A disease transmission model of SEIR type is discussed in a stochastic point of view. We start by formulating the SEIR epidemic model in form of a system of nonlinear differential equations and then change it to a sys...A disease transmission model of SEIR type is discussed in a stochastic point of view. We start by formulating the SEIR epidemic model in form of a system of nonlinear differential equations and then change it to a system of nonlinear stochastic differential equations (SDEs). The numerical simulation of the resulting SDEs is done by Euler-Maruyama scheme and the parameters are estimated by adaptive Markov chain Monte Carlo and extended Kalman filter methods. The stochastic results are discussed and it is observed that with the SDE type of modeling, the parameters are also identifiable.展开更多
This work aimed to construct an epidemic model with fuzzy parameters.Since the classical epidemic model doesnot elaborate on the successful interaction of susceptible and infective people,the constructed fuzzy epidemi...This work aimed to construct an epidemic model with fuzzy parameters.Since the classical epidemic model doesnot elaborate on the successful interaction of susceptible and infective people,the constructed fuzzy epidemicmodel discusses the more detailed versions of the interactions between infective and susceptible people.Thenext-generation matrix approach is employed to find the reproduction number of a deterministic model.Thesensitivity analysis and local stability analysis of the systemare also provided.For solving the fuzzy epidemic model,a numerical scheme is constructed which consists of three time levels.The numerical scheme has an advantage overthe existing forward Euler scheme for determining the conditions of getting the positive solution.The establishedscheme also has an advantage over existing non-standard finite difference methods in terms of order of accuracy.The stability of the scheme for the considered fuzzy model is also provided.From the plotted results,it can beobserved that susceptible people decay by rising interaction parameters.展开更多
In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start wi...In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R<sub>0</sub> ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.展开更多
The coronavirus disease outbreak of 2019(COVID-19)has been spreading rapidly to all corners of the word,in a very complex manner.A key research focus is in predicting the development trend of COVID-19 scientifically t...The coronavirus disease outbreak of 2019(COVID-19)has been spreading rapidly to all corners of the word,in a very complex manner.A key research focus is in predicting the development trend of COVID-19 scientifically through mathematical modelling.We conducted a systematic review of epidemic prediction models of COVID-19 and the public health intervention strategies by searching the Web of Science database.55 studies of the COVID-19 epidemic model were reviewed systematically.It was found that the COVID-19 epidemic models were different in the model type,acquisition method,hypothesis and distribution of key input parameters.Most studies used the gamma distribution to describe the key time period of COVID-19 infection,and some studies used the lognormal distribution,the Erlang distribution,and theWeibull distribution.The setting ranges of the incubation period,serial interval,infectious period and generation time were 4.9-7 days,4.41-8.4 days,2.3-10 days and 4.4-7.5 days,respectively,and more than half of the incubation periods were set to 5.1 or 5.2 days.Most models assumed that the latent period was consistent with the incubation period.Some models assumed that asymptomatic infections were infectious or pre-symptomatic transmission was possible,which overestimated the value of R0.For the prediction differences under different public health strategies,the most significant effect was in travel restrictions.There were different studies on the impact of contact tracking and social isolation,but it was considered that improving the quarantine rate and reporting rate,and the use of protective face mask were essential for epidemic prevention and control.The input epidemiological parameters of the prediction models had significant differences in the prediction of the severity of the epidemic spread.Therefore,prevention and control institutions should be cautious when formulating public health strategies by based on the prediction results of mathematical models.展开更多
For some infectious diseases such as mumps,HBV,there is evidence showing that vaccinated individuals always lose their immunity at different rates depending on the inoculation time.In this paper,we propose an age-stru...For some infectious diseases such as mumps,HBV,there is evidence showing that vaccinated individuals always lose their immunity at different rates depending on the inoculation time.In this paper,we propose an age-structured epidemic model using a step function to describe the rate at which vaccinated individuals lose immunity and reduce the age-structured epidemic model to the delay differential model.For the age-structured model,we consider the positivity,boundedness,and compactness of the semiflow and study global stability of equilibria by constructing appropriate Lyapunov functionals.Moreover,for the reduced delay differential equation model,we study the existence of the endemic equilibrium and prove the global stability of equilibria.Finally,some numerical simulations are provided to support our theoretical results and a brief discussion is given.展开更多
