There are many cases within epidemiology where infections compete to persist within a population.In studying models for such cases,one of the goals is to determine which infections can invade a population and persist ...There are many cases within epidemiology where infections compete to persist within a population.In studying models for such cases,one of the goals is to determine which infections can invade a population and persist when other infections are already resident within the population.Invasion reproductive numbers(IRN),which are tied to the stability of boundary endemic equilibria,can address this question.By reinterpreting resident infections epidemiologically,this study extends methods for finding IRNs to periodic systems,and presents some examples which illustrate the often complex computations required.Results identify conditions under which a simple time-average can be used to derive IRNs,and apply the methods to examine how seasonal fluctuations in influenza incidence facilitate the year-round persistence of bacterial respiratory infections.展开更多
Although invasion reproductive numbers(IRNs)are utilized frequently in continuous-time models with multiple interacting pathogens,they are yet to be explored in discrete-time systems.Here,we extend the concept of IRNs...Although invasion reproductive numbers(IRNs)are utilized frequently in continuous-time models with multiple interacting pathogens,they are yet to be explored in discrete-time systems.Here,we extend the concept of IRNs to discrete-time models by showing how to calculate them for a set of two-pathogen SIS models with coinfection.In our exploration,we address how sequencing events impacts the basic reproductive number(BRN)and IRN.As an illustrative example,our models are applied to rhinovirus and respiratory syncytial virus co-circulation.Results show that while the BRN is unaffected by variations in the order of events,the IRN differs.Furthermore,our models predict copersistence of multiple pathogen strains under cross-immunity,which is atypical of analogous continuous-time models.This investigation shows that sequencing events has important consequences for the IRN and can drastically alter competition dynamics.展开更多
Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual ...Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual CMJ processes. We discuss also some properties of the extinction probability and the generating operator of general branching processes. As an application in epidemics, in the final section we suggest a generalization of SIR model which can describe infectious diseases transmission in an inhomogeneous population.展开更多
We have proposed a new mathematical method,the SEIHCRD model,which has an excellent potential to predict the incidence of COVID-19 diseases.Our proposed SEIHCRD model is an extension of the SEIR model.Three-compartmen...We have proposed a new mathematical method,the SEIHCRD model,which has an excellent potential to predict the incidence of COVID-19 diseases.Our proposed SEIHCRD model is an extension of the SEIR model.Three-compartments have added death,hospitalized,and critical,which improves the basic understanding of disease spread and results.We have studiedCOVID-19 cases of six countries,where the impact of this disease in the highest are Brazil,India,Italy,Spain,the United Kingdom,and the United States.After estimating model parameters based on available clinical data,the modelwill propagate and forecast dynamic evolution.Themodel calculates the Basic reproduction number over time using logistic regression and the Case fatality rate based on the selected countries’age-category scenario.Themodel calculates two types of Case fatality rate one is CFR daily,and the other is total CFR.The proposed model estimates the approximate time when the disease is at its peak and the approximate time when death cases rarely occur and calculate how much hospital beds and ICU beds will be needed in the peak days of infection.The SEIHCRD model outperforms the classic ARXmodel and the ARIMA model.RMSE,MAPE,andRsquaredmatrices are used to evaluate results and are graphically represented using Taylor and Target diagrams.The result shows RMSE has improved by 56%–74%,and MAPE has a 53%–89%improvement in prediction accuracy.展开更多
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...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.展开更多
The classical Kermack-McKendrick homogeneous SIR （susceptible, infected and removed） model is well known, Its general solution is a function of the unique parameter （the reproduction number） that is equal to a mea...The classical Kermack-McKendrick homogeneous SIR （susceptible, infected and removed） model is well known, Its general solution is a function of the unique parameter （the reproduction number） that is equal to a mean number of secondary cases produced by a typical infected individual in a completely susceptible population. If the reproduction number is more than one （the threshold value） its value describes an epidemic scope： larger values correspond to more severe epidemics. In the more complex compartment SIR models the population is divided into several non-overlapping groups. It allows us to partly remove assumptions of the classical model. It is well known that for this kind of models, just as for the classical model there is the threshold parameter R0. Usually it is called by the same name--the reproduction number--though the physical meaning of this parameter has changed. The main purpose of the paper is to show that this new parameter is a not unique measure of an epidemic severity for any compartment SIR model. In particular it means that for such models comparison of the severity of two epidemics by simple comparing values of their reproduction numbers is incorrect. For compartment models these statements were proved with the help of the corresponding ODEs analysis. Very popular now individual-based models （IBMs） are more complex in comparison with the compartment ones since they use overlapping groups （school children are members of families also, for example）. In such a case Diekmann＇s calculation method for the reproduction number used in many papers is inapplicable as well as a presentation the simulation results obtained as functions of this parameter.展开更多
