This paper presents a restricted SIRmathematicalmodel to analyze the evolution of a contagious infectious disease outbreak(COVID-19)using available data.The new model focuses on two main concepts:first,it can present ...This paper presents a restricted SIRmathematicalmodel to analyze the evolution of a contagious infectious disease outbreak(COVID-19)using available data.The new model focuses on two main concepts:first,it can present multiple waves of the disease,and second,it analyzes how far an infection can be eradicated with the help of vaccination.The stability analysis of the equilibrium points for the suggested model is initially investigated by identifying the matching equilibrium points and examining their stability.The basic reproduction number is calculated,and the positivity of the solutions is established.Numerical simulations are performed to determine if it is multipeak and evaluate vaccination’s effects.In addition,the proposed model is compared to the literature already published and the effectiveness of vaccination has been recorded.展开更多
In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive relea...In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive release and general nonlinear incidence rate and investigate dynamical behaviors of the model. Under the reasonable assumptions, the sufficient conditions which guarantee the globally attractive of the disease-free periodic solution and the permanence of the infected fish are established, that is, the infected fish dies out if , whereas the disease persists if . To substantiate our theoretical results, extensive numerical simulations are performed for a hypothetical set of parameter values.展开更多
In this study, the mathematical SIR model (Susceptible-Infected-Recovered (cured and deceased)) was applied to the case of Senegal during the first two waves of the COVID-19 pandemic. During this period, from March 1,...In this study, the mathematical SIR model (Susceptible-Infected-Recovered (cured and deceased)) was applied to the case of Senegal during the first two waves of the COVID-19 pandemic. During this period, from March 1, 2020, to March 30, 2021, the transmission and recovery rates as well as the number of reproduction were calculated and analyzed for the impact of the decisions taken by the Senegalese government. In both waves, the variation of the basic reproduction number as a function of time, with values below one towards the end of each study period, confirms the success of the Senegalese government in controlling the epidemic. The results show that the solution of mandatory mask-wearing is the best decision to counter the spread of the disease. Indeed, the mean number of reproduction is 2.11 in the first wave, and the second wave has a lower mean value of 1.23, while the decisions are less restrictive during this latter wave. Also, a short-term prediction model (about 4 months) was validated on the second wave. The validation criteria of this model reveal a good match between the results of the simulated model and the COVID-19 data reported via the Ministry of Health, Solidarity, and Social Action of Senegal.展开更多
In the context of the COVID-19 sweeping the world,countries around the globe have adopted different approaches to control the spread of disease,and in order to find better control methods,this paper explores the influ...In the context of the COVID-19 sweeping the world,countries around the globe have adopted different approaches to control the spread of disease,and in order to find better control methods,this paper explores the influence of people’s awareness on SIR model.On the basis of the SIR model,this paper studies the SEIR model with the exposure period parameter,calculates the feasible region R-naught disease-free point,and analyzes the method of controlling the spread of the disease according to R-naught,which shows that lockdown has a significant effect on the control of COVID-19.In addition,this paper also established a model affected by disease awareness,adding a factor of news media and religious awareness.The feasible region is calculated,and the reality situation based on India is analyzed.The conclusion proved that people’s awareness has a greater influence on the spread of diseases.展开更多