Vaccination is a very important strategy for the elimination of infectious diseaVaccination is a very important strategy for the elimination of infectious diseases. A SIVS epidemic model with infection age and nonline...Vaccination is a very important strategy for the elimination of infectious diseaVaccination is a very important strategy for the elimination of infectious diseases. A SIVS epidemic model with infection age and nonlinear vaccination has been formulated in this paper. Using the theory of differential and integral equation, we show the local asymptotic stability of the infection-free equilibrium and the endemic equilibrium under some assumptions.展开更多
At present, the Omicron variant is still the dominant strain in the global novel coronavirus pneumonia pandemic, and has the characteristics of concealed transmission, which brings heavy pressure to the health systems...At present, the Omicron variant is still the dominant strain in the global novel coronavirus pneumonia pandemic, and has the characteristics of concealed transmission, which brings heavy pressure to the health systems of different countries. Omicron infections were first found in Chinese Mainland in Tianjin in December 2021, and Omicron epidemic broke out in many parts of China in 2022. In order to enable the country and government to make scientific and accurate decisions in the face of the epidemic, it is particularly important to predict and analyze the relevant factors of Omicron’s covert transmission. In this paper, based on the official data of Jilin City and the improved SEIR dynamic model, through parameter estimation, the contact infection probability of symptomatic infected persons in Omicron infected patients is 0.4265, and the attenuation factor is 0.1440. Secondly, the influence of infectious duration in different incubation periods, asymptomatic infected persons and other factors on the epidemic situation in this area was compared. Finally, the scale of epidemic development was predicted and analyzed.展开更多
Social network is the mainstream medium of current information dissemination,and it is particularly important to accurately predict its propagation law.In this paper,we introduce a social network propagation model int...Social network is the mainstream medium of current information dissemination,and it is particularly important to accurately predict its propagation law.In this paper,we introduce a social network propagation model integrating multiple linear regression and infectious disease model.Firstly,we proposed the features that affect social network communication from three dimensions.Then,we predicted the node influence via multiple linear regression.Lastly,we used the node influence as the state transition of the infectious disease model to predict the trend of information dissemination in social networks.The experimental results on a real social network dataset showed that the prediction results of the model are consistent with the actual information dissemination trends.展开更多
Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this p...Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this paper,we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels.In this approach,the overall population was separated into five cohorts.Furthermore,the descriptive behavior of the system was investigated,including prerequisites for the positivity of solutions,invariant domain of the solution,presence and stability of equilibrium points,and sensitivity analysis.We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions.Several numerical simulations for various fractional orders and randomization intensities are illustrated.展开更多
Ross’ epidemic model describing the transmission of malaria uses two classes of infection, one for humans and one for mosquitoes. This paper presents a stochastic extension of a deterministic vector-borne epidemic mo...Ross’ epidemic model describing the transmission of malaria uses two classes of infection, one for humans and one for mosquitoes. This paper presents a stochastic extension of a deterministic vector-borne epidemic model based only on the class of human infectious. The consistency of the model is established by proving that the stochastic delay differential equation describing the model has a unique positive global solution. The extinction of the disease is studied through the analysis of the stability of the disease-free equilibrium state and the persistence of the model. Finally, we introduce some numerical simulations to illustrate the obtained results.展开更多
<span style="font-family:Verdana;">In this paper we build and analyze two stochastic epidemic models with death. The model assume</span><span style="font-family:Verdana;"><span...