0 $$ was computed and the results showed that forward bifurcation occured. Local and global stability of the equilibrium points of the model was studied by geometric stability method and Lyapunov function. Finally, the particular data of China which was reported for Covid‐19 were used for numerical simulation. [ABSTRACT FROM AUTHOR]

China bears a heavy burden due to tuberculosis (TB) with hundreds of thousands of people falling ill with the disease every year. Therefore, it is necessary to understand the effectiveness of current control measures in China. In this paper, we first present a TB model that incorporates both vaccination and treatment. Additionally, the model considers TB transmission characteristics such as relapse and variable latency. We then define the basic reproduction number R 0 of the proposed model and indicate that the disease-free equilibrium state is globally asymptotically stable if R 0 < 1 , and the endemic equilibrium state is globally asymptotically stable if R 0 > 1 . We then apply the Grey Wolf Optimizer algorithm to obtain the parameters and initial values of the model by combining TB data collected in China from 2007 to 2020. Through the partial rank correlation coefficient method, we identify the parameters that are most sensitive to R 0 . Based on the analysis results of the model, we propose some suggestions for TB control measures in the conclusion section. [ABSTRACT FROM AUTHOR]

Based on China's summary of three years of experience and measures in the prevention and control of the COVID-19 epidemic, we have built a COVID-19 prevention and control model integrating health and medical detection, big data information technology to track the trend of the epidemic throughout the whole process, isolation of key epidemic areas, and dynamic prevention and control management throughout the whole process. This model provides a simple, feasible, and theoretically reliable prevention and control model for future large-scale infectious disease prevention and control. The Lyapnov functional method is replaced by the global exponential attractor theory, which provides a new mathematical method for studying the global stability of the multi parameter, multi variable infectious disease prevention and control system. We extracted mathematical methods and models suitable for non-mathematical infectious disease researchers from profound and difficult to understand mathematical theories. Using the results of the global exponential Attractor theory obtained in this paper, we studied the global dynamics of the COVID-19 model with an epidemiological investigation. The results demonstrated that the non-constant disease-free equilibrium is globally asymptotically stable when λ * < 0 , and the COVID-19 epidemic is persisting uniformly when λ * > 0 . In order to understand the impact of the epidemiological investigation under different prevention and control stages in China, we compare the control effects of COVID-19 under different levels of epidemiological investigation policies. We visually demonstrate the global stability and global exponential attractiveness of the COVID-19 model with transferors between regions and epidemiological investigation in a temporal-spatial heterogeneous environment with the help of numerical simulations. We find that the epidemiological investigation really has a significant effect on the prevention and control of the epidemic situation, and we can also intuitively observe the relationship between the flow of people (including tourism, shopping, work and so on) and epidemiological investigation policies. Our model is adapted to different stages of prevention and control; the emergency "circuit breaker" mechanism of the model is also consistent with actual prevention and control. [ABSTRACT FROM AUTHOR]

Schistosomiasis is a parasitic disease caused by Schistosoma Japonicum that is transmitted by freshwater snails. Humans and some mammals are hosts of Schistosoma Japonicum. In this paper, we propose a multi-host (human-snail-bovine) schistosomiasis model with seasonality and temperature-dependent delays. We first introduce the basic reproduction number $ \mathcal R_0 $ for the whole system and the basic reproduction number $ \mathcal {\hat R}_0 $ for the system in the absence of bovines, respectively. Then we determine the extinction and persistence of the disease in terms of $ \mathcal R_0 $ and $ \mathcal {\hat R}_0 $. In the presence of susceptible humans, snails and bovines, we show that the disease persists if $ \mathcal R_0>1 $ and dies out if $ \mathcal R_0<1 $. As an application of our model, we study the transmission tendency of the schistosomiasis in Hubei province, China. Our numerical simulations indicate that the schistosomiasis incidences in both humans and bovines decline in an oscillatory way, but cannot disappear completely in the near future. A sensitivity analysis suggests that enhancing environmental disinfection, increasing treatment rate for both infected humans and bovines, replacing cattle with machine, and controlling the growth of snail population should be the effective measures for the prevention and control of schistosomiasis. [ABSTRACT FROM AUTHOR]