To effectively track the impact of population migration between regions on the spread of infectious diseases, this paper proposes a visualized analysis and prediction system of infectious diseases based on the improve...To effectively track the impact of population migration between regions on the spread of infectious diseases, this paper proposes a visualized analysis and prediction system of infectious diseases based on the improved SIR model. The research contents including: using the multi graph link interaction mode, visualizing the space-time distribution and development trend of infectious diseases;The LightGBM model is used to track the changes of infection rate and recovery rate, and the Mi/Mo SIR model is constructed according to the initial data of different populations;Mi/Mo SIR model is used to predict infectious diseases in combination with visual panel, providing users with tools to analyze and explain the space-time characteristics and potential laws of infectious diseases. The study found that the closure of cities and the restriction of personnel mobility were necessary and effective, and the system provided an important basis for the prediction and early warning of infectious diseases.展开更多
The use of the SIR model to predict the time evolution of an epidemic is very frequent and has spatial information about its propagation which may be very useful to contrast its spread. In this paper we take a particu...The use of the SIR model to predict the time evolution of an epidemic is very frequent and has spatial information about its propagation which may be very useful to contrast its spread. In this paper we take a particular cellular automaton model that well reproduces the time evolution of the disease given by the SIR model;setting the automaton is generally an annoying problem because we need to run a lot of simulations, compare them to the solution of the SIR model and, finally, decide the parameters to use. In order to make this procedure easier, we will show a fast method that, in input, requires the parameters of the SIR continuous model that we want to reproduce, whereas, in output, it yields the parameters to use in the cellular automaton model. The problem of computing the most suitable parameters for the reticular model is reduced to the problem of finding the roots of a polynomial Equation.展开更多
An SIR model of Zika virus (ZIKV) spread is formulated that includes ZIKV infections to newborns. Analytically, the model has one disease free and one endemic equilibrium point. The free one is stable for some conditi...An SIR model of Zika virus (ZIKV) spread is formulated that includes ZIKV infections to newborns. Analytically, the model has one disease free and one endemic equilibrium point. The free one is stable for some conditions when R0 and unstable when R0>1. In Brazil, when R0≈2>1 ZIKV infections expand and for R0 = 0.875R0) of the model. There are parameters for human-mosquito transmission and some for sexual-transmission factor. It appears that controlling spread of ZIKV infections by human-mosquito transmission may greatly reduce the value of R0.展开更多
In this paper, a delayed SIR model with exponential demographic structure and the saturated incidence rate is formulated. The stability of the equilibria is analyzed with delay: the endemic equilibrium is locally stab...In this paper, a delayed SIR model with exponential demographic structure and the saturated incidence rate is formulated. The stability of the equilibria is analyzed with delay: the endemic equilibrium is locally stable without delay;and the endemic equilibrium is stable if the delay is under some condition. Moreover the dynamical behaviors from stability to instability will change with an appropriate?critical value. At last, some numerical simulations of the model are given to illustrate the main theoretical results.展开更多
This paper presents a new modified SIR model which incorporates appropriate delay parameters leading to a more precise prediction of COVID-19 real time data. The efficacy of the newly developed SIR model is proven by ...This paper presents a new modified SIR model which incorporates appropriate delay parameters leading to a more precise prediction of COVID-19 real time data. The efficacy of the newly developed SIR model is proven by comparing its predictions to real data obtained from four counties namely Germany, Italy, Kuwait, and Oman. Two included delay periods for incubation and recovery within the SIR model produce a sensible and more accurate representation of the real time data. In the absence of the two-delay period (<img src="Edit_8ce6d5c5-9b59-4640-9c0e-334e3948d11c.png" width="67" height="20" alt="" /><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">)</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> the dynamical behavior of the model will not correspond to today’s picture and lag the detection of the epidemic peak. The reproductive number <i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">R</span></i></span></span><span><span><span style="font-family:;" "=""><i><span style="font-family:Verdana;"><sub>0</sub></span></i><span