<span style="font-family:Verdana;">In this paper we build and analyze two stochastic epidemic models with death. The model assume</span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">s</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> that only susceptible individuals (S) can get infected (I) and may die from this disease or a recovered individual becomes susceptible again (SIS model) or completely immune (SIR Model) for the remainder of the study period. Moreover, it is assumed there are no births, deaths, immigration or emigration during the study period;the community is said to be closed. In these infection disease models, there are two central questions: first it is the disease extinction or not and the second studies the time elapsed for such extinction, this paper will deal with this second question because the first answer corresponds to the basic reproduction number defined in the bibliography. More concretely, we study the mean-extinction of the diseases and the technique used here first builds the backward Kolmogorov differential equation and then solves it numerically using finite element method with FreeFem++. Our contribution and novelty </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">are</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> the following: however the reproduction number effectively concludes the extinction or not of the disease, it does not help to know its extinction times because example with the same reproduction numbers has very different time. Moreover, the SIS model is slower, a result that is not surprising, but this difference seems to increase in the stochastic models with respect to the deterministic ones, it is reasonable to assume some uncertainly.</span></span></span>展开更多
In this paper, to complete the global dynamics of a multi-strains SIS epidemic model, we establish a precise result on coexistence for the cases of the partial and complete duplicated multiple largest reproduction rat...In this paper, to complete the global dynamics of a multi-strains SIS epidemic model, we establish a precise result on coexistence for the cases of the partial and complete duplicated multiple largest reproduction ratios for this model.展开更多
This study aims to improve control schemes for COVID-19 by a numerical model with estimation of parameters.We established a multi-level and multi-objective nonlinear SEIDR model to simulate the virus transmission.The ...This study aims to improve control schemes for COVID-19 by a numerical model with estimation of parameters.We established a multi-level and multi-objective nonlinear SEIDR model to simulate the virus transmission.The early spread in Japan was adopted as a case study.The first 96 days since the infection were divided into five stages with parameters estimated.Then,we analyzed the trend of the parameter value,age structure ratio,and the defined PCR test index(standardization of the scale of PCR tests).It was discovered that the self-healing rate and confirmed rate were linear with the age structure ratio and the PCR test index using the stepwise regression method.The transmission rates were related to the age structure ratio,PCR test index,and isolation efficiency.Both isolation measures and PCR test medical screening can effectively reduce the number of infected cases based on the simulation results.However,the strategy of increasing PCR test medical screening would encountered a bottleneck effect on the virus control when the index reached 0.3.The effectiveness of the policy would decrease and the basic reproduction number reached the extreme value at 0.6.This study gave a feasible combination for isolation and PCR test by simulation.The isolation intensity could be adjusted to compensate the insufficiency of PCR test to control the pandemic.展开更多
In this research,we propose a new change in classical epidemic models by including the change in the rate of death in the overall population.The existing models like Susceptible-Infected-Recovered(SIR)and Susceptible-...In this research,we propose a new change in classical epidemic models by including the change in the rate of death in the overall population.The existing models like Susceptible-Infected-Recovered(SIR)and Susceptible-Infected-Recovered-Susceptible(SIRS)include the death rate as one of the parameters to estimate the change in susceptible,infected and recovered populations.Actually,because of the deficiencies in immunity,even the ordinary flu could cause death.If people’s disease resistance is strong,then serious diseases may not result in mortalities.The classical model always assumes a closed system where there is no new birth or death,no immigration or emigration,while in reality,such assumptions are not realistic.Moreover,the classical epidemic model does not report the change in population due to death caused by a disease.With this study,we try to incorporate the rate of change in the population of death caused by a disease,where the model is framed to reduce the curve of death along with the susceptible and infected populations.Since the rate of change turned out to be very small,we have tried to estimate it fractionally.Thus,the model is defined using fuzzy logic and is solved by two different methods:a Laplace Adomian decomposition method(LADM)and a differential transform method(DTM)for an arbitrary order α.To test its accuracy,we compared the results of both DTM and LADM with the fourth-order Runge-Kutta method(RKM-4)at α=1.展开更多
A SIQS epidemic model with saturated incidence rate is studied. Two equilibrium points exist for the system, disease-free and endemic equilibrium. The stability of the disease-free equilibrium and endemic equilibrium ...A SIQS epidemic model with saturated incidence rate is studied. Two equilibrium points exist for the system, disease-free and endemic equilibrium. The stability of the disease-free equilibrium and endemic equilibrium exists when the basic reproduction number R0, is less or greater than unity respectively. The global stability of the disease-free and endemic equilibrium is proved using Lyapunov functions and Poincare-Bendixson theorem plus Dulac’s criterion respectively.展开更多