In this paper, a SEIR epidemic model related to media coverage and exogenous reinfections is established to explore the transmission dynamics of COVID-19. The basic reproduction number is calculated using the next generation matrix method. First, the existence of equilibrium points is investigated, and different kinds of equilibrium points indicate that the disease may disappear, or exist that result in different quantity of susceptible individuals, pre-symptomatic infected individuals and symptomatic infected individuals. The stability of the equilibria is discussed by a geometric approach, and it is found that controlling reproduction number to be lower than 1 is not sufficient for eradication of COVID-19. Second, transcritical bifurcation is explored, and it is found that improving the ratio of exogenous reinfection may lead to backward bifurcation under poor medical conditions, which indicates that two endemic equilibrium points appear. Third, to investigate the influence of parameters on the basic reproduction, sensitivity analysis is done to choose relatively sensitive parameters, and the parameters for treatment and media coverage are selected. An optimal control model is established to balance the treatment and media awareness. By exploring the existence and the uniqueness of the optimal control solution, the optimal control strategies are given. Finally, we run numerical simulations to verify the theoretical analysis on actual data of China, and the data from the four different states of India is used for forecasting the situation of infected individuals in a short period. It is found by the simulation that the co-function of treatment and media coverage results in the reduced number of infectious individuals. [ABSTRACT FROM AUTHOR]

Age heterogeneity in influenza transmission leads to significant differences in infection risk among different age groups. In this paper, an influenza model with vaccination and discrete age structure is constructed. First, we obtain the basic reproduction number R0$$ {R}_0 $$ and prove that the disease‐free equilibrium E0$$ {E}_0 $$ is globally stable at R0<1$$ {R}_0<1 $$. When R0>1$$ {R}_0>1 $$, the disease will persist uniformly, and there is a unique positive equilibrium, which is globally asymptotically stable under certain conditions. The model is used to analyze influenza data from 2016 to 2017 in China. By comparing various prevention and control measures, it can be found that by wearing masks to reduce contact between different age groups, while increasing vaccine coverage and reducing vaccine failure rates, the prevention and control goals can be achieved in the shortest time. However, if only the vaccine coverage rate is increased and the vaccine protection rate is strengthened, the time to reach the control target is 8 months later than the above case, and the cost is the lowest. [ABSTRACT FROM AUTHOR]

Since the global COVID-19 pandemic in 2020, some people who have dropped out of online game have become re-addicted to it due to the order of stay-at-home, making the phenomenon of online game addiction even worse. Controlling the prevalence of online game addiction is of great significance to protect people's healthy life. For this purpose, a mathematical model of online game addiction with incomplete recovery and relapse is established. First, we analyze the basic properties of the model and obtain the expression of the basic reproduction number and all equilibria. By constructing suitable Lyapunov functions, the global asymptotical stability of the equilibria are proved. Then in the numerical simulation, we use the least squares estimation method to fit the real data of e-sports users in China from 2010 to 2020, and obtain the estimated value of all parameters. The approximation value of the basic reproduction number is obtained as R 0 ≈ 5.05 . The result reflects that the spread of game addiction in China is very serious. The stability of the equilibria are proved by using the estimated parameter values. Finally, the simulation results between with control and without control during 2020 to 2050 are compared, and the optimal control strategy is found by comparing the total infectious people. The results of optimal control suggest that if we increase our continuous attention to incompletely recovered people, we can prevent more people from becoming addicted to games. The findings in this paper reveal new mechanisms of game addiction transmission and demonstrate a more detailed and reliable control strategy. [ABSTRACT FROM AUTHOR]

