Stochasticity is introduced into a susceptible-exposed but not infectious-infectious-removed （SEIR） model describing epidemics＇ transmission, via the technique of parameter perturbation which is standard in stochas...Stochasticity is introduced into a susceptible-exposed but not infectious-infectious-removed （SEIR） model describing epidemics＇ transmission, via the technique of parameter perturbation which is standard in stochastic population modeling. The existence and uniqueness of the model have been proved in this paper. And E detailed analysis on global asymptotic stability is also carried out.展开更多
An epidemic model is a simplified means of describing the transmission of infectious diseases through individuals. The modeling of infectious diseases is a tool which has been used to study the mechanisms by which dis...An epidemic model is a simplified means of describing the transmission of infectious diseases through individuals. The modeling of infectious diseases is a tool which has been used to study the mechanisms by which diseases spread, to predict the future course of an outbreak and to evaluate strategies to control an epidemic. Epidemic models are of many types. Here, SEIR model is discussed. We first discuss the basics of SEIR model. Then it is applied for vector borne diseases. Steady state conditions are derived. A threshold parameter R0 is defined and is shown that the disease will spread only if its value exceeds 1. We have applied the basic model to one specific diseases-malaria and did the sensitivity analysis too using the data for India. We found sensitivity analysis very important as it told us the most sensitive parameter to be taken care of. This makes the work more of practical use. Numerical simulation is done for vector and host which shows the population dynamics in different compartments.展开更多
A kind of stochastic susceptible-exposed but not infectiousinfectious-removed (SEIR) model with constant immigration in incubation period is presented, based on a deterministic SEIR model, via the technique of paramet...A kind of stochastic susceptible-exposed but not infectiousinfectious-removed (SEIR) model with constant immigration in incubation period is presented, based on a deterministic SEIR model, via the technique of parameter perturbation which is standard in stochastic population modeling. The influence of the environmental noise as a standard Gaussian white noise on the epidemics' transmission is studied. Furthermore,the condition for the epidemics' persistence is obtained by formulating the corresponding function and using It 's formula. And the asymptotic behavior of the model near the endemic disease equilibrium is also studied. In this way, the decision support is provided in the application of this kind of stochastic SEIR model on the epidemics' prevention and control.展开更多
The numerical approximation of stochastic partial differential equations(SPDEs),particularly those including q-diffusion,poses considerable challenges due to the requirements for high-order precision,stability amongst...The numerical approximation of stochastic partial differential equations(SPDEs),particularly those including q-diffusion,poses considerable challenges due to the requirements for high-order precision,stability amongst random perturbations,and processing efficiency.Because of their simplicity,conventional numerical techniques like the Euler-Maruyama method are frequently employed to solve stochastic differential equations;nonetheless,they may have low-order accuracy and lower stability in stiff or high-resolution situations.This study proposes a novel computational scheme for solving SPDEs arising from a stochastic SEIR model with q-diffusion and a general incidence rate function.A proposed computational scheme can be used to solve stochastic partial differential equations.For spatial discretization,a compact scheme is chosen.The compact scheme can provide a sixth-order accurate solution.The proposed scheme can be considered an extension of the Euler Maruyama method.Stability and consistency in the mean square sense are also provided.For application purposes,the stochastic SEIR model is considered using q-diffusion effects.The scheme is used to solve the stochastic model and compared with the Euler-Maruyama method.The scheme is also compared with nonstandard finite difference method for solving deterministic models.In both cases,it performs better than existing schemes.Incorporating q-diffusion further enhanced the model’s ability to represent realistic spatial-temporal disease dynamics,especially in scenarios where classical diffusion is insufficient.展开更多
The SEIR epidemic model studied here includes constant inflows of new susceptibles, exposeds, infectives, and recovereds. This model also incorporates a population size dependent contact rate and a disease-related dea...The SEIR epidemic model studied here includes constant inflows of new susceptibles, exposeds, infectives, and recovereds. This model also incorporates a population size dependent contact rate and a disease-related death. As the infected fraction cannot be eliminated from the population, this kind of model has only the unique endemic equilibrium that is globally asymptotically stable. Under the special case where the new members of immigration are all susceptible, the model considered here shows a threshold phenomenon and a sharp threshold has been obtained. In order to prove the global asymptotical stability of the endemic equilibrium, the authors introduce the change of variable, which can reduce our four-dimensional system to a three-dimensional asymptotical autonomous system with limit equation.展开更多
