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The emergence of mutant strains of COVID-19 reduces the effectiveness of vaccines in preventing infection, but remains effective in preventing severe illness and death. This paper established a heterogeneous mixing model of age groups with pharmaceutical and non-pharmaceutical interventions by analyzing the transmission mechanism of breakthrough infection caused by the heterogeneity of protection period under the action of vaccine-preventable infection with the original strain. The control reproduction number R c of the system is analyzed, and the existence and stability of equilibrium are given by the comparison principle. Numerical simulation was conducted to evaluate the vaccination program and intervention measures in the customized scenario, demonstrating that the group-3 coverage rate p 3 plays a key role in R c. It is proposed that accelerating the rate of admission and testing is conducive to epidemic control by further fitting data of COVID-19 transmission in real scenarios. The findings provide a general modeling idea for the emergence of new vaccines to prevent infection by mutant strains, as well as a solid theoretical foundation for mainland China to formulate future vaccination strategies for new vaccines. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics". • A modeling framework of heterogeneous mixing for COVID-19 with NPIs and vaccines. • Breakthrough infection and vaccines to reduce infection were incorporated into model. • Dynamical properties are analyzed, including threshold and stabilities of equilibria. • The vaccination strategies in custom scenario were explored with multiple indicators. [ABSTRACT FROM AUTHOR]

• An age-structured mathematical model on mumps outbreaks in Jiangsu, China is proposed and analyzed. • Three different stages of no vaccine, effectively controlled and resurgence stages are considered. • Patterns of mumps dynamics are simulated and compared based on data in Jiangsu from January 2005 to May 2019. • The time average basic reproduction number may be lower or over estimated the real one. • Changes in seasonal transmission patterns and demographic structures may be reasons of mumpsre-emerging. Measles, mumps and rubella (MMR) vaccine program was introduced in Jiangsu province of China in May 2008 and has been greatly contributed to decreasing of mumps cases. However, mumps has been resurging since May 2015. A number of studies have put forward that the resurgence of mumps is due to vaccine failure. In this paper, we investigated the other reasons for the resurging of mumps, such as the changes in seasonal transmission patterns and demographic structures, by using an age-structured mathematical model. We divided the history (January 2005 to May 2019) of mumps epidemics of Jiangsu province into three different stages: No vaccine stage (January 2005 to December 2008), effectively controlled stage (January 2009 to December 2014) and resurgence stage (January 2015 to May 2019). The features of mumps epidemics in three stages are compared under different demographic structures with same physical contact rate. The mumps transmission rate was increased in summer and dropped in November in stage III compared with that in stage I. The changes in demographic structures give a good explanation why the mumps outbreaked among children around 10 years old in stage I and around 5 years old in stage III. We have a conclusion that the vaccine failure, changes in seasonality and demographic structures were associated with the mumps outbreaks in recent years in Jiangsu province, China. We give the patterns of mumps dynamics considering age, vaccine, seasonality and demographic structures, which can help health program planners to implement more preventive interventions in mumps control during the period of higher risk of infection. [ABSTRACT FROM AUTHOR]

In a previous study we noticed that there might be co-infections of HBV and HIV by comparing incidence rates of these two diseases in China. The comparisons between the incidence data of HBV and sexually transmitted diseases (including AIDS, HIV, syphilis and gonorrhea) in China demonstrate that sexual transmission is an important route of spread of HBV in China. On the basis of this fact, in this paper we propose a compartmental model including under-aged children, male adults, and female adults. The effect of sexual transmission on the spread and prevalence of HBV in China is studied. The model is employed to simulate the HBV incidence data reported by the Chinese Center for Disease Control and Prevention for under-aged children, adult males, and adult females, respectively. The sensitivity analysis of the basic reproduction number indicates that it is important and crucial to increase the immunization rate for both under-aged children and adults in order to control the transmission of HBV in China. Our study suggests that effective control measures for hepatitis B in China include enhancing public education and awareness about hepatitis B virus, particularly about the fact that hepatitis B is a sexually transmitted disease, and increasing the immunization rate for both under-aged children and adults, especially for those groups of high risk. [ABSTRACT FROM AUTHOR]