In this paper, to investigate the synthetic effect of PrEP (pre‐exposure prophylaxis) and ART (antiretrovial therapy) on HIV transmission among MSM (men who have sex with men) in heterogenous environment, a realistic HIV epidemic model with spatial diffusion is established. Here, HIV infectious people are divided into three immunity based compartments, that is, CD4+ T cell count less than 350, between 350 and 500, and more than 500, respectively. The basic reproduction number R0 is established and proved as a threshold parameter: The global asymptotic stability of the disease‐free steady state holds for R0<1, and the disease will be present if R0>1. Considering the substantial advantages of PrEP and ART in controlling HIV transmissions among MSM, the optimal control problem is presented for the case of positive constant diffusion coefficients, which minimize the total population of susceptible individual and HIV infected individual, the cost of PrEP and ART therapy. As an illustration of our theoretical results, we conduct numerical simulations. We also conduct an optimal control case study where model parameters are estimated from the demographic and epidemiological data from China. This work suggests the following: (1) Spatial factors cannot be ignored during the HIV intervention; (2)taking the PrEP intervention measure for HIV transmissions among MSM as early as possible will help to improve the control efficiency and reduces its cost; (3) reducing the PrEP drug costs will promote the efficiency of PrEP treatment in preventing the spread of HIV among MSM. [ABSTRACT FROM AUTHOR]

In this paper, we discuss an EIQJR model with stochastic perturbation. First, a globally positive solution of the proposed model has been discussed. In addition, the global asymptotic stability and exponential mean-square stability of the disease-free equilibrium have been proven under suitable conditions for our model. This means that the disease will die over time. We investigate the asymptotic behavior around the endemic equilibrium of the deterministic model to show when the disease will prevail. Constructing a suitable Lyapunov functional method is crucial to our investigation. Parameter estimations and numerical simulations are performed to depict the transmission process of COVID-19 pandemic in China and to support analytical results. [ABSTRACT FROM AUTHOR]

Many countries worldwide have been affected by the outbreak of the novel coronavirus (COVID‐19) that was first reported in China. To understand and forecast the transmission dynamics of this disease, fractional‐order derivative‐based modeling can be beneficial. We propose in this paper a fractional‐order mathematical model to examine the COVID‐19 disease outbreak. This model outlines the multiple mechanisms of transmission within the dynamics of infection. The basic reproduction number and the equilibrium points are calculated from the model to assess the transmissibility of the COVID‐19. Sensitivity analysis is discussed to explain the significance of the epidemic parameters. The existence and uniqueness of the solution to the proposed model have been proven using the fixed‐point theorem and by helping the Arzela–Ascoli theorem. Using the predictor–corrector algorithm, we approximated the solution of the proposed model. The results obtained are represented by using figures that illustrate the behavior of the predicted model classes. Finally, the study of the stability of the numerical method is carried out using some results and primary lemmas. [ABSTRACT FROM AUTHOR]

According to the report of the WHO, there is a strong relationship between AIDS and tuberculosis (TB). Therefore, it is very important to study how to control TB in the context of the global AIDS epidemic. In this paper, we establish an age structured mathematical model of HIV-TB co-infection to study the transmission dynamics of this co-infection, and consider awareness in the modeling. We give the basic reproduction numbers for each of the two diseases and find four equilibria, namely, disease-free equilibrium, TB-free equilibrium, HIV-free equilibrium and endemic disease equilibrium. Then we discuss the local stability of the equilibria according to the range of values of the two basic reproduction numbers, and find the endemic equilibrium is unstable. We also discuss the global stability of the disease-free equilibrium and the TB-free equilibrium. Based on the new HIV-positive cases and TB cases data in China, the best-fit parameter values and initial values of the model are identified by the MCMC algorithm. Then we perform uncertainty and sensitivity analysis to identify the parameters that have significant impact on the basic reproduction number R T R T. Finally, combined with the established model, we give some measures that may help China achieve the goal of WHO of reducing the incidence of TB by 80% by 2030 compared to 2015. [ABSTRACT FROM AUTHOR]

