Preliminary prediction of the control reproduction number of COVID-19 in Shaanxi Province,China

Objectives Firstly,according to the characteristics of COVID-19 epidemic and the control measures of the government of Shaanxi Province,a general population epidemic model is es-tablished.Then,the control reproduction number of general population epidemic model is obtained.Based on the epidemic model of general population,the epidemic model of general population and college population is further established,and the control reproduction number is also obtained.Methods For the established epidemic model,firstly,the expression of the control reproduc-tion number is obtained by using the next generation matrix.Secondly,the real-time reported data of COVID-19 in Shaanxi Province is used to fit the epidemic model,and the parameters in the model are estimated by least square method and MCMC.Thirdly,the Latin hypercube sampling method and partial rank correlation coefficient(PRCC)are adopted to analyze the sensitivity of the model.Conclusions The control reproduction number remained at 3 from January 23 to January 31,then gradually decreased from 3 to slightly greater than 0.2 by using the real-time reports on the number of COVID-19 infected cases from Health Committee of Shaanxi Province in China.In order to further control the spread of the epidemic,the following measures can be taken:(i)reducing infection by wearing masks,paying attention to personal hygiene and limiting travel;(i)improving isolation of suspected patients and treatment of symptomatic individuals.In particular,the epidemic model of the collge population and the general population is estab-lished,and the control reproduction number is given,which will provide theoretical basis for the prevention and control of the epidemic in the colleges.

Assessment of immunization procedures for foot-and-mouth disease in large-scale pig farms in China based on actual data and dynamics

Foot-and-mouth disease(FMD)is an acute,highly infectious and pathogenic animal disease.In recent years,with the rapid development of the swine breeding industry in China,pig farms have shown a trend of larger-scale development.Large-scale pig farms employ standardized management,a high level of automation,and a strict_system.However,these farms have a large trading volume,and increased transmission intensity of FMD is noted inside the farm.At present,the main control measure against FMD is pig vaccination.However,a standard for immunization procedures is not available,and currently adopted immunization procedures have not been effectively and systematically evaluated.Taking a typical large-scale pig farm in China as the research subject and considering the breeding pattern,piggery structure,age structure and immunization procedures,an individual-based state probability model is established to evaluate the effectiveness of the immune procedure.Based on numerical simulation,it is concluded that the optimal immunization program involves primary immunization at 40 days of age and secondary immunization at 80 days of age for commercial pigs.Breeding boars and breeding sows are immunized 4 times a year,and reserve pigs are immunized at 169 and 259 days of age.According to the theoretical analysis,the average control reproduction number of individuals under the optimal immunization procedure in the farm is 0.4927.In the absence of immunization,the average is 1.7498,indicating that the epidemic cannot be controlled without immunization procedures.

Dynamics of a two-group model for assessing the impacts of pre-exposure prophylaxis,testing and risk behaviour change on the spread and control of HIV/AIDS in an MSM population

Although much progress has been made in reducing the public health burden of the human immunodeficiency virus(HIV),which causes acquired immunodeficiency syndrome(AIDS),since its emergence in the 1980s(largely due to the large-scale use and availability of potent antiviral therapy,improved diagnostic and intervention and mitigation measures),HIV remains an important public health challenge globally,including in the United States.This study is based on the use of mathematical modeling approaches to assess the population-level impact of pre-exposure prophylaxis(PrEP),voluntary testing(to detect undetected HIV-infected individuals),and changes in human behavior(with respect to risk structure),on the spread and control of HIV/AIDS in an MSM(men-who-have sex-with-men)population.Specifically,a novel two-group mathematical model,which stratifies the total MSM population based on risk(low or high)of acquisition of HIV infection,is formulated.The model undergoes a PrEP-induced backward bifurcation when the control reproduction number of the model is less than one if the efficacy of PrEP to prevent a high-risk susceptible MSM individual from acquiring HIV infection is not perfect(the consequence of which is that,while necessary,having the reproduction number of the model less than one is no longer sufficient for the elimination of the disease in the MSM population).For the case where the efficacy of PrEP is perfect,this study shows that the disease-free equilibrium of the two-group model is globally-asymptotically stable when the associated control reproduction number of the model is less than one.Global sensitivity analysis was carried out to identify the main parameters of the model that have the highest influence on the value of the control reproduction number of the model(thereby,having the highest influence on the disease burden in the MSM population).Numerical simulations of the model,using a plausible range of parameter values,show that if half of the MSM population considered adhere strictly to the specified PrEP regimen(while other interventions are maintained at their baseline values),a reduction of about 22%of the new yearly HIV cases recorded at the peak of the disease could be averted(compared to the worst-case scenario where PrEP-based intervention is not implemented in the MSM population).The yearly reduction at the peak increases to about 50%if the PrEP coverage in the MSM population increases to 80%.This study showed,based on the parameter values used in the simulations,that the prospects of elimination of HIV/AIDS in the MSM community are promising if high-risk susceptible individuals are no more than 15%more likely to acquire HIV infection,in comparison to their low-risk counterparts.Furthermore,these prospects are significantly improved if undetected HIV-infected individuals are detected within an optimal period of time.