In this work, we present results of an investigation of environmental precursors of infectious epidemic of dengue fever in the Metropolitan Area of Rio de Janeiro, RJ, Brazil, obtained by a numerical model with repres...In this work, we present results of an investigation of environmental precursors of infectious epidemic of dengue fever in the Metropolitan Area of Rio de Janeiro, RJ, Brazil, obtained by a numerical model with representation of infection and reinfection of the population. The period considered extend between 2000 and 2011, in which it was possible to pair meteorological data and the reporting of dengue patients worsening. These data should also be considered in the numerical model, by assimilation, to obtain simulations of Dengue epidemics. The model contains compartments for the human population, for the vector Aedes aegypti and four virus serotypes. The results provide consistent evidence that worsening infection and disease outbreaks are due to the occurrence of environmental precursors, as the dynamics of the accumulation of water in the breeding and energy availability in the form of metabolic activation enthalpy during pre-epidemic periods.展开更多
In this paper, we investigate the dynamic properties of an SIR epidemic model with saturated growth rate. Under the conditions of an arbitrary initial value, we prove that the system exists unique positive solution, a...In this paper, we investigate the dynamic properties of an SIR epidemic model with saturated growth rate. Under the conditions of an arbitrary initial value, we prove that the system exists unique positive solution, and give the sufficient conditions caused by random environmental factors leading to the extinction of infectious diseases. Moreover, we verify the conditions for the persistence of infectious diseases in the mean sense. Finally, we provide the biology interpretation and some strategies to control the infectious diseases.展开更多
A stochastic susceptible-infective-recovered(SIR)epidemic model with jumps was considered.The contributions of this paper are as follows.(1) The stochastic differential equation(SDE)associated with the model has a uni...A stochastic susceptible-infective-recovered(SIR)epidemic model with jumps was considered.The contributions of this paper are as follows.(1) The stochastic differential equation(SDE)associated with the model has a unique global positive solution;(2) the results reveal that the solution of this epidemic model will be stochastically ultimately bounded,and the non-linear SDE admits a unique stationary distribution under certain parametric conditions;(3) the coefficients play an important role in the extinction of the diseases.展开更多
The structure-preserving features of the nonlinear stochastic models are positivity,dynamical consistency and boundedness.These features have a significant role in different fields of computational biology and many mo...The structure-preserving features of the nonlinear stochastic models are positivity,dynamical consistency and boundedness.These features have a significant role in different fields of computational biology and many more.Unfortunately,the existing stochastic approaches in literature do not restore aforesaid structure-preserving features,particularly for the stochastic models.Therefore,these gaps should be occupied up in literature,by constructing the structure-preserving features preserving numerical approach.This writing aims to describe the structure-preserving dynamics of the stochastic model.We have analysed the effect of reproduction number in stochastic modelling the same as described in the literature for deterministic modelling.The usual explicit stochastic numerical approaches are time-dependent.We have developed the implicitly driven explicit approach for the stochastic epidemic model.We have proved that the newly developed approach is preserving the structural,dynamical properties as positivity,boundedness and dynamical consistency.Finally,convergence analysis of a newly developed approach and graphically illustration is also presented.展开更多
A new stochastic epidemic model, that is, a general continuous time birth and death chain model, is formulated based on a deterministic model including vaccination. We use continuous time Markov chain to construct the...A new stochastic epidemic model, that is, a general continuous time birth and death chain model, is formulated based on a deterministic model including vaccination. We use continuous time Markov chain to construct the birth and death process. Through the Kolmogorov forward equation and the theory of moment generating function, the corresponding population expectations are studied. The theoretical result of the stochastic model and deterministic version is also given. Finally, numerical simulations are carried out to substantiate the theoretical results of random walk.展开更多
文摘A disease transmission model of SEIR type is discussed in a stochastic point of view. We start by formulating the SEIR epidemic model in form of a system of nonlinear differential equations and then change it to a system of nonlinear stochastic differential equations (SDEs). The numerical simulation of the resulting SDEs is done by Euler-Maruyama scheme and the parameters are estimated by adaptive Markov chain Monte Carlo and extended Kalman filter methods. The stochastic results are discussed and it is observed that with the SDE type of modeling, the parameters are also identifiable.