This paper concentrates on the tuberculosis data of China from January 2005 to December 2012. We set up a mathematical model to fit those data with the goodness of fit and obtain the optimal parameter values of the model. By the Chi-square test of the statistical inference, the optimal parameter values of the model are reasonable. We get the effective reproductive number of the disease for each year, and also investigate the preventive measures to control the tuberculosis. [ABSTRACT FROM AUTHOR]

Abstract: Echinococcosis, which is one of the zoonotic diseases, can threaten human health and hinder the development of animal husbandry seriously. Especially in Xinjiang Uygur Autonomous Region of China, Echinococcosis is regarded as one of the most serious endemic diseases.The number of human Echinococcosis has increased dramatically in the last 10 years, partially due to poor understanding of the transmission dynamics of Echinococcosis and lack of effective control measures of the disease. In this paper, in order to explore effective control and prevention measures we propose a deterministic model to study the transmission dynamics of Echinococcosis in Xinjiang. The results show that the dynamics of the model is completely determined by the basic reproductive number R 0. If , the disease-free equilibrium is globally asymptotically stable. When , the disease-free equilibrium is unstable, and the endemic equilibrium is globally asymptotically stable. Based on the data reported by Xinjiang Center for Disease Control and Prevention (Xinjiang CDC), the numerical simulation result matches Echinococcosis data well. The model provides an approximate estimate of the basic reproduction number R 0=1.67. This indicates that Echinococcosis is endemic in Xinjiang with the current control measures. Finally, we perform some sensitivity analysis of several model parameters and give some useful comments on controlling the transmission of Echinococcosis. [Copyright &y& Elsevier]

Abstract: Rabies is a major public health problem in some developing countries including China. One of the reasons is that there is a very large number of dogs, both domestic and stray, especially in Guangdong Province which has the third most rabies cases (after Guangxi and Hunan) among the 31 provinces, autonomous regions and municipalities in Mainland China, and at least 18.2% of the human rabies cases are caused by stray dogs. In this paper, based on the reported data and characteristics of the rabies infection in Guangdong Province, we propose a mathematical model for the dog–human transmission of rabies. We first determine the basic reproduction number R 0 and discuss the stability of the disease-free equilibrium and persistence of the disease. By carrying out sensitivity analysis of the basic reproduction number in terms of some parameters, we find that the domestic dog vaccination rate, the recruitment rate of domestic dogs, and the quantity of stray dogs play important roles in the transmission of rabies. This study suggests that rabies control and prevention strategies should include public education and awareness about rabies, increase of the domestic dog vaccination rate and reduction of the stray dog population. [Copyright &y& Elsevier]

• Authors take pig farms as the research individuals, the trade among farms as the transmission route to establish a dynamical model. • By the dynamical analysis of the model, it is found that there will appear backward branching under some conditions. • Carrying out data fitting and parameter estimation to confirm the model rationality. • Establishing four evaluation indexes to assess the effect of corresponding effect factors and control measures of the disease. In China, foot-and-mouth disease (FMD) serotype O remains prevalent, and its main host is pigs. Infected but undiscovered pigs can carry foot-and-mouth disease virus (FMDV) for a longtime. And, the virus can spread among farms through pig trade. Although individual vaccination at least 2 times a year and monthly monitoring disease and culling all individual in same group for pigs are adopted vigorously in China, the epidemic remains prevalent. Therefore, in this paper, based on these propagation characteristics and control measures of the epidemic in China, we take the pig farms as research individuals, the trade among farms as transmission routes to establish a dynamic model with nonlinear incidence. In addition, we use this model to assess the impact of trade and transport of pigs among farms on the spread of foot-and-mouth disease virus (FMDV), and to assess the effect of the immunization, monitoring and culling adopted presently in China on the control of the epidemic. By the dynamical analysis of the model, it is found that there will appear backward branching under some conditions, which means that there are two spreading thresholds for the disease, and the disease development trend is also related to the current epidemic situation. Besides, we give the threshold conditions of key parameters to control the spread of FMD. By carrying out data fitting and parameter estimation, we confirm the model rationality, and give four evaluation indexes: the basic reproduction number R 0 of FMD serotype O in China, the value of the infected farms at the equilibria, annual probability of a susceptible farm being infected and annual transmission intensity of an infected farm. By carrying out the sensitivity analysis of key parameters on four evaluation indexes, the effect of parameters on the spread of the disease can be intuitively observed. All these can provide a theoretical basis for understanding of the trading-based transmission mechanism, control and prevention of foot-and-mouth disease in pigs in China. [ABSTRACT FROM AUTHOR]