style="font-family:Verdana;"></span></span></span></span></i> <span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">is defined for the model for values of recovery time delay <i></i></span></span></span><i><span style="font-family:Verdana;"><span style="font-family:Verdana;"><i><span style="font-family:Verdana;"><img src="Edit_882b068a-f7fa-478e-9fb9-4d78388010f3.png" width="25" height="20" alt="" /></span></i></span></span></i><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><sub></sub></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> of the infective case. The effect of recovery time <img src="Edit_882b068a-f7fa-478e-9fb9-4d78388010f3.png" width="25" height="20" alt="" /></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">may produce second wave, and/or an oscillation which could destabilize the behavior of the system and a periodic oscillation can arise due to Hopf bifurcation phenomenon.</span></span></span>展开更多
The SIR(D) epidemiological model is defined through a system of transcendental equations, not solvable by elementary functions. In the present paper those equations are successfully replaced by approximate ones, whose...The SIR(D) epidemiological model is defined through a system of transcendental equations, not solvable by elementary functions. In the present paper those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, originating, piece-wisely, from generalized logistic functions: they ensure exact (in the numerical sense) asymptotic values, besides to be quite practical to use, for example with fit to data algorithms;moreover they unveil a useful feature, that in fact, at least with very strict approximation, is also owned by the (numerical) solutions of the exact equations. The novelties in the work are: the way the approximate equations are obtained, using simple, analytic geometry considerations;the easy and practical formulation of the final approximate solutions;the mentioned useful feature, never disclosed before. The work’s method and result prove to be robust over a range of values of the well known non-dimensional parameter called basic reproduction ratio, that covers at least all the known epidemic cases, from influenza to measles: this is a point which doesn’t appear much discussed in analogous works.展开更多
In this paper, we propose random fluctuation on contact and recovery rates in deterministic SIR model with disease deaths in nonparametric manner and derive a new stochastic SIR model with distributed time delay and g...In this paper, we propose random fluctuation on contact and recovery rates in deterministic SIR model with disease deaths in nonparametric manner and derive a new stochastic SIR model with distributed time delay and general diffusion coefficients. By analysis of the introduced model, we obtain the sufficient conditions for the regularity, existence and uniqueness of a global solution by means of Lyapunov function. Moreover, we also investigate the stochastic asymptotic stability of disease free equilibria and endemic equilibria of this model. Finally, we illustrate our general results by applications.展开更多
Calculating analytical approximate solutions for non-linear infectious disease models is a difficult task. Such models often require computational tools to analyse analytical approximate methods which appear in some t...Calculating analytical approximate solutions for non-linear infectious disease models is a difficult task. Such models often require computational tools to analyse analytical approximate methods which appear in some theoretical and practical applications in systems biology. They represent key critical elements and give some approximate solutions for such systems. The SIR epidemic disease model is given as the non-linear system of ODE’s. Then, we use a proper scaling to reduce the number of parameters. We suggest Elzaki transform method to find analytical approximate solutions for the simplified model. The technique plays an important role in calculating the analytical approximate solutions. The local and global dynamics of the model are also studied. An investigation of the behaviour at infinity was conducted via finding the lines and singular points at infinity. Model dynamic results are computed in numerical simulations using Pplane8 and SimBiology Toolbox for Mathlab. Results provide a good step forward for describing the model dynamics. More interestingly, the simplified model could be accurate, robust, and used by biologists for different purposes such as identifying critical model elements.展开更多