基金the support of Prince Sultan University for paying the article processing charges(APC)of this publication.
文摘This work aimed to construct an epidemic model with fuzzy parameters.Since the classical epidemic model doesnot elaborate on the successful interaction of susceptible and infective people,the constructed fuzzy epidemicmodel discusses the more detailed versions of the interactions between infective and susceptible people.Thenext-generation matrix approach is employed to find the reproduction number of a deterministic model.Thesensitivity analysis and local stability analysis of the systemare also provided.For solving the fuzzy epidemic model,a numerical scheme is constructed which consists of three time levels.The numerical scheme has an advantage overthe existing forward Euler scheme for determining the conditions of getting the positive solution.The establishedscheme also has an advantage over existing non-standard finite difference methods in terms of order of accuracy.The stability of the scheme for the considered fuzzy model is also provided.From the plotted results,it can beobserved that susceptible people decay by rising interaction parameters.
文摘In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R<sub>0</sub> ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.
基金This work was supported by the National Natural Science Foundation of China(51778382)the National Key R&D Program of China(2016YFC0700400).
文摘The coronavirus disease outbreak of 2019(COVID-19)has been spreading rapidly to all corners of the word,in a very complex manner.A key research focus is in predicting the development trend of COVID-19 scientifically through mathematical modelling.We conducted a systematic review of epidemic prediction models of COVID-19 and the public health intervention strategies by searching the Web of Science database.55 studies of the COVID-19 epidemic model were reviewed systematically.It was found that the COVID-19 epidemic models were different in the model type,acquisition method,hypothesis and distribution of key input parameters.Most studies used the gamma distribution to describe the key time period of COVID-19 infection,and some studies used the lognormal distribution,the Erlang distribution,and theWeibull distribution.The setting ranges of the incubation period,serial interval,infectious period and generation time were 4.9-7 days,4.41-8.4 days,2.3-10 days and 4.4-7.5 days,respectively,and more than half of the incubation periods were set to 5.1 or 5.2 days.Most models assumed that the latent period was consistent with the incubation period.Some models assumed that asymptomatic infections were infectious or pre-symptomatic transmission was possible,which overestimated the value of R0.For the prediction differences under different public health strategies,the most significant effect was in travel restrictions.There were different studies on the impact of contact tracking and social isolation,but it was considered that improving the quarantine rate and reporting rate,and the use of protective face mask were essential for epidemic prevention and control.The input epidemiological parameters of the prediction models had significant differences in the prediction of the severity of the epidemic spread.Therefore,prevention and control institutions should be cautious when formulating public health strategies by based on the prediction results of mathematical models.