Background: The global spread of the novel coronavirus pneumonia is still continuing, and a new round of more serious outbreaks has even begun in some countries. In this context, this paper studies the dynamics of a type of delayed reaction-diffusion novel coronavirus pneumonia model with relapse and self-limiting treatment in a temporal-spatial heterogeneous environment.Methods: First, focus on the self-limiting characteristics of COVID-19, incorporate the relapse and self-limiting treatment factors into the diffusion model, and study the influence of self-limiting treatment on the diffusion of the epidemic. Second, because the traditional Lyapunov stability method is difficult to determine the spread of the epidemic with relapse and self-limiting treatment, we introduce a completely different method, relying on the existence conditions of the exponential attractor of our newly established in the infinite-dimensional dynamic system to determine the diffusion of novel coronavirus pneumonia. Third, relapse and self-limiting treatment have led to a change in the structure of the delayed diffusion COVID-19 model, and the traditional basic reproduction number [Formula: see text] no longer has threshold characteristics. With the help of the Krein-Rutman theorem and the eigenvalue method, we studied the threshold characteristics of the principal eigenvalue and found that it can be used as a new threshold to describe the diffusion of the epidemic.Results: Our results prove that the principal eigenvalue [Formula: see text] of the delayed reaction-diffusion COVID-19 system with relapse and self-limiting treatment can replace the basic reproduction number [Formula: see text] to describe the threshold effect of disease transmission. Combine with the latest official data and the prevention and control strategies, some numerical simulations on the stability and global exponential attractiveness of the diffusion of the COVID-19 epidemic in China and the USA are given.Conclusions: Through the comparison of numerical simulations, we find that self-limiting treatment can significantly promote the prevention and control of the epidemic. And if the free activities of asymptomatic infected persons are not restricted, it will seriously hinder the progress of epidemic prevention and control. [ABSTRACT FROM AUTHOR]

• A dengue model is proposed with parameters linked to climate and human factors. • Both local and global stability of the disease-free equilibrium are analyzed. • Sensitive analysis reveals a decisive role of temperature in dengue spread. • Sensitive analysis discloses a local role of precipitation and human population. • Climate changes aggregate dengue burden more than human population. Dengue fever (DF) is a re-emerging disease spread by mosquitoes. It is primarily found in the tropics and subtropics, and its prevalence is heavily influenced by global warming. A comprehensive understanding of how the changes in climate and human population affect future dengue epidemics is crucial for effective prevention and control. In this paper we extend a mechanistic compartmental model for mosquito dynamics of immature and mature stages, coupled with human population dynamics. Stability analysis of the disease-free equilibrium is carried out analytically, and the basic reproduction number is derived. Model parameters are explicitly linked to climatic variables and human population density. Model validation suggests that the basic reproduction number acts as a reliable measure of the spread ability of DF in response to future scenarios of climate and human population change. Our model predicts that the risk area of DF will expand considerably in mainland China, and the expansion fronts are mainly extended in the center and east. Most importantly, sensitivity analysis and model prediction both show that while temperature is critical in determining the threshold suitability for DF transmission, precipitation and human population density act locally to regulate the spreading DF patterns, where high values of these two factors may significantly accelerate the spreading process. Our results indicate a strong call for increased attention in the areas that are currently safe from DF, but climatically suitable for DF spread as consequence of the fast-economic growth and rapid urbanization. [ABSTRACT FROM AUTHOR]

This paper presents a deterministic compartmental model for echinococcosis transmission dynamics. The basic reproduction number of the model determines the existence and stability of the disease-free and disease-endemic equilibrium points. We further formulate the optimal control problem and obtain the necessary conditions to minimize the number of infected individuals and the associated costs. Numerical simulations show that optimal control strategies can significantly reduce the number of infected individuals to lower levels. Environmental disinfection may be essential for the elimination of infections. The results of this study will be beneficial for the prevention and control of echinococcosis in the Ganzi Tibetan Autonomous Prefecture and other areas of China. [ABSTRACT FROM AUTHOR]