In this paper,we establish an ShIhAhSvIvW model to investigate the impact of media communication on the transmission mechanism of dengue fever.Firstly,the basic reproduction number R0of the model is obtained by using ...In this paper,we establish an ShIhAhSvIvW model to investigate the impact of media communication on the transmission mechanism of dengue fever.Firstly,the basic reproduction number R0of the model is obtained by using the method of the next generation matrix.It shows that disease-free equilibrium is globally asymptotically stable when R0<1;the disease is uniformly persistent when R_(0)>1.Secondly,we select dengue fever case data from Guangdong Province from 2006 to 2019 for numerical simulations and predict its development trend.Finally,we conduct parameter sensitivity analysis,and the results show that increasing media publicity can to some extent reduce the number of patients.展开更多
Streptococcus suis(S.suis)is a major disease impacting pig farming globally.It can also be transferred to humans by eating raw pork.A comprehensive study was recently carried out to determine the indices throughmultip...Streptococcus suis(S.suis)is a major disease impacting pig farming globally.It can also be transferred to humans by eating raw pork.A comprehensive study was recently carried out to determine the indices throughmultiple geographic regions in China.Methods:The well-posed theorems were employed to conduct a thorough analysis of the model’s feasible features,including positivity,boundedness equilibria,reproduction number,and parameter sensitivity.Stochastic Euler,Runge Kutta,and EulerMaruyama are some of the numerical techniques used to replicate the behavior of the streptococcus suis infection in the pig population.However,the dynamic qualities of the suggested model cannot be restored using these techniques.Results:For the stochastic delay differential equations of the model,the non-standard finite difference approach in the sense of stochasticity is developed to avoid several problems such as negativity,unboundedness,inconsistency,and instability of the findings.Results from traditional stochastic methods either converge conditionally or diverge over time.The stochastic non-negative step size convergence nonstandard finite difference(NSFD)method unconditionally converges to the model’s true states.Conclusions:This study improves our understanding of the dynamics of streptococcus suis infection using versions of stochastic with delay approaches and opens up new avenues for the study of cognitive processes and neuronal analysis.Theplotted interaction behaviour and new solution comparison profiles.展开更多
In this paper,we study the epidemic model of respiratory syncytial virus SIRS with age structure.Firstly,the basic reproduction number R_(0) of the model is calculated and the positivity and ultimate boundedness of th...In this paper,we study the epidemic model of respiratory syncytial virus SIRS with age structure.Firstly,the basic reproduction number R_(0) of the model is calculated and the positivity and ultimate boundedness of the solution to the model under initial conditions are proven.Secondly,it is proven that when R_(0)<1,the disease-free equilibrium is locally and globally asymptotically stable;and when R_(0)>1,the disease is uniformly persistent and there is at least a positive equilibrium.Finally,the effectiveness of the theoretical results is demonstrated by numerical simulation,and the impact of vaccination on disease transmission is predicted.展开更多
Livestock transportation is a key factor that contributes to the spatial spread of brucellosis.To analyze the impact of sheep transportation on brucellosis transmission,we develop a human–sheep coupled brucellosis mo...Livestock transportation is a key factor that contributes to the spatial spread of brucellosis.To analyze the impact of sheep transportation on brucellosis transmission,we develop a human–sheep coupled brucellosis model within a metapopulation network framework.Theoretically,we examine the positively invariant set,the basic reproduction number,the existence,uniqueness,and stability of disease-free equilibrium and the existence of the endemic equilibrium of the model.For practical application,using Heilongjiang province as a case study,we simulate brucellosis transmission across 12 cities based on data using three network types:the BA network,the ER network,and homogeneous mixing network.The simulation results indicate that the network's average degree plays a role in the spread of brucellosis.For BA and ER networks,the basic reproduction number and cumulative incidence of brucellosis stabilize when the network's average degree reaches 4 or 5.In contrast,sheep transport in a homogeneous mixing network accelerates the cross-regional spread of brucellosis,whereas transportation in a BA network helps to control it effectively.Furthermore,the findings suggest that the movement of sheep is not always detrimental to controlling the spread of brucellosis.For cities with smaller sheep populations,such as Shuangyashan and Qitaihe,increasing the transport of sheep outward amplifies the spatial spread of the disease.In contrast,in cities with larger sheep populations,such as Qiqihar,Daqing,and Suihua,moderate sheep outflow can help reduce the spread.In addition,cities with large livestock populations play a dominant role in the overall transmission dynamics,underscoring the need for stricter supervision in these areas.展开更多
In this paper, the existence of periodic solutions for a time dependent age-structured population model is studied. The averaged net reproductive number is introduced as the main parameter to determine the dynamical b...In this paper, the existence of periodic solutions for a time dependent age-structured population model is studied. The averaged net reproductive number is introduced as the main parameter to determine the dynamical behaviors of the model. The existence of a global parameterized branch of periodic solutions of the model is obtained by using the contracting mapping theorem in a periodic and continuous function space. The global stability of the trivial equilibrium is studied and a very practical stability criteria for the model is obtained. The dynamics of the linear time-periodic model is similar to that of the linear model.展开更多