基金supported by The National Natural Science Foundation of China[12026236,12026222,12061079,11601293,12071418]Science and Technology Activities Priority Program for Overseas Researchers in Shanxi Province[20210049]The Natural Science Foundation of Shanxi Province[201901D211160,201901D211461,201901D111295]。
文摘For some infectious diseases such as mumps,HBV,there is evidence showing that vaccinated individuals always lose their immunity at different rates depending on the inoculation time.In this paper,we propose an age-structured epidemic model using a step function to describe the rate at which vaccinated individuals lose immunity and reduce the age-structured epidemic model to the delay differential model.For the age-structured model,we consider the positivity,boundedness,and compactness of the semiflow and study global stability of equilibria by constructing appropriate Lyapunov functionals.Moreover,for the reduced delay differential equation model,we study the existence of the endemic equilibrium and prove the global stability of equilibria.Finally,some numerical simulations are provided to support our theoretical results and a brief discussion is given.
基金Supported by the NSF of China(No.10971178No.10911120387)+1 种基金the Sciences Foundation of Shanxi(20090110053)the Sciences Exploited Foundation of Shanxi(20081045)
文摘Vaccination is a very important strategy for the elimination of infectious diseaVaccination is a very important strategy for the elimination of infectious diseases. A SIVS epidemic model with infection age and nonlinear vaccination has been formulated in this paper. Using the theory of differential and integral equation, we show the local asymptotic stability of the infection-free equilibrium and the endemic equilibrium under some assumptions.
文摘At present, the Omicron variant is still the dominant strain in the global novel coronavirus pneumonia pandemic, and has the characteristics of concealed transmission, which brings heavy pressure to the health systems of different countries. Omicron infections were first found in Chinese Mainland in Tianjin in December 2021, and Omicron epidemic broke out in many parts of China in 2022. In order to enable the country and government to make scientific and accurate decisions in the face of the epidemic, it is particularly important to predict and analyze the relevant factors of Omicron’s covert transmission. In this paper, based on the official data of Jilin City and the improved SEIR dynamic model, through parameter estimation, the contact infection probability of symptomatic infected persons in Omicron infected patients is 0.4265, and the attenuation factor is 0.1440. Secondly, the influence of infectious duration in different incubation periods, asymptomatic infected persons and other factors on the epidemic situation in this area was compared. Finally, the scale of epidemic development was predicted and analyzed.
基金This work was supported by the 2021 Project of the“14th Five-Year Plan”of Shaanxi Education Science“Research on the Application of Educational Data Mining in Applied Undergraduate Teaching-Taking the Course of‘Computer Application Technology’as an Example”(SGH21Y0403)the Teaching Reform and Research Projects for Practical Teaching in 2022“Research on Practical Teaching of Applied Undergraduate Projects Based on‘Combination of Courses and Certificates”-Taking Computer Application Technology Courses as an Example”(SJJG02012)the 11th batch of Teaching Reform Research Project of Xi’an Jiaotong University City College“Project-Driven Cultivation and Research on Information Literacy of Applied Undergraduate Students in the Information Times-Taking Computer Application Technology Course Teaching as an Example”(111001).
文摘Social network is the mainstream medium of current information dissemination,and it is particularly important to accurately predict its propagation law.In this paper,we introduce a social network propagation model integrating multiple linear regression and infectious disease model.Firstly,we proposed the features that affect social network communication from three dimensions.Then,we predicted the node influence via multiple linear regression.Lastly,we used the node influence as the state transition of the infectious disease model to predict the trend of information dissemination in social networks.The experimental results on a real social network dataset showed that the prediction results of the model are consistent with the actual information dissemination trends.
文摘Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this paper,we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels.In this approach,the overall population was separated into five cohorts.Furthermore,the descriptive behavior of the system was investigated,including prerequisites for the positivity of solutions,invariant domain of the solution,presence and stability of equilibrium points,and sensitivity analysis.We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions.Several numerical simulations for various fractional orders and randomization intensities are illustrated.