• A new dynamic compartmental model was proposed to investigate the disease burdens of cancer. • The number of undiagnosed gastric cancer (GC) cases was estimated. • The effect of endoscopic screening coverage, frequency and initiating time on GC disease burdens in China were evaluated. Gastric cancer (GC) incidence and mortality in China remained high due to delayed diagnosis and accounted for about half of the world's GC cases and deaths. Early detection with endoscopic screening and consequent timely treatment can significantly improve survival. This study aimed to explore the long-term population impact of endoscopic screening on national GC disease burdens in China. Most of previous studies investigated the disease burdens of cancer using Markov model or age-period-cohort (APC) model, which are difficult to estimate the population size of undiagnosed cases. In this paper, we proposed a new dynamic compartmental model based on GC natural history and calibrated model outputs to diagnosed GC cases and GC-related death counts using Markov Chain Monte Carlo methods. We investigated the impact of screening strategies with various coverage (10%, 40%, 70%) and frequency (every 1, 3, 5 years) on disease burdens. We estimated that 2.22 (95%CI: 1.97–2.47) million Chinese are living with GC in 2019, among which, 42.7% (40.3–45.0%) remained undiagnosed. Without systematic screening, we projected 10.46 (9.07–11.86) million incident cases and 7.35 (6.59–8.11) million GC-related deaths over the next 30 years (2019–2049). Screening with coverage rate at 10%, 40%, 70% every 3 years could prevent 0.85 (0.63–1.06), 2.32 (1.79–2.86), and 3.04 (2.38–3.70) million incident cases, and prevent 1.17 (1.01–1.32), 3.08 (2.70–3.46), and 3.93 (3.46–4.40) million deaths respectively, compared with 'no screening' scenario. Screening would substantially increase the number of diagnosed GC cases within the first three years of program initiation, but this number would quickly reduce below 'no screening' scenario. Three-yearly screening at the above coverage rates would reduce the proportion of undiagnosed GC cases to 38.8% (36.9–40.7%), 25.5% (23.4–27.6%), and 17.8% (16.0–19.6%) by 2049, respectively. Delaying implementation of the screening program would substantially reduce its effectiveness. Initiating national endoscopic screening programmes would likely have a major effect on reducing GC incidence and mortality in China. Health resources should be substantially increased and directed to treatment of GC to cope with the initial rise in diagnosed GC cases. [ABSTRACT FROM AUTHOR]

To estimate the risk of human immunodeficiency virus (HIV) infection through sexual transmission in China from 2013 to 2017 accurately, we divide the total population into three groups, namely, men who have sex with men (MSM) group; non-marital and commercial sex group: female sex workers (FSW) and their clients (FSWC); non-marital and non-commercial sex group: general women (GW) and general men (GM). First, the risks of HIV infection among men who have contacts with infected men or infected women decrease annually. Second, the number of contacts between susceptible FSWC and infected FSW per unit time is greater than that between susceptible MSM and infected MSM, and also greater than that between susceptible FSW and infected FSWC, which suggests that the intervention for commercial sex of heterosexual men should be strengthened. Third, the effective reproduction numbers of the MSM group and non-commercial sex group decrease annually, while the effective reproduction number of the commercial sex group decreases first, then increases, because the risk of women being infected by men decreases first, then increases. Additionally, the effective reproduction number of the commercial sex group exceeds that of the MSM group after 2015, which indicates that commercial sex contributes more and more to the HIV/AIDS epidemic., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023 Elsevier Ltd. All rights reserved.)

Shanghai suffered a large outbreak of Omicron mutant of COVID-19 at the beginning of March 2022. To figure out the spatiotemporal patterns of the epidemic, a retrospective statistical investigation, coupled with a dynamic model, is implemented in this study. The hotspots of SARS-CoV-2 transmissions are identified, and strong aggregative effects in the decay stage are found. Besides, the visualization of disease diffusion is provided to show how COVID-19 disease invades all districts of Shanghai in the early stage. Furthermore, the calculations from the dynamic model manifest the effect of detections to suppress the epidemic dissemination. These results reveal the strategies to improve the spatial control of disease., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier Ltd. All rights reserved.)