Cases of COVID-19 and its variant omicron are raised all across the world.The most lethal form and effect of COVID-19 are the omicron version,which has been reported in tens of thousands of cases daily in numerous nat...Cases of COVID-19 and its variant omicron are raised all across the world.The most lethal form and effect of COVID-19 are the omicron version,which has been reported in tens of thousands of cases daily in numerous nations.Following WHO(World health organization)records on 30 December 2021,the cases of COVID-19 were found to be maximum for which boarding individuals were found 1,524,266,active,recovered,and discharge were found to be 82,402 and 34,258,778,respectively.While there were 160,989 active cases,33,614,434 cured cases,456,386 total deaths,and 605,885,769 total samples tested.So far,1,438,322,742 individuals have been vaccinated.The coronavirus or COVID-19 is inciting panic for several reasons.It is a new virus that has affected the whole world.Scientists have introduced certain ways to prevent the virus.One can lower the danger of infection by reducing the contact rate with other persons.Avoiding crowded places and social events withmany people reduces the chance of one being exposed to the virus.The deadly COVID-19 spreads speedily.It is thought that the upcoming waves of this pandemicwill be evenmore dreadful.Mathematicians have presented severalmathematical models to study the pandemic and predict future dangers.The need of the hour is to restrict the mobility to control the infection from spreading.Moreover,separating affected individuals from healthy people is essential to control the infection.We consider the COVID-19 model in which the population is divided into five compartments.The present model presents the population’s diffusion effects on all susceptible,exposed,infected,isolated,and recovered compartments.The reproductive number,which has a key role in the infectious models,is discussed.The equilibrium points and their stability is presented.For numerical simulations,finite difference(FD)schemes like nonstandard finite difference(NSFD),forward in time central in space(FTCS),and Crank Nicolson(CN)schemes are implemented.Some core characteristics of schemes like stability and consistency are calculated.展开更多
COVID-19 acts as a serious challenge to the whole world.Epidemiological data of COVID-19 is collected through media and web sources to analyze and investigate a system of nonlinear ordinary differential equation to un...COVID-19 acts as a serious challenge to the whole world.Epidemiological data of COVID-19 is collected through media and web sources to analyze and investigate a system of nonlinear ordinary differential equation to understand the outbreaks of this epidemic disease.We analyze the diseases free and endemic equilibrium point including stability of the model.The certain threshold value of the basic reproduction number R0 is found to observe whether population is in disease free state or endemic state.Moreover,the epidemic peak has been obtained and we expect a considerable number of cases.Finally,some numerical results are presented which show the effect of parameters estimation and different step size on our obtained solutions at the real data of some countries to check the actual behavior of the COVID-19 at different countries.展开更多
Recently,the world is facing the terror of the novel corona-virus,termed as COVID-19.Various health institutes and researchers are continuously striving to control this pandemic.In this article,the SEIAR(susceptible,e...Recently,the world is facing the terror of the novel corona-virus,termed as COVID-19.Various health institutes and researchers are continuously striving to control this pandemic.In this article,the SEIAR(susceptible,exposed,infected,symptomatically infected,asymptomatically infected and recovered)infection model of COVID-19 with a constant rate of advection is studied for the disease propagation.A simple model of the disease is extended to an advection model by accommodating the advection process and some appropriate parameters in the system.The continuous model is transposed into a discrete numerical model by discretizing the domains,finitely.To analyze the disease dynamics,a structure preserving non-standard finite difference scheme is designed.Two steady states of the continuous system are described i.e.,virus free steady state and virus existing steady state.Graphical results show that both the steady states of the numerical design coincide with the fixed points of the continuous SEIAR model.Positivity of the state variables is ensured by applying the M-matrix theory.A result for the positivity property is established.For the proposed numerical design,two different types of the stability are investigated.Nonlinear stability and linear stability for the projected scheme is examined by applying some standard results.Von Neuman stability test is applied to ensure linear stability.The reproductive number is described and its pivotal role in stability analysis is also discussed.Consistency and convergence of the numerical model is also studied.Numerical graphs are presented via computer simulations to prove the worth and efficiency of the quarantine factor is explored graphically,which is helpful in controlling the disease dynamics.In the end,the conclusion of the study is also rendered.展开更多
In this article, we consider the construction of a SVIR (Susceptible, Vaccinated, Infected, Recovered) stochastic compartmental model of measles. We prove that the deterministic solution is asymptotically the average ...In this article, we consider the construction of a SVIR (Susceptible, Vaccinated, Infected, Recovered) stochastic compartmental model of measles. We prove that the deterministic solution is asymptotically the average of the stochastic solution in the case of small population size. The choice of this model takes into account the random fluctuations inherent to the epidemiological characteristics of rural populations of Niger, notably a high prevalence of measles in children under 5, coupled with a very low immunization coverage.展开更多