In this paper,an SEIR model with nonlinear incidence rates are studied.The basic reproduction number R_0 characterizes the disease transmission dynamics: if R_0≤ 1,the disease-free equilibrium is globally asymptotica...In this paper,an SEIR model with nonlinear incidence rates are studied.The basic reproduction number R_0 characterizes the disease transmission dynamics: if R_0≤ 1,the disease-free equilibrium is globally asymptotically stable and the disease always dies out,if R_0> 1 then there is a unique endemic equilibrium which is globally asymptotically stable and the disease persists.展开更多
Since the first outbreak of Middle East Respiratory Syndrome(MERS),Korea has a quite rapid MERS spread compared to other countries.Possible causes for such a sudden increase include the undiagnosed initial patient and...Since the first outbreak of Middle East Respiratory Syndrome(MERS),Korea has a quite rapid MERS spread compared to other countries.Possible causes for such a sudden increase include the undiagnosed initial patient and lapses in infection control practices.To characterize MERS infection and transmission,this paper applies the period-based discrete SEIR model.Infected people of SEIR model shows a good fit to observed patients and MERS will become extinct around 113 days since the first outbreak.Through an effective quarantine plan,if we can reduce exposable people by 20%,it is estimated that the maximum number of infectious people may decrease by about 69%and MERS fade-out period will be shortened by about 30%.Simulations on assumed model support that Korean government’s two policies to control MERS infection rate are effective in lessening its spread.Simulation on reproduction ratio scenarios in SEIR model indicates that success in early infection control practices is critical for shortening the period of disease fade-out.Even there are some restrictions and assumptions on SEIR model simulation,our simulation results are to be helpful in developing strategies to prevent the infectious diseases like MERS.展开更多
In this article, an infectious model with saturation effect is considered. By using compound matrix theory and a series of theorems associated to qualitative theory of differential equations which are introduced by Mu...In this article, an infectious model with saturation effect is considered. By using compound matrix theory and a series of theorems associated to qualitative theory of differential equations which are introduced by Muldowney and Micheal Li, we study globally stable problem of the model.展开更多
In this paper, we investigate the global stability of an SEIR (Susceptible-Exposed-Infected-Remove) epidemic model with infectious force under intervention strategies. To address this issue, we prove that the basic re...In this paper, we investigate the global stability of an SEIR (Susceptible-Exposed-Infected-Remove) epidemic model with infectious force under intervention strategies. To address this issue, we prove that the basic reproduction number R0 plays an essential role in determining whether the disease extincts or persists. If , there is a unique disease-free equilibrium point of the model which is globally asymptotically stable and the disease dies out, and if , there exists a unique endemic equilibrium point which is globally asymptotically stable and the disease persists.展开更多
基金the International Economics and Foreign Trade Subject Group Research Projects on the Special Development Fund(2013-2014) for Higher Education from the Central to Support the Local,China(No.Y13022)
文摘Stochasticity is introduced into a susceptible-exposed but not infectious-infectious-removed （SEIR） model describing epidemics＇ transmission, via the technique of parameter perturbation which is standard in stochastic population modeling. The existence and uniqueness of the model have been proved in this paper. And E detailed analysis on global asymptotic stability is also carried out.
文摘An epidemic model is a simplified means of describing the transmission of infectious diseases through individuals. The modeling of infectious diseases is a tool which has been used to study the mechanisms by which diseases spread, to predict the future course of an outbreak and to evaluate strategies to control an epidemic. Epidemic models are of many types. Here, SEIR model is discussed. We first discuss the basics of SEIR model. Then it is applied for vector borne diseases. Steady state conditions are derived. A threshold parameter R0 is defined and is shown that the disease will spread only if its value exceeds 1. We have applied the basic model to one specific diseases-malaria and did the sensitivity analysis too using the data for India. We found sensitivity analysis very important as it told us the most sensitive parameter to be taken care of. This makes the work more of practical use. Numerical simulation is done for vector and host which shows the population dynamics in different compartments.
基金Humanities and Social Science Research Planning Fund of the Education Ministry of China(No.15YJCZH2010)the Research Innovation Program of Shanghai Municipal Education Commission,China(No.14YZ134)Shanghai 085 Project for Municipal Universities,China
文摘A kind of stochastic susceptible-exposed but not infectiousinfectious-removed (SEIR) model with constant immigration in incubation period is presented, based on a deterministic SEIR model, via the technique of parameter perturbation which is standard in stochastic population modeling. The influence of the environmental noise as a standard Gaussian white noise on the epidemics' transmission is studied. Furthermore,the condition for the epidemics' persistence is obtained by formulating the corresponding function and using It 's formula. And the asymptotic behavior of the model near the endemic disease equilibrium is also studied. In this way, the decision support is provided in the application of this kind of stochastic SEIR model on the epidemics' prevention and control.