A Novel Analysis Approach of Uniform Persistence for an Epidemic Model with Quarantine and Standard Incidence Rate

Inspired by the transmission characteristics of the coronavirus disease 2019(COVID-19),an epidemic model with quarantine and standard incidence rate is first developed,then a novel analysis approach is proposed for finding the ultimate lower bound of the number of infected individuals,which means that the epidemic is uniformly persistent if the control reproduction number R_(c)>1.This approach can be applied to the related biomat hem at ical models,and some existing works can be improved by using that.In addition,the infection-free equilibrium V^(0)of the model is locally asymptotically stable(LAS)if R_(c)<1 and linearly stable if R_(c)=1;while V^(0)is unstable if R_(c)>1.

Understanding the impact of HIV on mpox transmission in the MSM population: A mathematical modeling study

The recent mpox outbreak(in 2022e2023)has different clinical and epidemiological features compared with previous outbreaks of the disease.During this outbreak,sexual contact was believed to be the primary transmission route of the disease.In addition,the community of men having sex with men(MSM)was disproportionately affected by the outbreak.This population is also disproportionately affected by HIV infection.Given that both diseases can be transmitted sexually,the endemicity of HIV,and the high sexual behavior associated with the MSM community,it is essential to understand the effect of the two diseases spreading simultaneously in an MSM population.Particularly,we aim to understand the potential effects of HIV on an mpox outbreak in the MSM population.We develop a mechanistic mathematical model of HIV and mpox co-infection.Our model incorporates the dynamics of both diseases and considers HIV treatment with antiretroviral therapy(ART).In addition,we consider a potential scenario where HIV infection increases susceptibility to mpox,and investigate the potential impact of this mechanism on mpox dynamics.Our analysis shows that HIV can facilitate the spread of mpox in an MSM population,and that HIV treatment with ART may not be sufficient to control the spread of mpox in the population.However,we showed that a moderate use of condoms or reduction in sexual contact in the population combined with ART is beneficial in controlling mpox transmission.Based on our analysis,it is evident that effective control of HIV,specifically through substantial ART use,moderate condom compliance,and reduction in sexual contact,is imperative for curtailing the transmission of mpox in an MSM population and mitigating the compounding impact of these intertwined epidemics.

Risk estimation and prediction of the transmission of coronavirus disease-2019(COVID-19)in the mainland of China excluding Hubei province