As a common infectious disease, scarlet fever has exposed a tendency of slow fluctuating ups and downs in recent years with a certain periodicity. In this work, a novel differential equation epidemic model with freely transmitted viruses is introduced to investigate the transmission dynamics of scarlet fever in Northwest China. First, the correlation analysis reveals that the incidence rate of scarlet fever is significantly positively correlated with air pressure (r = 0.61), conversely negatively correlated with precipitation (r = -0.15). Furthermore, the basic reproduction number R 0 is derived, and this paper proves that the unique disease-free periodic solution P 0 is globally symptotically stable when R 0 < 1, while the disease is uniformly persistent and at least one positive periodic solution exists when R 0 > 1. Moreover, by studying the qualitative of correlation between the effective reproduction number and air pollutants or meteorological factors, the seasonal variation pattern of incidence is summarized. Our investigations suggest that the relevant epidemic prevention departments should pay close attention to changes in environmental factors of the five provinces of Northwest China to formulate timely prevention strategies before the arrival of the high-risk period., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier Ltd. All rights reserved.)

Vaccination is effective in preventing human papillomavirus (HPV) infection. It still remains debatable whether males should be included in a vaccination program and unclear how to allocate the vaccine in genders to achieve the maximum benefits. In this paper, we use a two-sex model to assess HPV vaccination strategies and use the data from Guangxi Province in China as a case study. Both mathematical analysis and numerical simulations show that the basic reproduction number, an important indicator of the transmission potential of the infection, achieves its minimum when the priority of vaccination is given to the gender with a smaller recruit rate. Given a fixed amount of vaccine, splitting the vaccine evenly usually leads to a larger basic reproduction number and a higher prevalence of infection. Vaccination becomes less effective in reducing the infection once the vaccine amount exceeds the smaller recruit rate of the two genders. In the case study, we estimate the basic reproduction number is 1.0333 for HPV 16/18 in people aged 15-55. The minimal bivalent HPV vaccine needed for the disease prevalence to be below 0.05% is 24050 per year, which should be given to females. However, with this vaccination strategy it would require a very long time and a large amount of vaccine to achieve the goal. In contrast with allocating the same vaccine amount every year, we find that a variable vaccination strategy with more vaccine given in the beginning followed by less vaccine in later years can save time and total vaccine amount. The variable vaccination strategy illustrated in this study can help to better distribute the vaccine to reduce the HPV prevalence. Although this work is for HPV infection and the case study is for a province in China, the model, analysis and conclusions may be applicable to other sexually transmitted diseases in other regions or countries., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier Ltd. All rights reserved.)

Internal phosphorus recycling in lakes is an important nutrient source that promotes algal growth. Its persistence impedes the effort to improve water quality and thus poses a challenge to the management of eutrophication in lakes, especially in shallow lakes where the occurrence of internal phosphorus recycling is reportedly more common. This paper aims to provide crucial insights on the effects of internal phosphorus recycling on eutrophication dynamics for effective management of lake eutrophication. For this purpose, a mathematical model for lake eutrophication, comprising two compartments of algae and phosphorus, is first formulated for application to a eutrophic tropical lake named Tasik Harapan in Universiti Sains Malaysia. Numerical bifurcation analysis of the model is then performed to assess the combined influences of internal phosphorus recycling, algal mortality and external phosphorus loading on Tasik Harapan eutrophication dynamics. Specifically, co-dimension one bifurcation analysis of algal mortality rate is carried out by means of XPPAUT for various external phosphorus loading rates. The emergence of limit cycle for a certain range of algal mortality rate could be related to the hydra effect (i.e., algal concentration increases in response to greater algal mortality) and the paradox of enrichment (i.e., destabilization of algae in nutrient rich environment). To trace the locus of co-dimension one bifurcation, co-dimension two bifurcation analysis is performed by means of MatCont. The analysis demonstrated that the inclusion of the internal phosphorus recycling term induces rich and complex dynamics of the model. These dynamics include saddle-node bifurcation, cusp, Bogdanov-Takens bifurcation, Generalized Hopf bifurcation and limit point bifurcation of cycles. The results suggest that high internal phosphorus recycling rate promotes bistability and catastrophic shift in a shallow and tropical lake like Tasik Harapan. Hence, the key to effective management of eutrophication in shallow and tropical lakes is the control of internal phosphorus recycling., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2021 Elsevier Ltd. All rights reserved.)