Coronavirus spread in Wuhan, China, in December 2019. A few weeks later, the virus was present in over 100 countries around the globe. Governments have adopted extreme measures to contain the spreading virus. Quarantine is considered the most effective way to control the spreading speed of COVID-19. In this study, a mathematical model is developed to explore the influence of quarantine and the latent period on the spatial spread of COVID-19. We use the mathematical model with quarantine, and delay to predict the spreading speed of the virus. In particular, we transform the model to a single integral equation and then apply the Laplace transform to find implicit equations for the spreading speeds. The basic reproduction number of COVID-19 is also found and calculated. Numerical simulations are performed to confirm our theoretical results. To validate the proposed model, we compare our outcomes with the actual reported data published by the National Health Commission of China and the Health Commission of local governments. The model demonstrates good qualitative agreement with the actual data reported. The results show that delay and quarantine highly influence the spreading speeds of COVID-19. Also, we can only contain the disease if we quarantine 75% of the infected people. [ABSTRACT FROM AUTHOR]

• The paper proposes the stochastic dynamics of SIQR model structure with Lévy jumps and three time delays. • The existence and uniqueness of the positive solution, the dynamic properties around the disease-free equilibrium and the endemic equilibrium are obtained by constructing some suitable Lyapunov functions. • The inuence of isolation and vaccination rate on the disease dynamics is also examined by sensitivity analysis. • The unknown parameters are estimated by the least-square method and the trend of COVID-19 epidemic was predicted. Isolation and vaccination are the two most effective measures in protecting the public from the spread of illness. The SIQR model with vaccination is widely used to investigate the dynamics of an infectious disease at population level having the compartments: susceptible, infectious, quarantined and recovered. The paper mainly aims to extend the deterministic model to a stochastic SQIR case with Lévy jumps and three-time delays, which is more suitable for modeling complex and instable environment. The existence and uniqueness of the global positive solution are obtained by using the Lyapunov method. The dynamic properties of stochastic solution are studied around the disease-free and endemic equilibria of the deterministic model. Our results reveal that stochastic perturbation affect the asymptotic properties of the model. Numerical simulation shows the effects of interested parameters of theoretical results, including quarantine, vaccination and jump parameters. Finally, we apply both the stochastic and deterministic models to analyze the outbreak of mutant COVID-19 epidemic in Gansu Province, China. [ABSTRACT FROM AUTHOR]

Tuberculosis (TB) is an infectious disease transmitted through the respiratory system. China is one of the countries with a high burden of TB. Since 2004, an average of more than 800,000 cases of active TB has been reported each year in China. Analyzing the case data from 2004 to 2018, we found significant differences in TB incidence by age group. A model of TB is put forward to explore the effect of age heterogeneity on TB transmission. The nonlinear least squares method is used to obtain the key parameters in the model, and the basic reproduction number Rv = 0.8017 is calculated and the sensitivity analysis of Rv to the parameters is given. The simulation results show that reducing the number of new infections in the elderly population and increasing the recovery rate of elderly patients with the disease could significantly reduce the transmission of TB. Furthermore, the feasibility of achieving the goals of the World Health Organization (WHO) End TB Strategy in China is assessed, and we obtained that with existing TB control measures it will take another 30 years for China to reach the WHO goal to reduce 90% of the number of new cases by the year 2049. However, in theory it is feasible to reach the WHO strategic goal of ending TB by 2035 if the group contact rate in the elderly population can be reduced, though it is difficult to reduce the contact rate. [ABSTRACT FROM AUTHOR]