This paper handles with a time-space SIR model in two regions which have a common interface.The model is defined as coupled reaction-diffusion system with a robin boundary in interface to predict the immigration betwe...This paper handles with a time-space SIR model in two regions which have a common interface.The model is defined as coupled reaction-diffusion system with a robin boundary in interface to predict the immigration between the two regions.As known,the immigration has an influence on the spread of disease,this is caused by immigrants who could carry the disease from their areas to other places.For this reason,this paper deals with the existence of solutions to SIR model with disease spread between different regions by the Fadeo-Galerkin method and validate this result by the numerical simulations.展开更多
Background:Under-reporting and,thus,uncertainty around the true incidence of health events is common in all public health reporting systems.While the problem of underreporting is acknowledged in epidemiology,the guida...Background:Under-reporting and,thus,uncertainty around the true incidence of health events is common in all public health reporting systems.While the problem of underreporting is acknowledged in epidemiology,the guidance and methods available for assessing and correcting the resulting bias are obscure.Objective:We aim to design a simple modification to the Susceptible e Infected e Removed(SIR)model for estimating the fraction or proportion of reported infection cases.Methods:The suggested modification involves rescaling of the classical SIR model producing its mathematically equivalent version with explicit dependence on the reporting parameter(true proportion of cases reported).We justify the rescaling using the phase plane analysis of the SIR model system and show how this rescaling parameter can be estimated from the data along with the other model parameters.Results:We demonstrate how the proposed method is cross-validated using simulated data with known disease cases and then apply it to two empirical reported data sets to estimate the fraction of reported cases in Missoula County,Montana,USA,using:(1)flu data for 2016e2017 and(2)COVID-19 data for fall of 2020.Conclusions:We establish with the simulated and COVID-19 data that when most of the disease cases are presumed reported,the value of the additional reporting parameter in the modified SIR model is close or equal to one,so that the original SIR model is appropriate for data analysis.Conversely,the flu example shows that when the reporting parameter is close to zero,the original SIR model is not accurately estimating the usual rate parameters,and the re-scaled SIR model should be used.This research demonstrates the role of under-reporting of disease data and the importance of accounting for underreporting when modeling simulated,endemic,and pandemic disease data.Correctly reporting the“true”number of disease cases will have downstream impacts on predictions of disease dynamics.A simple parameter adjustment to the SIR modeling framework can help alleviate bias and uncertainty around crucial epidemiological metrics(e.g.:basic disease reproduction number)and public health decision making.展开更多
BIM(building information modeling,BIM)外包已成为一种有效的BIM应用策略。当前BIM外包应用效果未达预期,BIM外包模式与项目特征不匹配是导致该现象的重要因素,不同形态的BIM外包模式在跨组织边界的信息传递路径及风险传导机制上存在...BIM(building information modeling,BIM)外包已成为一种有效的BIM应用策略。当前BIM外包应用效果未达预期,BIM外包模式与项目特征不匹配是导致该现象的重要因素,不同形态的BIM外包模式在跨组织边界的信息传递路径及风险传导机制上存在显著差异。为明确不同BIM外包模式下信息沟通效率的差异,本文聚焦于2种主要模式:咨询企业主导(以下简称咨询主导)和业主主导的BIM外包模式。以实际案例为基础,构建不同BIM外包模式下的信息沟通网络,分别从静态和动态的视角对不同BIM外包模式中信息沟通的效率进行对比:在静态视角中,应用社会网络分析方法对网络结构进行对比分析,以此明确不同BIM外包模式的信息传递路径;在动态视角中,应用SIR(susceptible-infected-recovered,SIR)模型对错误的传播和扩散进行对比分析,探究不同BIM外包模式的风险传导机制。仿真结果表明,在咨询主导下的BIM外包模式中,BIM决策效率较高,但协同效率较低,信息传递效率也较低;相反,在业主主导下的BIM外包模式中,BIM协同效率较高,信息传递效率也较高。本研究为建筑工程企业在实际工程项目中BIM外包模式的选择提供决策参考和理论支持。展开更多
基金Research Partnership Program no.RP-21-09-06 from the Deanship of Scientific Research of Imam Mohammad Ibn Saud Islamic University(IMSIU).
文摘This paper presents a restricted SIRmathematicalmodel to analyze the evolution of a contagious infectious disease outbreak(COVID-19)using available data.The new model focuses on two main concepts:first,it can present multiple waves of the disease,and second,it analyzes how far an infection can be eradicated with the help of vaccination.The stability analysis of the equilibrium points for the suggested model is initially investigated by identifying the matching equilibrium points and examining their stability.The basic reproduction number is calculated,and the positivity of the solutions is established.Numerical simulations are performed to determine if it is multipeak and evaluate vaccination’s effects.In addition,the proposed model is compared to the literature already published and the effectiveness of vaccination has been recorded.