Listeriosis is an illness caused by the germ<span style="font-family:Verdana;"> Listeria monocytogenes<span style="font-family:Verdana;">. Generally, humans are infected with listeriosi...Listeriosis is an illness caused by the germ<span style="font-family:Verdana;"> Listeria monocytogenes<span style="font-family:Verdana;">. Generally, humans are infected with listeriosis after eating contaminated food. Listeriosis mostly affects people with weakened immune systems, pregnant women and newborns. In this paper, a model describing the dynamics o<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">f Listeriosis is developed and analysed using ordinary differential equations. The model was analysed both quantitatively and qualitatively for its local and global stability, basic reproductive number and parameter contributions to the basic reproductive number to understand the impact of each parameter on the disease spread. The Listeriosis model has been extended to include time dependent control variables such as treatment of both humans and animals, vaccination and education of humans. Pontryagin<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">’<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">s Maximum Principle was introduced to obtain the best optimal control strategies required for curbing Listeriosis infections. Numerical simulation was performed and the results displayed graphically and discussed. Cost effectiveness analysis was conducted using the intervention averted ratio (IAR) concepts and it was revealed that the most effective intervention strategy is the treatment of infect<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">ed<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> humans and animals.展开更多
This paper investigates the stability and bifurcation phenomena of a cholera transmission model in which individuals who have recovered from the disease may become susceptible again.The threshold for determining disea...This paper investigates the stability and bifurcation phenomena of a cholera transmission model in which individuals who have recovered from the disease may become susceptible again.The threshold for determining disease prevalence is established,and the parameter conditions for the existence of equilibria are discussed.The Routh-Hurwitz criterion is applied to demonstrate the local asymptotic stability of equilibria.By utilizing composite matrices and geometric techniques,the global dynamic behavior of the endemic equilibrium is investigated,and the sufficient conditions for its global asymptotic stability are derived.Furthermore,the disease-free equilibrium is a saddle-node when the basic reproductive number is 1,and tthe transcritical bifurcation in this case is discussed.展开更多
Wastewater surveillance(WWS)can leverage its wide coverage,population-based sampling,and high monitoring frequency to capture citywide pandemic trends independent of clinical surveillance.Here we conducted a nine mont...Wastewater surveillance(WWS)can leverage its wide coverage,population-based sampling,and high monitoring frequency to capture citywide pandemic trends independent of clinical surveillance.Here we conducted a nine months daily WWS for severe acute respiratory syndrome coronavirus 2(SARSCoV-2)from 12 wastewater treatment plants(WWTPs),covering approximately 80%of the population,to monitor infection dynamics in Hong Kong,China.We found that the SARS-CoV-2 virus concentration in wastewater was correlated with the daily number of reported cases and reached two pandemic peaks three days earlier during the study period.In addition,two different methods were established to estimate the prevalence/incidence rates from wastewater measurements.The estimated results from wastewater were consistent with findings from two independent citywide clinical surveillance programmes(rapid antigen test(RAT)surveillance and serology surveillance),but higher than the cases number reported by the Centre for Health Protection(CHP)of Hong Kong,China.Moreover,the effective reproductive number(R_(t))was estimated from wastewater measurements to reflect both citywide and regional transmission dynamics.Our findings demonstrate that large-scale intensive WWS from WWTPs provides cost-effective and timely public health information,especially when the clinical surveillance is inadequate and costly.This approach also provides insights into pandemic dynamics at higher spatiotemporal resolutions,facilitating the formulation of effective control policies and targeted resource allocation.展开更多
This paper studied a structured model by age of tuberculosis. A population divided into two parts was considered for the study. Each subpopulation is submitted to a program of vaccination. It was allowed the migration...This paper studied a structured model by age of tuberculosis. A population divided into two parts was considered for the study. Each subpopulation is submitted to a program of vaccination. It was allowed the migration of vaccinated people only between the two patches. After the determination of and , the local and global stability of the disease-free equilibrium was studied. It showed the existence of three endemic equilibrium points. The theoretical results were illustrated by a numeric simulation.展开更多
A simulation model based on nonlinear ordinary differential equations to interpret the transmission dynamics of Zika Virus (ZIKV), is formulated and analyzed, integrating the asymptomatic human population and coupled ...A simulation model based on nonlinear ordinary differential equations to interpret the transmission dynamics of Zika Virus (ZIKV), is formulated and analyzed, integrating the asymptomatic human population and coupled to the Aedes aegypti dynamics, the epidemic threshold Basic Reproduction Number R0 is determined, as the spectral radius of Next-Generation Matrix and the system is simulated with MAPLE computing program taking the parameter values from literature.展开更多
文摘There are many cases within epidemiology where infections compete to persist within a population.In studying models for such cases,one of the goals is to determine which infections can invade a population and persist when other infections are already resident within the population.Invasion reproductive numbers(IRN),which are tied to the stability of boundary endemic equilibria,can address this question.By reinterpreting resident infections epidemiologically,this study extends methods for finding IRNs to periodic systems,and presents some examples which illustrate the often complex computations required.Results identify conditions under which a simple time-average can be used to derive IRNs,and apply the methods to examine how seasonal fluctuations in influenza incidence facilitate the year-round persistence of bacterial respiratory infections.