文摘Ross’ epidemic model describing the transmission of malaria uses two classes of infection, one for humans and one for mosquitoes. This paper presents a stochastic extension of a deterministic vector-borne epidemic model based only on the class of human infectious. The consistency of the model is established by proving that the stochastic delay differential equation describing the model has a unique positive global solution. The extinction of the disease is studied through the analysis of the stability of the disease-free equilibrium state and the persistence of the model. Finally, we introduce some numerical simulations to illustrate the obtained results.
文摘<span style="font-family:Verdana;">In this paper we build and analyze two stochastic epidemic models with death. The model assume</span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">s</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> that only susceptible individuals (S) can get infected (I) and may die from this disease or a recovered individual becomes susceptible again (SIS model) or completely immune (SIR Model) for the remainder of the study period. Moreover, it is assumed there are no births, deaths, immigration or emigration during the study period;the community is said to be closed. In these infection disease models, there are two central questions: first it is the disease extinction or not and the second studies the time elapsed for such extinction, this paper will deal with this second question because the first answer corresponds to the basic reproduction number defined in the bibliography. More concretely, we study the mean-extinction of the diseases and the technique used here first builds the backward Kolmogorov differential equation and then solves it numerically using finite element method with FreeFem++. Our contribution and novelty </span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">are</span></span></span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;"> the following: however the reproduction number effectively concludes the extinction or not of the disease, it does not help to know its extinction times because example with the same reproduction numbers has very different time. Moreover, the SIS model is slower, a result that is not surprising, but this difference seems to increase in the stochastic models with respect to the deterministic ones, it is reasonable to assume some uncertainly.</span></span></span>
文摘In this paper, to complete the global dynamics of a multi-strains SIS epidemic model, we establish a precise result on coexistence for the cases of the partial and complete duplicated multiple largest reproduction ratios for this model.
基金National Natural Science Foundation of China under Grant Nos.61803152,31920103016,and 11871475Doctoral Start-Up Foundation of Hunan Normal University under Grant No.0531120-3827Hunan Provincial Education Department under Grant No.HNKCSZ-2020-0813.
文摘This study aims to improve control schemes for COVID-19 by a numerical model with estimation of parameters.We established a multi-level and multi-objective nonlinear SEIDR model to simulate the virus transmission.The early spread in Japan was adopted as a case study.The first 96 days since the infection were divided into five stages with parameters estimated.Then,we analyzed the trend of the parameter value,age structure ratio,and the defined PCR test index(standardization of the scale of PCR tests).It was discovered that the self-healing rate and confirmed rate were linear with the age structure ratio and the PCR test index using the stepwise regression method.The transmission rates were related to the age structure ratio,PCR test index,and isolation efficiency.Both isolation measures and PCR test medical screening can effectively reduce the number of infected cases based on the simulation results.However,the strategy of increasing PCR test medical screening would encountered a bottleneck effect on the virus control when the index reached 0.3.The effectiveness of the policy would decrease and the basic reproduction number reached the extreme value at 0.6.This study gave a feasible combination for isolation and PCR test by simulation.The isolation intensity could be adjusted to compensate the insufficiency of PCR test to control the pandemic.
文摘In this research,we propose a new change in classical epidemic models by including the change in the rate of death in the overall population.The existing models like Susceptible-Infected-Recovered(SIR)and Susceptible-Infected-Recovered-Susceptible(SIRS)include the death rate as one of the parameters to estimate the change in susceptible,infected and recovered populations.Actually,because of the deficiencies in immunity,even the ordinary flu could cause death.If people’s disease resistance is strong,then serious diseases may not result in mortalities.The classical model always assumes a closed system where there is no new birth or death,no immigration or emigration,while in reality,such assumptions are not realistic.Moreover,the classical epidemic model does not report the change in population due to death caused by a disease.With this study,we try to incorporate the rate of change in the population of death caused by a disease,where the model is framed to reduce the curve of death along with the susceptible and infected populations.Since the rate of change turned out to be very small,we have tried to estimate it fractionally.Thus,the model is defined using fuzzy logic and is solved by two different methods:a Laplace Adomian decomposition method(LADM)and a differential transform method(DTM)for an arbitrary order α.To test its accuracy,we compared the results of both DTM and LADM with the fourth-order Runge-Kutta method(RKM-4)at α=1.