The COVID-19 pandemic has led to widespread attention given to the notions of "flattening the curve" during lockdowns, and successful contact tracing programs suppressing outbreaks. However a more nuanced picture of these interventions' effects on epidemic trajectories is necessary. By mathematical modeling each as reactive quarantine measures, dependent on current infection rates, with different mechanisms of action, we analytically derive distinct nonlinear effects of these interventions on final and peak outbreak size. We simultaneously fit the model to provincial reported case and aggregated quarantined contact data from China. Lockdowns compressed the outbreak in China inversely proportional to population quarantine rates, revealing their critical dependence on timing. Contact tracing had significantly less impact on final outbreak size, but did lead to peak size reduction. Our analysis suggests that altering the cumulative cases in a rapidly spreading outbreak requires sustained interventions that decrease the reproduction number close to one, otherwise some type of swift lockdown measure may be needed., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2021. Published by Elsevier Ltd.)

The outbreak of coronavirus disease 2019 (COVID-19), caused by the virus severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has already created emergency situations in almost every country of the world. The disease spreads all over the world within a very short period of time after its first identification in Wuhan, China in December, 2019. In India, the outbreak, starts on 2 nd March, 2020 and after that the cases are increasing exponentially. Very high population density, the unavailability of specific medicines or vaccines, insufficient evidences regarding the transmission mechanism of the disease also make it more difficult to fight against the disease properly in India. Mathematical models have been used to predict the disease dynamics and also to assess the efficiency of the intervention strategies in reducing the disease burden. In this work, we propose a mathematical model to describe the disease transmission mechanism between the individuals. Our proposed model is fitted to the daily new reported cases in India during the period 2 nd March, 2020 to 12 th November, 2020. We estimate the basic reproduction number, effective reproduction number and epidemic doubling time from the incidence data for the above-mentioned period. We further assess the effect of implementing preventive measures in reducing the new cases. Our model projects the daily new COVID-19 cases in India during 13 th November, 2020 to 25 th February, 2021 for a range of intervention strength. We also investigate that higher intervention effort is required to control the disease outbreak within a shorter period of time in India. Moreover, our analysis reveals that the strength of the intervention should be increased over the time to eradicate the disease effectively., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2021 Elsevier Ltd. All rights reserved.)

Tuberculosis (TB) is still an important public health issue in Jiangsu province, China. In this study, based on the TB transmission routes and the statistical data of TB cases, we formulate a novel TB epidemic model accounting for the effects of the contaminated environments on TB transmission dynamics. The value of this study lies in two aspects. Mathematically, we define the basic reproduction number, R 0 , and prove that R 0 can be used to govern the threshold dynamics of the model. Epidemiologically, we find that the annual average R 0 is 1.13,>1 and TB in Jiangsu is an endemic disease. Therefore, in order to control the TB in Jiangsu efficiently, we must decrease the virus shedding rate or increase the recovery rates, and increase the environmental clearance rate., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020 Elsevier Ltd. All rights reserved.)

In mainland China, there are three prevalent serotypes of foot and mouth disease virus (FMDV) and they circulate in different susceptible animals, which respond to viral infection in various ways and present different prevalent features. Although powerful control measures are carried on regularly, the epidemic are still prevalent in livestock. Therefore it is essential to assess the disease trends of foot and mouth disease (FMD) in domestic animals in mainland China. The participation of contaminated environment in the transmission dynamics has been confirmed in laboratory research and it can alter the conditions for FMDV invasion and persistence. So environment transmission plays a key role in disease spreading process. In this paper, we establish a dynamical switching model with environment transmission to investigate the relevant internal force mechanism with respect to the threshold switching, effect of saturation of the quantity of FMDV in environment, and prevalent characteristics of the disease in mainland China. Through the dynamical analysis of the model, we understand that under different conditions, there may appear coexistence of one, two, three or even four steady states, and bistability might occur, showing that the development trend of epidemic not only depends on the model parameters, but also is associated with the initial condition. We further study the influence of key parameters on the dynamical behavior and classify the parameter space into several regions with different composition patterns. Applying the model to assess the development trend of FMD in livestock in mainland China, we find that under certain conditions, some of the serotypes persists and some may disappear, thus we can provide some suggestions for disease control of prevailing serotype., (Copyright © 2018 Elsevier Ltd. All rights reserved.)