文摘Although invasion reproductive numbers(IRNs)are utilized frequently in continuous-time models with multiple interacting pathogens,they are yet to be explored in discrete-time systems.Here,we extend the concept of IRNs to discrete-time models by showing how to calculate them for a set of two-pathogen SIS models with coinfection.In our exploration,we address how sequencing events impacts the basic reproductive number(BRN)and IRN.As an illustrative example,our models are applied to rhinovirus and respiratory syncytial virus co-circulation.Results show that while the BRN is unaffected by variations in the order of events,the IRN differs.Furthermore,our models predict copersistence of multiple pathogen strains under cross-immunity,which is atypical of analogous continuous-time models.This investigation shows that sequencing events has important consequences for the IRN and can drastically alter competition dynamics.
文摘Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual CMJ processes. We discuss also some properties of the extinction probability and the generating operator of general branching processes. As an application in epidemics, in the final section we suggest a generalization of SIR model which can describe infectious diseases transmission in an inhomogeneous population.
基金The work has been supported by a grant received from the Ministry of Education,Government of India under the Scheme for the Promotion of Academic and Research Collaboration(SPARC)(ID:SPARC/2019/1396).
文摘We have proposed a new mathematical method,the SEIHCRD model,which has an excellent potential to predict the incidence of COVID-19 diseases.Our proposed SEIHCRD model is an extension of the SEIR model.Three-compartments have added death,hospitalized,and critical,which improves the basic understanding of disease spread and results.We have studiedCOVID-19 cases of six countries,where the impact of this disease in the highest are Brazil,India,Italy,Spain,the United Kingdom,and the United States.After estimating model parameters based on available clinical data,the modelwill propagate and forecast dynamic evolution.Themodel calculates the Basic reproduction number over time using logistic regression and the Case fatality rate based on the selected countries’age-category scenario.Themodel calculates two types of Case fatality rate one is CFR daily,and the other is total CFR.The proposed model estimates the approximate time when the disease is at its peak and the approximate time when death cases rarely occur and calculate how much hospital beds and ICU beds will be needed in the peak days of infection.The SEIHCRD model outperforms the classic ARXmodel and the ARIMA model.RMSE,MAPE,andRsquaredmatrices are used to evaluate results and are graphically represented using Taylor and Target diagrams.The result shows RMSE has improved by 56%–74%,and MAPE has a 53%–89%improvement in prediction accuracy.
基金Supported by the Fundamental Research Funds for the Central Universities,CHD(300102129201)the Nat ural Science Basic Research Plan in Shaanxi Province of China(2018JM1011)the National Natural Science Foundation of China(11701041)。
文摘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.
基金Acknowledgements This work was assisted through participation in ＂Optimal Control and Optimization for Individual- based and Agent-based Models＂ Investigative Workshop at the National Institute for Mathematical and Biological Synthesis, sponsored by the National Science Foundation, the U.S. Department of Homeland Security, and the U.S. Department of Agriculture through NSF Award #EF-0832858, with additional support from The University of Tennessee, Knoxville.
文摘The classical Kermack-McKendrick homogeneous SIR （susceptible, infected and removed） model is well known, Its general solution is a function of the unique parameter （the reproduction number） that is equal to a mean number of secondary cases produced by a typical infected individual in a completely susceptible population. If the reproduction number is more than one （the threshold value） its value describes an epidemic scope： larger values correspond to more severe epidemics. In the more complex compartment SIR models the population is divided into several non-overlapping groups. It allows us to partly remove assumptions of the classical model. It is well known that for this kind of models, just as for the classical model there is the threshold parameter R0. Usually it is called by the same name--the reproduction number--though the physical meaning of this parameter has changed. The main purpose of the paper is to show that this new parameter is a not unique measure of an epidemic severity for any compartment SIR model. In particular it means that for such models comparison of the severity of two epidemics by simple comparing values of their reproduction numbers is incorrect. For compartment models these statements were proved with the help of the corresponding ODEs analysis. Very popular now individual-based models （IBMs） are more complex in comparison with the compartment ones since they use overlapping groups （school children are members of families also, for example）. In such a case Diekmann＇s calculation method for the reproduction number used in many papers is inapplicable as well as a presentation the simulation results obtained as functions of this parameter.