文摘In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive release and general nonlinear incidence rate and investigate dynamical behaviors of the model. Under the reasonable assumptions, the sufficient conditions which guarantee the globally attractive of the disease-free periodic solution and the permanence of the infected fish are established, that is, the infected fish dies out if , whereas the disease persists if . To substantiate our theoretical results, extensive numerical simulations are performed for a hypothetical set of parameter values.
文摘In this study, the mathematical SIR model (Susceptible-Infected-Recovered (cured and deceased)) was applied to the case of Senegal during the first two waves of the COVID-19 pandemic. During this period, from March 1, 2020, to March 30, 2021, the transmission and recovery rates as well as the number of reproduction were calculated and analyzed for the impact of the decisions taken by the Senegalese government. In both waves, the variation of the basic reproduction number as a function of time, with values below one towards the end of each study period, confirms the success of the Senegalese government in controlling the epidemic. The results show that the solution of mandatory mask-wearing is the best decision to counter the spread of the disease. Indeed, the mean number of reproduction is 2.11 in the first wave, and the second wave has a lower mean value of 1.23, while the decisions are less restrictive during this latter wave. Also, a short-term prediction model (about 4 months) was validated on the second wave. The validation criteria of this model reveal a good match between the results of the simulated model and the COVID-19 data reported via the Ministry of Health, Solidarity, and Social Action of Senegal.
文摘In the context of the COVID-19 sweeping the world,countries around the globe have adopted different approaches to control the spread of disease,and in order to find better control methods,this paper explores the influence of people’s awareness on SIR model.On the basis of the SIR model,this paper studies the SEIR model with the exposure period parameter,calculates the feasible region R-naught disease-free point,and analyzes the method of controlling the spread of the disease according to R-naught,which shows that lockdown has a significant effect on the control of COVID-19.In addition,this paper also established a model affected by disease awareness,adding a factor of news media and religious awareness.The feasible region is calculated,and the reality situation based on India is analyzed.The conclusion proved that people’s awareness has a greater influence on the spread of diseases.
文摘To effectively track the impact of population migration between regions on the spread of infectious diseases, this paper proposes a visualized analysis and prediction system of infectious diseases based on the improved SIR model. The research contents including: using the multi graph link interaction mode, visualizing the space-time distribution and development trend of infectious diseases;The LightGBM model is used to track the changes of infection rate and recovery rate, and the Mi/Mo SIR model is constructed according to the initial data of different populations;Mi/Mo SIR model is used to predict infectious diseases in combination with visual panel, providing users with tools to analyze and explain the space-time characteristics and potential laws of infectious diseases. The study found that the closure of cities and the restriction of personnel mobility were necessary and effective, and the system provided an important basis for the prediction and early warning of infectious diseases.
文摘The use of the SIR model to predict the time evolution of an epidemic is very frequent and has spatial information about its propagation which may be very useful to contrast its spread. In this paper we take a particular cellular automaton model that well reproduces the time evolution of the disease given by the SIR model;setting the automaton is generally an annoying problem because we need to run a lot of simulations, compare them to the solution of the SIR model and, finally, decide the parameters to use. In order to make this procedure easier, we will show a fast method that, in input, requires the parameters of the SIR continuous model that we want to reproduce, whereas, in output, it yields the parameters to use in the cellular automaton model. The problem of computing the most suitable parameters for the reticular model is reduced to the problem of finding the roots of a polynomial Equation.
文摘An SIR model of Zika virus (ZIKV) spread is formulated that includes ZIKV infections to newborns. Analytically, the model has one disease free and one endemic equilibrium point. The free one is stable for some conditions when R0 and unstable when R0>1. In Brazil, when R0≈2>1 ZIKV infections expand and for R0 = 0.875R0) of the model. There are parameters for human-mosquito transmission and some for sexual-transmission factor. It appears that controlling spread of ZIKV infections by human-mosquito transmission may greatly reduce the value of R0.