Background In December 2019,an outbreak of coronavirus disease(later named as COVID-19)was identified in Wuhan,China and,later on,detected in other parts of China.Our aim is to evaluate the effectiveness of the evolution of interventions and self-protection measures,estimate the risk of partial lifting control measures and predict the epidemic trend of the virus in the mainland of China excluding Hubei province based on the published data and a novel mathematical model.Methods A novel COVID-19 transmission dynamic model incorporating the intervention measures implemented in China is proposed.COVID-19 daily data of the mainland of China excluding Hubei province,including the cumulative confirmed cases,the cumulative deaths,newly confirmed cases and the cumulative recovered cases between 20 January and 3 March 2020,were archived from the National Health Commission of China(NHCC).We parameterize the model by using the Markov Chain Monte Carlo(MCMC)method and estimate the control reproduction number(Rc),as well as the effective daily reproduction ratio-Re(t),of the disease transmission in the mainland of China excluding Hubei province.Results The estimation outcomes indicate that Rc is 3.36(95%CI:3.20–3.64)and Re(t)has dropped below 1 since 31 January 2020,which implies that the containment strategies implemented by the Chinese government in the mainland of China are indeed effective and magnificently suppressed COVID-19 transmission.Moreover,our results show that relieving personal protection too early may lead to a prolonged disease transmission period and more people would be infected,and may even cause a second wave of epidemic or outbreaks.By calculating the effective reproduction ratio,we prove that the contact rate should be kept at least less than 30%of the normal level by April,2020.Conclusions To ensure the pandemic ending rapidly,it is necessary to maintain the current integrated restrict interventions and self-protection measures,including travel restriction,quarantine of entry,contact tracing followed by quarantine and isolation and reduction of contact,like wearing masks,keeping social distance,etc.People should be fully aware of the real-time epidemic situation and keep sufficient personal protection until April.If all the above conditions are met,the outbreak is expected to be ended by April in the mainland of China apart from Hubei province.

Global Stability of a Mumps Transmission Model with Quarantine Measure

In this paper,a model of mumps transmission with quarantine measure is proposed and then the control reproduction number Rc of the model is obtained.This model admits a unique endemic equilibrium P*if and only if Rc>1,while the disease-free equilibrium P0 always exists.By using the technique of constructing Lyapunov functions and the generalized Lyapunov-LaSalle theorem,we first show that the equilibrium P0 is globally asymptotically stable(GAS)if Rc≤1;second,we prove that the equilibrium P*is GAS if Rc>1.Our results reveal that mumps can be eliminated from the community for Rc≤1 and it will be persistent for Rc>1,and quarantine measure can also effectively control the mumps transmission.

Recursive Zero-COVID model and quantitation of control efforts of the Omicron epidemic in Jilin province

Since the beginning of March 2022,the epidemic due to the Omicron variant has developed rapidly in Jilin Province.To figure out the key controlling factors and validate the model to show the success of the Zero-COVID policy in the province,we constructed a Recursive Zero-COVID Model quantifying the strength of the control measures,and defined the control reproduction number as an index for describing the intensity of interventions.Parameter estimation and sensitivity analysis were employed to estimate and validate the impact of changes in the strength of different measures on the intensity of public health preventions qualitatively and quantitatively.The recursive Zero-COVID model predicted that the dates of elimination of cases at the community level of Changchun and Jilin Cities to be on April 8 and April 17,respectively,which are consistent with the real situation.Our results showed that the strict implementation of control measures and adherence of the public are crucial for controlling the epidemic.It is also essential to strengthen the control intensity even at the final stage to avoid the rebound of the epidemic.In addition,the control reproduction number we defined in the paper is a novel index to measure the intensity of the prevention and control measures of public health.

Meta-population model about immigrants and natives with heterogeneity mixing and vaccine strategy of tuberculosis in China

China is one of the countries in the world carrying a heavy burden of tuberculosis.Due to the unbalanced economic development,the number of people working in other parts of country is huge,and the mobility of personnel has exacerbated the increase in tuberculosis cases.Most patients affected by this are in their middle and young ages.It is having a great impact among the family and society.Therefore,research on how to control this disease is absolutely necessary.The population is divided into two categories such as local population and the immigrant population.A pulmonary tuberculosis dynamic model with population heterogeneity is established.We calculate the basic reproductive number and the controlled reproductive number,and discuss the two types of population under the constraints given by the amount of vaccine and the optimal immunization ratio obtained is(0.118,0.107),which can reduce the effective reproduction number from 5.85 to 0.227.It is understood that immunizing the local population will control the spread of the epidemic to a large extent,and we simulate the final scale of infection after immunization under the optimal immunization ratio.It can take a minimum of at least 10 years to reduce the spread of this disease,but to eliminate it forever,it needs at least a minimum of 100 years.