基金Supported by the Natural Science Basic Research Plan in Shaanxi Province of China(2022JM-023)。
文摘In this paper,we establish an ShIhAhSvIvW model to investigate the impact of media communication on the transmission mechanism of dengue fever.Firstly,the basic reproduction number R0of the model is obtained by using the method of the next generation matrix.It shows that disease-free equilibrium is globally asymptotically stable when R0<1;the disease is uniformly persistent when R_(0)>1.Secondly,we select dengue fever case data from Guangdong Province from 2006 to 2019 for numerical simulations and predict its development trend.Finally,we conduct parameter sensitivity analysis,and the results show that increasing media publicity can to some extent reduce the number of patients.
基金supported by the Deanship of Scientific Research,Vice Presidency for Graduate Studies and Scientific Research,King Faisal University,Saudi Arabia[KFU250259].
文摘Streptococcus suis(S.suis)is a major disease impacting pig farming globally.It can also be transferred to humans by eating raw pork.A comprehensive study was recently carried out to determine the indices throughmultiple geographic regions in China.Methods:The well-posed theorems were employed to conduct a thorough analysis of the model’s feasible features,including positivity,boundedness equilibria,reproduction number,and parameter sensitivity.Stochastic Euler,Runge Kutta,and EulerMaruyama are some of the numerical techniques used to replicate the behavior of the streptococcus suis infection in the pig population.However,the dynamic qualities of the suggested model cannot be restored using these techniques.Results:For the stochastic delay differential equations of the model,the non-standard finite difference approach in the sense of stochasticity is developed to avoid several problems such as negativity,unboundedness,inconsistency,and instability of the findings.Results from traditional stochastic methods either converge conditionally or diverge over time.The stochastic non-negative step size convergence nonstandard finite difference(NSFD)method unconditionally converges to the model’s true states.Conclusions:This study improves our understanding of the dynamics of streptococcus suis infection using versions of stochastic with delay approaches and opens up new avenues for the study of cognitive processes and neuronal analysis.Theplotted interaction behaviour and new solution comparison profiles.
基金supported by the Natural Science Foundation of Xinjiang(No.2022D01E41)the National Natural Science Foundation of China(No.12261087)the Open Project of Key Laboratory of Applied Mathematics of Xinjiang Autonomous Region(No.2021D04014)。
文摘In this paper,we study the epidemic model of respiratory syncytial virus SIRS with age structure.Firstly,the basic reproduction number R_(0) of the model is calculated and the positivity and ultimate boundedness of the solution to the model under initial conditions are proven.Secondly,it is proven that when R_(0)<1,the disease-free equilibrium is locally and globally asymptotically stable;and when R_(0)>1,the disease is uniformly persistent and there is at least a positive equilibrium.Finally,the effectiveness of the theoretical results is demonstrated by numerical simulation,and the impact of vaccination on disease transmission is predicted.
基金Project supported by the National Natural Science Foundation of China(Grant No.12101443,12371493)the Natural Science Foundation of Shanxi Province(Grant Nos.20210302124260 and 202303021221024)。
文摘Livestock transportation is a key factor that contributes to the spatial spread of brucellosis.To analyze the impact of sheep transportation on brucellosis transmission,we develop a human–sheep coupled brucellosis model within a metapopulation network framework.Theoretically,we examine the positively invariant set,the basic reproduction number,the existence,uniqueness,and stability of disease-free equilibrium and the existence of the endemic equilibrium of the model.For practical application,using Heilongjiang province as a case study,we simulate brucellosis transmission across 12 cities based on data using three network types:the BA network,the ER network,and homogeneous mixing network.The simulation results indicate that the network's average degree plays a role in the spread of brucellosis.For BA and ER networks,the basic reproduction number and cumulative incidence of brucellosis stabilize when the network's average degree reaches 4 or 5.In contrast,sheep transport in a homogeneous mixing network accelerates the cross-regional spread of brucellosis,whereas transportation in a BA network helps to control it effectively.Furthermore,the findings suggest that the movement of sheep is not always detrimental to controlling the spread of brucellosis.For cities with smaller sheep populations,such as Shuangyashan and Qitaihe,increasing the transport of sheep outward amplifies the spatial spread of the disease.In contrast,in cities with larger sheep populations,such as Qiqihar,Daqing,and Suihua,moderate sheep outflow can help reduce the spread.In addition,cities with large livestock populations play a dominant role in the overall transmission dynamics,underscoring the need for stricter supervision in these areas.