文摘In this paper, a delayed SIR model with exponential demographic structure and the saturated incidence rate is formulated. The stability of the equilibria is analyzed with delay: the endemic equilibrium is locally stable without delay;and the endemic equilibrium is stable if the delay is under some condition. Moreover the dynamical behaviors from stability to instability will change with an appropriate?critical value. At last, some numerical simulations of the model are given to illustrate the main theoretical results.
文摘This paper presents a new modified SIR model which incorporates appropriate delay parameters leading to a more precise prediction of COVID-19 real time data. The efficacy of the newly developed SIR model is proven by comparing its predictions to real data obtained from four counties namely Germany, Italy, Kuwait, and Oman. Two included delay periods for incubation and recovery within the SIR model produce a sensible and more accurate representation of the real time data. In the absence of the two-delay period (<img src="Edit_8ce6d5c5-9b59-4640-9c0e-334e3948d11c.png" width="67" height="20" alt="" /><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">)</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> the dynamical behavior of the model will not correspond to today’s picture and lag the detection of the epidemic peak. The reproductive number <i></i></span></span></span><i><span><span><i><span style="font-family:Verdana;">R</span></i></span></span><span><span><span style="font-family:;" "=""><i><span style="font-family:Verdana;"><sub>0</sub></span></i><span style="font-family:Verdana;"></span></span></span></span></i> <span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">is defined for the model for values of recovery time delay <i></i></span></span></span><i><span style="font-family:Verdana;"><span style="font-family:Verdana;"><i><span style="font-family:Verdana;"><img src="Edit_882b068a-f7fa-478e-9fb9-4d78388010f3.png" width="25" height="20" alt="" /></span></i></span></span></i><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"><sub></sub></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> of the infective case. The effect of recovery time <img src="Edit_882b068a-f7fa-478e-9fb9-4d78388010f3.png" width="25" height="20" alt="" /></span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">may produce second wave, and/or an oscillation which could destabilize the behavior of the system and a periodic oscillation can arise due to Hopf bifurcation phenomenon.</span></span></span>
文摘The SIR(D) epidemiological model is defined through a system of transcendental equations, not solvable by elementary functions. In the present paper those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, originating, piece-wisely, from generalized logistic functions: they ensure exact (in the numerical sense) asymptotic values, besides to be quite practical to use, for example with fit to data algorithms;moreover they unveil a useful feature, that in fact, at least with very strict approximation, is also owned by the (numerical) solutions of the exact equations. The novelties in the work are: the way the approximate equations are obtained, using simple, analytic geometry considerations;the easy and practical formulation of the final approximate solutions;the mentioned useful feature, never disclosed before. The work’s method and result prove to be robust over a range of values of the well known non-dimensional parameter called basic reproduction ratio, that covers at least all the known epidemic cases, from influenza to measles: this is a point which doesn’t appear much discussed in analogous works.
文摘In this paper, we propose random fluctuation on contact and recovery rates in deterministic SIR model with disease deaths in nonparametric manner and derive a new stochastic SIR model with distributed time delay and general diffusion coefficients. By analysis of the introduced model, we obtain the sufficient conditions for the regularity, existence and uniqueness of a global solution by means of Lyapunov function. Moreover, we also investigate the stochastic asymptotic stability of disease free equilibria and endemic equilibria of this model. Finally, we illustrate our general results by applications.
文摘Calculating analytical approximate solutions for non-linear infectious disease models is a difficult task. Such models often require computational tools to analyse analytical approximate methods which appear in some theoretical and practical applications in systems biology. They represent key critical elements and give some approximate solutions for such systems. The SIR epidemic disease model is given as the non-linear system of ODE’s. Then, we use a proper scaling to reduce the number of parameters. We suggest Elzaki transform method to find analytical approximate solutions for the simplified model. The technique plays an important role in calculating the analytical approximate solutions. The local and global dynamics of the model are also studied. An investigation of the behaviour at infinity was conducted via finding the lines and singular points at infinity. Model dynamic results are computed in numerical simulations using Pplane8 and SimBiology Toolbox for Mathlab. Results provide a good step forward for describing the model dynamics. More interestingly, the simplified model could be accurate, robust, and used by biologists for different purposes such as identifying critical model elements.