COVID-19 pandemic erupted from Wuhan/China, has impacted the whole world in many ways drastically. Understanding such a pandemic, taking necessary precautions, and controlling a potential epidemic is essential. Modules and communities are typically and frequently represented in networks and analyzed with specific methods. Epidemic network analysis is a powerful method that provides us different information to interpret and make accurate decisions for pandemic events. The randomness of epidemic networks is considerably high; hence, it is essential to obtain consistent information from such networks. In this study, we proposed the network-based community detection of the early-stage COVID-19 associated with the basic reproduction number and the geographical distance between country locations. Worldwide confirmed cases between 22/01/2020 and 08/06/2020 had been analyzed for tenday periods. For this purpose, the Community Detection method was used. Therefore, (i) the community regions, (ii) the change of these regions and weighted nodal degrees of confirmed cases during the COVID-19, (iii) the relations between locations, and (iv) locations or regions which played an important role during the spread of this disease were obtained. The results of this study may help to reduce the reproduction number by lowering the average rate of contact in the early stage of a new pandemic. [ABSTRACT FROM AUTHOR]

Background: Health education plays a vital role in the prevention and control of schistosomiasis in China and throughout the world. However, the coverage of health education varies from place to place for various reasons. Moreover, people with different levels of health education migrate between different regions. Methods: In order to analyze the effects of different coverages of health education on schistosomiasis transmission, a schistosomiasis mathematical model with people's inter-regional migration is constructed in two regions with different coverages of health education. The basic reproduction number is calculated, the global stability of the system is analyzed qualitatively, and a numerical simulation is carried out. Results: (1) The transmission trend of schistosomiasis could be reduced by increasing the migration of the susceptible population from the region with a high coverage of health education to the region with low coverage, or by increasing the migration of the infected population between the two regions. Schistosomiasis can even be eliminated if the migration of the susceptible or infected population from the region with a high coverage of health education to the region with a low coverage is sufficiently large. This is quite different from the prevention and control of other epidemics in which the movement of people should be restricted. (2) A low coverage of health education will have an impact on the number of patients and infected snails in both of the two regions. This result indicates that increasing the coverage of health education can reduce the risk of schistosomiasis not only in the local population but also in the surrounding regions to which people migrate. Conclusions: There is no need to restrict the migration of the infected population between the two regions nor the migration of the susceptible population from the region with a high coverage of health education to the region with a low coverage. However, there is a need to restrict the migration of the susceptible population from the region with a low coverage of health education to the region with a high coverage. These are some suggestions to prevent and control schistosomiasis. [ABSTRACT FROM AUTHOR]

In this paper, we study a stochastic SIQR epidemic model with imperfect quarantine. We perform a detailed mathematical analysis of the dynamics of the stochastic model. The basic reproduction number R 0 s turns out to be a sharp threshold, that is, if R 0 s < 1 , then the disease-free equilibrium of the stochastic model is globally stable almost surely, whereas if R 0 s > 1 , the Markov process is positive recurrence which indicates that the disease will prevail. We also adopt the data of weekly infected cases for northern China from the first week of 2014 to the 26th week of 2014, to fit the model and estimate the parameters. [ABSTRACT FROM AUTHOR]

The ongoing coronavirus disease 2019 (COVID-19) pandemic poses a huge threat to global public health. Motivated by China's experience of using Fangcang shelter hospitals (FSHs) to successfully combat the epidemic in its initial stages, we present a two-stage delay model considering the average waiting time of patients' admission to study the impact of hospital beds and centralized quarantine on mitigating and controlling of the outbreak. We compute the basic reproduction number in terms of the hospital resources and perform a sensitivity analysis of the average waiting times of patients before admission to the hospitals. We conclude that, while designated hospitals save lives in severely infected individuals, the FSHs played a key role in mitigating and eventually curbing the epidemic. We also quantified some key epidemiological indicators, such as the final size of infections and deaths, the peak height and its timing, and the maximum occupation of beds in FSHs. Our study suggests that, for a jurisdiction (region or country) still struggling with COVID-19, when possible, it is essential to increase testing capacity and use a centralized quarantine to massively reduce the severity and magnitude of the epidemic that follows. [ABSTRACT FROM AUTHOR]