文摘In this paper, the existence of periodic solutions for a time dependent age-structured population model is studied. The averaged net reproductive number is introduced as the main parameter to determine the dynamical behaviors of the model. The existence of a global parameterized branch of periodic solutions of the model is obtained by using the contracting mapping theorem in a periodic and continuous function space. The global stability of the trivial equilibrium is studied and a very practical stability criteria for the model is obtained. The dynamics of the linear time-periodic model is similar to that of the linear model.
基金supported by the research grants Seed ProjectPrince Sultan UniversitySaudi Arabia SEED-2022-CHS-100.
文摘Cases of COVID-19 and its variant omicron are raised all across the world.The most lethal form and effect of COVID-19 are the omicron version,which has been reported in tens of thousands of cases daily in numerous nations.Following WHO(World health organization)records on 30 December 2021,the cases of COVID-19 were found to be maximum for which boarding individuals were found 1,524,266,active,recovered,and discharge were found to be 82,402 and 34,258,778,respectively.While there were 160,989 active cases,33,614,434 cured cases,456,386 total deaths,and 605,885,769 total samples tested.So far,1,438,322,742 individuals have been vaccinated.The coronavirus or COVID-19 is inciting panic for several reasons.It is a new virus that has affected the whole world.Scientists have introduced certain ways to prevent the virus.One can lower the danger of infection by reducing the contact rate with other persons.Avoiding crowded places and social events withmany people reduces the chance of one being exposed to the virus.The deadly COVID-19 spreads speedily.It is thought that the upcoming waves of this pandemicwill be evenmore dreadful.Mathematicians have presented severalmathematical models to study the pandemic and predict future dangers.The need of the hour is to restrict the mobility to control the infection from spreading.Moreover,separating affected individuals from healthy people is essential to control the infection.We consider the COVID-19 model in which the population is divided into five compartments.The present model presents the population’s diffusion effects on all susceptible,exposed,infected,isolated,and recovered compartments.The reproductive number,which has a key role in the infectious models,is discussed.The equilibrium points and their stability is presented.For numerical simulations,finite difference(FD)schemes like nonstandard finite difference(NSFD),forward in time central in space(FTCS),and Crank Nicolson(CN)schemes are implemented.Some core characteristics of schemes like stability and consistency are calculated.
文摘COVID-19 acts as a serious challenge to the whole world.Epidemiological data of COVID-19 is collected through media and web sources to analyze and investigate a system of nonlinear ordinary differential equation to understand the outbreaks of this epidemic disease.We analyze the diseases free and endemic equilibrium point including stability of the model.The certain threshold value of the basic reproduction number R0 is found to observe whether population is in disease free state or endemic state.Moreover,the epidemic peak has been obtained and we expect a considerable number of cases.Finally,some numerical results are presented which show the effect of parameters estimation and different step size on our obtained solutions at the real data of some countries to check the actual behavior of the COVID-19 at different countries.
文摘Recently,the world is facing the terror of the novel corona-virus,termed as COVID-19.Various health institutes and researchers are continuously striving to control this pandemic.In this article,the SEIAR(susceptible,exposed,infected,symptomatically infected,asymptomatically infected and recovered)infection model of COVID-19 with a constant rate of advection is studied for the disease propagation.A simple model of the disease is extended to an advection model by accommodating the advection process and some appropriate parameters in the system.The continuous model is transposed into a discrete numerical model by discretizing the domains,finitely.To analyze the disease dynamics,a structure preserving non-standard finite difference scheme is designed.Two steady states of the continuous system are described i.e.,virus free steady state and virus existing steady state.Graphical results show that both the steady states of the numerical design coincide with the fixed points of the continuous SEIAR model.Positivity of the state variables is ensured by applying the M-matrix theory.A result for the positivity property is established.For the proposed numerical design,two different types of the stability are investigated.Nonlinear stability and linear stability for the projected scheme is examined by applying some standard results.Von Neuman stability test is applied to ensure linear stability.The reproductive number is described and its pivotal role in stability analysis is also discussed.Consistency and convergence of the numerical model is also studied.Numerical graphs are presented via computer simulations to prove the worth and efficiency of the quarantine factor is explored graphically,which is helpful in controlling the disease dynamics.In the end,the conclusion of the study is also rendered.