基金supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-DDRSP2501).
文摘The numerical approximation of stochastic partial differential equations(SPDEs),particularly those including q-diffusion,poses considerable challenges due to the requirements for high-order precision,stability amongst random perturbations,and processing efficiency.Because of their simplicity,conventional numerical techniques like the Euler-Maruyama method are frequently employed to solve stochastic differential equations;nonetheless,they may have low-order accuracy and lower stability in stiff or high-resolution situations.This study proposes a novel computational scheme for solving SPDEs arising from a stochastic SEIR model with q-diffusion and a general incidence rate function.A proposed computational scheme can be used to solve stochastic partial differential equations.For spatial discretization,a compact scheme is chosen.The compact scheme can provide a sixth-order accurate solution.The proposed scheme can be considered an extension of the Euler Maruyama method.Stability and consistency in the mean square sense are also provided.For application purposes,the stochastic SEIR model is considered using q-diffusion effects.The scheme is used to solve the stochastic model and compared with the Euler-Maruyama method.The scheme is also compared with nonstandard finite difference method for solving deterministic models.In both cases,it performs better than existing schemes.Incorporating q-diffusion further enhanced the model’s ability to represent realistic spatial-temporal disease dynamics,especially in scenarios where classical diffusion is insufficient.
基金This research is supported by the NNSF of China (19971066)
文摘The SEIR epidemic model studied here includes constant inflows of new susceptibles, exposeds, infectives, and recovereds. This model also incorporates a population size dependent contact rate and a disease-related death. As the infected fraction cannot be eliminated from the population, this kind of model has only the unique endemic equilibrium that is globally asymptotically stable. Under the special case where the new members of immigration are all susceptible, the model considered here shows a threshold phenomenon and a sharp threshold has been obtained. In order to prove the global asymptotical stability of the endemic equilibrium, the authors introduce the change of variable, which can reduce our four-dimensional system to a three-dimensional asymptotical autonomous system with limit equation.
基金Supported by the National Natural Science Foundation of China(11101323)Supported by the Natural Science Basic Research Plan in Shaanxi Province of China(2014JQ1038)Supported by the Xi’an Polytechnic University Innovation Fund for Graduate Students(CX201608)
文摘In this paper,an SEIR model with nonlinear incidence rates are studied.The basic reproduction number R_0 characterizes the disease transmission dynamics: if R_0≤ 1,the disease-free equilibrium is globally asymptotically stable and the disease always dies out,if R_0> 1 then there is a unique endemic equilibrium which is globally asymptotically stable and the disease persists.
基金supported by the Dong-A University research fund.
文摘Since the first outbreak of Middle East Respiratory Syndrome(MERS),Korea has a quite rapid MERS spread compared to other countries.Possible causes for such a sudden increase include the undiagnosed initial patient and lapses in infection control practices.To characterize MERS infection and transmission,this paper applies the period-based discrete SEIR model.Infected people of SEIR model shows a good fit to observed patients and MERS will become extinct around 113 days since the first outbreak.Through an effective quarantine plan,if we can reduce exposable people by 20%,it is estimated that the maximum number of infectious people may decrease by about 69%and MERS fade-out period will be shortened by about 30%.Simulations on assumed model support that Korean government’s two policies to control MERS infection rate are effective in lessening its spread.Simulation on reproduction ratio scenarios in SEIR model indicates that success in early infection control practices is critical for shortening the period of disease fade-out.Even there are some restrictions and assumptions on SEIR model simulation,our simulation results are to be helpful in developing strategies to prevent the infectious diseases like MERS.
基金The NNSF (10171010) of China Major Project of Education Ministry (01061) of China, Key Library for Vegetation Ecology, Education Ministry of China.
文摘In this article, an infectious model with saturation effect is considered. By using compound matrix theory and a series of theorems associated to qualitative theory of differential equations which are introduced by Muldowney and Micheal Li, we study globally stable problem of the model.
文摘In this paper, we investigate the global stability of an SEIR (Susceptible-Exposed-Infected-Remove) epidemic model with infectious force under intervention strategies. To address this issue, we prove that the basic reproduction number R0 plays an essential role in determining whether the disease extincts or persists. If , there is a unique disease-free equilibrium point of the model which is globally asymptotically stable and the disease dies out, and if , there exists a unique endemic equilibrium point which is globally asymptotically stable and the disease persists.