文摘A SIQS epidemic model with saturated incidence rate is studied. Two equilibrium points exist for the system, disease-free and endemic equilibrium. The stability of the disease-free equilibrium and endemic equilibrium exists when the basic reproduction number R0, is less or greater than unity respectively. The global stability of the disease-free and endemic equilibrium is proved using Lyapunov functions and Poincare-Bendixson theorem plus Dulac’s criterion respectively.
文摘In this work, we present results of an investigation of environmental precursors of infectious epidemic of dengue fever in the Metropolitan Area of Rio de Janeiro, RJ, Brazil, obtained by a numerical model with representation of infection and reinfection of the population. The period considered extend between 2000 and 2011, in which it was possible to pair meteorological data and the reporting of dengue patients worsening. These data should also be considered in the numerical model, by assimilation, to obtain simulations of Dengue epidemics. The model contains compartments for the human population, for the vector Aedes aegypti and four virus serotypes. The results provide consistent evidence that worsening infection and disease outbreaks are due to the occurrence of environmental precursors, as the dynamics of the accumulation of water in the breeding and energy availability in the form of metabolic activation enthalpy during pre-epidemic periods.
文摘In this paper, we investigate the dynamic properties of an SIR epidemic model with saturated growth rate. Under the conditions of an arbitrary initial value, we prove that the system exists unique positive solution, and give the sufficient conditions caused by random environmental factors leading to the extinction of infectious diseases. Moreover, we verify the conditions for the persistence of infectious diseases in the mean sense. Finally, we provide the biology interpretation and some strategies to control the infectious diseases.
基金Natural Science Foundation of Hunan University of Technology,China(No.2012HZX08)the Special Foundation of National Independent Innovation Demonstration Area Construction of Zhuzhou(Applied Basic Research),China
文摘A stochastic susceptible-infective-recovered(SIR)epidemic model with jumps was considered.The contributions of this paper are as follows.(1) The stochastic differential equation(SDE)associated with the model has a unique global positive solution;(2) the results reveal that the solution of this epidemic model will be stochastically ultimately bounded,and the non-linear SDE admits a unique stationary distribution under certain parametric conditions;(3) the coefficients play an important role in the extinction of the diseases.
基金The authors are grateful to Vice-Chancellor,Air University,Islamabad for providing an excellent research environment and facilities.The first author also thanks Prince Sultan University for funding this work through research-group number RG-DES2017-01-17.
文摘The structure-preserving features of the nonlinear stochastic models are positivity,dynamical consistency and boundedness.These features have a significant role in different fields of computational biology and many more.Unfortunately,the existing stochastic approaches in literature do not restore aforesaid structure-preserving features,particularly for the stochastic models.Therefore,these gaps should be occupied up in literature,by constructing the structure-preserving features preserving numerical approach.This writing aims to describe the structure-preserving dynamics of the stochastic model.We have analysed the effect of reproduction number in stochastic modelling the same as described in the literature for deterministic modelling.The usual explicit stochastic numerical approaches are time-dependent.We have developed the implicitly driven explicit approach for the stochastic epidemic model.We have proved that the newly developed approach is preserving the structural,dynamical properties as positivity,boundedness and dynamical consistency.Finally,convergence analysis of a newly developed approach and graphically illustration is also presented.
文摘A new stochastic epidemic model, that is, a general continuous time birth and death chain model, is formulated based on a deterministic model including vaccination. We use continuous time Markov chain to construct the birth and death process. Through the Kolmogorov forward equation and the theory of moment generating function, the corresponding population expectations are studied. The theoretical result of the stochastic model and deterministic version is also given. Finally, numerical simulations are carried out to substantiate the theoretical results of random walk.