文摘In this article, we consider the construction of a SVIR (Susceptible, Vaccinated, Infected, Recovered) stochastic compartmental model of measles. We prove that the deterministic solution is asymptotically the average of the stochastic solution in the case of small population size. The choice of this model takes into account the random fluctuations inherent to the epidemiological characteristics of rural populations of Niger, notably a high prevalence of measles in children under 5, coupled with a very low immunization coverage.
文摘Listeriosis is an illness caused by the germ<span style="font-family:Verdana;"> Listeria monocytogenes<span style="font-family:Verdana;">. Generally, humans are infected with listeriosis after eating contaminated food. Listeriosis mostly affects people with weakened immune systems, pregnant women and newborns. In this paper, a model describing the dynamics o<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">f Listeriosis is developed and analysed using ordinary differential equations. The model was analysed both quantitatively and qualitatively for its local and global stability, basic reproductive number and parameter contributions to the basic reproductive number to understand the impact of each parameter on the disease spread. The Listeriosis model has been extended to include time dependent control variables such as treatment of both humans and animals, vaccination and education of humans. Pontryagin<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">’<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">s Maximum Principle was introduced to obtain the best optimal control strategies required for curbing Listeriosis infections. Numerical simulation was performed and the results displayed graphically and discussed. Cost effectiveness analysis was conducted using the intervention averted ratio (IAR) concepts and it was revealed that the most effective intervention strategy is the treatment of infect<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">ed<span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> humans and animals.
基金supported by the National Natural Science Foundation of China(No.12171337)the Central Government Guided Local Science and Technology Development Projects(No.2024ZYD0059)+1 种基金the Natural Science Foundation of Sichuan Province(No.2022NSFSC0529)the Open Research Fund Program of Data Recovery Key Laboratory of Sichuan Province(No.DRN2405)。
文摘This paper investigates the stability and bifurcation phenomena of a cholera transmission model in which individuals who have recovered from the disease may become susceptible again.The threshold for determining disease prevalence is established,and the parameter conditions for the existence of equilibria are discussed.The Routh-Hurwitz criterion is applied to demonstrate the local asymptotic stability of equilibria.By utilizing composite matrices and geometric techniques,the global dynamic behavior of the endemic equilibrium is investigated,and the sufficient conditions for its global asymptotic stability are derived.Furthermore,the disease-free equilibrium is a saddle-node when the basic reproductive number is 1,and tthe transcritical bifurcation in this case is discussed.
基金financially supported by the Health and Medical Research Fund(COVID1903015)the Food and Health Bureau,the Government of the Hong Kong Special Administrative Region(SAR),China+1 种基金supported by the AIR@InnoHK(KL,GML,and JTW)Health@InnoHK(MP and LLMP)administered by the Innovation and Technology Commission of the Government of the Hong Kong SAR.
文摘Wastewater surveillance(WWS)can leverage its wide coverage,population-based sampling,and high monitoring frequency to capture citywide pandemic trends independent of clinical surveillance.Here we conducted a nine months daily WWS for severe acute respiratory syndrome coronavirus 2(SARSCoV-2)from 12 wastewater treatment plants(WWTPs),covering approximately 80%of the population,to monitor infection dynamics in Hong Kong,China.We found that the SARS-CoV-2 virus concentration in wastewater was correlated with the daily number of reported cases and reached two pandemic peaks three days earlier during the study period.In addition,two different methods were established to estimate the prevalence/incidence rates from wastewater measurements.The estimated results from wastewater were consistent with findings from two independent citywide clinical surveillance programmes(rapid antigen test(RAT)surveillance and serology surveillance),but higher than the cases number reported by the Centre for Health Protection(CHP)of Hong Kong,China.Moreover,the effective reproductive number(R_(t))was estimated from wastewater measurements to reflect both citywide and regional transmission dynamics.Our findings demonstrate that large-scale intensive WWS from WWTPs provides cost-effective and timely public health information,especially when the clinical surveillance is inadequate and costly.This approach also provides insights into pandemic dynamics at higher spatiotemporal resolutions,facilitating the formulation of effective control policies and targeted resource allocation.
文摘This paper studied a structured model by age of tuberculosis. A population divided into two parts was considered for the study. Each subpopulation is submitted to a program of vaccination. It was allowed the migration of vaccinated people only between the two patches. After the determination of and , the local and global stability of the disease-free equilibrium was studied. It showed the existence of three endemic equilibrium points. The theoretical results were illustrated by a numeric simulation.
文摘A simulation model based on nonlinear ordinary differential equations to interpret the transmission dynamics of Zika Virus (ZIKV), is formulated and analyzed, integrating the asymptomatic human population and coupled to the Aedes aegypti dynamics, the epidemic threshold Basic Reproduction Number R0 is determined, as the spectral radius of Next-Generation Matrix and the system is simulated with MAPLE computing program taking the parameter values from literature.