文摘This paper handles with a time-space SIR model in two regions which have a common interface.The model is defined as coupled reaction-diffusion system with a robin boundary in interface to predict the immigration between the two regions.As known,the immigration has an influence on the spread of disease,this is caused by immigrants who could carry the disease from their areas to other places.For this reason,this paper deals with the existence of solutions to SIR model with disease spread between different regions by the Fadeo-Galerkin method and validate this result by the numerical simulations.
基金supported by National Institute of General Medical Sciences of the National Institutes of Health,United States(Award numbers P20GM130418 and U54GM104944).
文摘Background:Under-reporting and,thus,uncertainty around the true incidence of health events is common in all public health reporting systems.While the problem of underreporting is acknowledged in epidemiology,the guidance and methods available for assessing and correcting the resulting bias are obscure.Objective:We aim to design a simple modification to the Susceptible e Infected e Removed(SIR)model for estimating the fraction or proportion of reported infection cases.Methods:The suggested modification involves rescaling of the classical SIR model producing its mathematically equivalent version with explicit dependence on the reporting parameter(true proportion of cases reported).We justify the rescaling using the phase plane analysis of the SIR model system and show how this rescaling parameter can be estimated from the data along with the other model parameters.Results:We demonstrate how the proposed method is cross-validated using simulated data with known disease cases and then apply it to two empirical reported data sets to estimate the fraction of reported cases in Missoula County,Montana,USA,using:(1)flu data for 2016e2017 and(2)COVID-19 data for fall of 2020.Conclusions:We establish with the simulated and COVID-19 data that when most of the disease cases are presumed reported,the value of the additional reporting parameter in the modified SIR model is close or equal to one,so that the original SIR model is appropriate for data analysis.Conversely,the flu example shows that when the reporting parameter is close to zero,the original SIR model is not accurately estimating the usual rate parameters,and the re-scaled SIR model should be used.This research demonstrates the role of under-reporting of disease data and the importance of accounting for underreporting when modeling simulated,endemic,and pandemic disease data.Correctly reporting the“true”number of disease cases will have downstream impacts on predictions of disease dynamics.A simple parameter adjustment to the SIR modeling framework can help alleviate bias and uncertainty around crucial epidemiological metrics(e.g.:basic disease reproduction number)and public health decision making.
文摘BIM(building information modeling,BIM)外包已成为一种有效的BIM应用策略。当前BIM外包应用效果未达预期,BIM外包模式与项目特征不匹配是导致该现象的重要因素,不同形态的BIM外包模式在跨组织边界的信息传递路径及风险传导机制上存在显著差异。为明确不同BIM外包模式下信息沟通效率的差异,本文聚焦于2种主要模式:咨询企业主导(以下简称咨询主导)和业主主导的BIM外包模式。以实际案例为基础,构建不同BIM外包模式下的信息沟通网络,分别从静态和动态的视角对不同BIM外包模式中信息沟通的效率进行对比:在静态视角中,应用社会网络分析方法对网络结构进行对比分析,以此明确不同BIM外包模式的信息传递路径;在动态视角中,应用SIR(susceptible-infected-recovered,SIR)模型对错误的传播和扩散进行对比分析,探究不同BIM外包模式的风险传导机制。仿真结果表明,在咨询主导下的BIM外包模式中,BIM决策效率较高,但协同效率较低,信息传递效率也较低;相反,在业主主导下的BIM外包模式中,BIM协同效率较高,信息传递效率也较高。本研究为建筑工程企业在实际工程项目中BIM外包模式的选择提供决策参考和理论支持。