Brucellosis, a zoonotic disease, has brought about enormous human suffering and tremendous economic burden to animal husbandry in China. However, Inner Mongolia is the hardest hit area of brucellosis in China. A total of 132,037 human cases have been reported from 2010 to 2020. Endogenous mechanisms of brucellosis spreading across Inner Mongolia till remains to be revealed. We propose a periodic epidemic model to investigate the effect of periodic parameter changes on brucellosis epidemics. Then we evaluate the basic reproduction number R 0 and analyze the global dynamics of the model. Furthermore, key parameters related to periodic transmission are estimated based on the monthly data of human brucellosis cases and the trend of newly infected human brucellosis cases are predicted in Inner Mongolia. Our modeling results illustrate that periodical birth and sheep shearing play a significant role in inducing periodical outbreak of brucellosis in Inner Mongolia. Moreover, it is exhibited that the annual peak number and the final scale of human brucellosis cases will be reduced dramatically with the delayed peak time of sheep birth. While the annual peak time will be lagged and the annual peak number will be decreased as the peak time of sheep shearing is postponed. In addition, we discover that it is difficult to stem brucellosis even if all sheep are vaccinated besides ewes. Nevertheless, the detection rate exceed a certain value 0.032 or the decaying rate of Brucella surpass a critical value 0.585, the human brucellosis can be regulated in Inner Mongolia according to the sensitivity analysis of R 0 . The insights shed herein may contribute to the careful implementation of brucellosis control strategies in other regions. [ABSTRACT FROM AUTHOR]

The first case of Corona Virus Disease 2019 (COVID-19) was reported in Wuhan, China in December 2019. Since then, COVID-19 has quickly spread out to all provinces in China and over 150 countries or territories in the world. With the first level response to public health emergencies (FLRPHE) launched over the country, the outbreak of COVID-19 in China is achieving under control in China. We develop a mathematical model based on the epidemiology of COVID-19, incorporating the isolation of healthy people, confirmed cases and contact tracing measures. We calculate the basic reproduction numbers 2.5 in China (excluding Hubei province) and 2.9 in Hubei province with the initial time on January 30 which shows the severe infectivity of COVID-19, and verify that the current isolation method effectively contains the transmission of COVID-19. Under the isolation of healthy people, confirmed cases and contact tracing measures, we find a noteworthy phenomenon that is the second epidemic of COVID-19 and estimate the peak time and value and the cumulative number of cases. Simulations show that the contact tracing measures can efficiently contain the transmission of the second epidemic of COVID-19. With the isolation of all susceptible people or all infectious people or both, there is no second epidemic of COVID-19. Furthermore, resumption of work and study can increase the transmission risk of the second epidemic of COVID-19. [ABSTRACT FROM AUTHOR]

With the expansion of the global novel coronavirus disease (COVID-19) pandemic, unprecedented interventions have been widely implemented in many countries, including China. In view of this scenario, this research aims to explore the effectiveness of population mobility restriction in alleviating epidemic transmission during different stages of the outbreak. Taking Shenzhen, a city with a large immigrant population in China, as a case study, the real-time reproduction number of COVID-19 is estimated by statistical methods to represent the dynamic spatiotemporal transmission pattern of COVID-19. Furthermore, migration data between Shenzhen and other provinces are collected to investigate the impact of nationwide population flow on near-real-time dynamic reproductive numbers. The results show that traffic flow control between populated cities has an inhibitory effect on urban transmission, but this effect is not significant in the late stage of the epidemic spread in China. This finding implies that the government should limit international and domestic population movement starting from the very early stage of the outbreak. This work confirms the effectiveness of travel restriction measures in the face of COVID-19 in China and provides new insight for densely populated cities in imposing intervention measures at various stages of the transmission cycle. [ABSTRACT FROM AUTHOR]

Coronavirus disease 2019 (COVID-19) is a worldwide infectious disease and very contagious. A mathematical model using ordinary differential equations was introduced to study the dynamics of COVID-19. Local and global stability analysis was proved, which depends on the basic reproduction number ℛ 0 . The value of parameters was estimated using the COVID-19 outbreak in China. Based on the index sensitivity results, an optimal control problem was formulated to represent the implementation of a movement control order. Finally, it is numerically shown that the spread of COVID-19 can be smothered viably by implementing an optimal control strategy. [ABSTRACT FROM AUTHOR]

Stock networks, which are constructed from stock price time series, are useful tools for analyzing complex behaviors in stock markets. Following former researches, the epidemic model has been usually used to detect dynamic characteristics in a stock price complex systems. Recently, multilayer networks have been demonstrated well when working on heterogeneous nodes rather than integrated networks. In this paper, we proposed a two-layer SIR propagation model with an infective medium to analyze the spread of financial shocks. In consideration of strict financial regulation in the A shares, the model assumed that capital cannot flow directly between layers but through the Hong Kong stock market. By applying the model to constituent stocks included in three prominent indices, Standard & Poor 500, Shanghai and Shenzhen 300, and Hang Seng(medium), we established a two-layer Granger networks. Betweenness showed that the Hong Kong stock market had a promoting transition function of financial shocks between the US stock markets and the mainland China stock markets. In addition, with a big basic reproduction number, stock markets system appeared to be vulnerable during extreme financial shock such as the outbreak of COVID-19 epidemic and the meltdown of stock markets. Furthermore, sensitivity analysis and the spreading simulation indicated that the US stock markets were much more robust to financial shocks than the mainland China stock markets. • New two-layer SIR propagation model with an infected medium for financial shocks. • Two-layer Granger networks based on the US stock markets, the mainland China stock markets, and the Hong Kong stock market. • Focusing on economic influence caused by COVID-19 epidemic. • Monte Carlo algorithm simulates the model in different conditions. [ABSTRACT FROM AUTHOR]

Studies have shown that sexual transmission, both heterosexually and homosexually, is one of the main ways of HBV infection. Based on this fact, we propose a mathematical model to study the sexual transmission of HBV among adults by classifying adults into men and women and considering both same-sex and opposite-sex transmissions of HBV in adults. Firstly, we calculate the basic reproduction number R 0 and the disease-free equilibrium point E 0 . Secondly, by analysing the sensitivity of R 0 in terms of model parameters, we find that the infection rate among people who have same-sex partners, the frequency of homosexual contact and the immunity rate of adults play important roles in the transmission of HBV. Moreover, we use our model to fit the reported data in China and forecast the trend of hepatitis B. Our results demonstrate that popularizing the basic knowledge of HBV among residents, advocating healthy and reasonable sexual life style, reducing the number of adult carriers, and increasing the immunization rate of adults are effective measures to prevent and control hepatitis B. [ABSTRACT FROM AUTHOR]

For epidemics such as COVID-19, with a significant population having asymptomatic, untested infection, model predictions are often not compatible with data reported only for the cases confirmed by laboratory tests. Additionally, most compartmental models have instantaneous recovery from infection, contrary to observation. Tuning such models with observed data to obtain the unknown infection rate is an ill-posed problem. Here, we derive from the first principle an epidemiological model with delay between the newly infected (N) and recovered (R) populations. To overcome the challenge of incompatibility between model and case data, we solve for the ratios of the observed quantities and show that log(N(t)/R(t)) should follow a straight line. This simple prediction tool is accurate in hindcasts verified using data for China and Italy. In traditional epidemiology, an epidemic wanes when much of the population is infected so that 'herd immunity' is achieved. For a highly contagious and deadly disease, herd immunity is not a feasible goal without human intervention or vaccines. Even before the availability of vaccines, the epidemic was suppressed with social measures in China and South Korea with much less than 5% of the population infected. Effects of social behaviour should be and are incorporated in our model. [ABSTRACT FROM AUTHOR]