Nonlinearity and randomness are both the essential attributes for the real world,and the case is the same for the models of infectious diseases,for which the deterministic models can not give a complete picture of the...Nonlinearity and randomness are both the essential attributes for the real world,and the case is the same for the models of infectious diseases,for which the deterministic models can not give a complete picture of the evolution.However,although there has been a lot of work on stochastic epidemic models,most of them focus mainly on qualitative properties,which makes us somewhat ignore the original meaning of the parameter value.In this paper we extend the classic susceptible-infectious-removed(SIR)epidemic model by adding a white noise excitation and then we utilize the large deviation theory to quantitatively study the long-term coexistence exit problem with epidemic.Finally,in order to extend the meaning of parameters in the corresponding deterministic system,we tentatively introduce two new thresholds which then prove rational.展开更多
The prediction of the behavior of people in a disaster has a useful role to play in the design of urban structures such as department stores, schools, and office buildings. We focus on using emergency exit signs to ef...The prediction of the behavior of people in a disaster has a useful role to play in the design of urban structures such as department stores, schools, and office buildings. We focus on using emergency exit signs to effectively guide the evacuation of people on a floor with a dynamically changing layout. A multi-agent simulation is developed to simulate the behavior of evacuees on a floor. A mathematical model is constructed to obtain optimal sign locations to efficiently assist evacuation under the condition that obstacles are dynamically generated on the floor. The optimal sign locations are calculated by the mathematical model. Then, the developed simulation is performed to evaluate the effectiveness of the emergency exit signs and the behavior of evacuees on simple layout models using the calculated optimal sign locations.展开更多
基金supported by the National Natural Science Foundation of China(No.12172167)。
文摘Nonlinearity and randomness are both the essential attributes for the real world,and the case is the same for the models of infectious diseases,for which the deterministic models can not give a complete picture of the evolution.However,although there has been a lot of work on stochastic epidemic models,most of them focus mainly on qualitative properties,which makes us somewhat ignore the original meaning of the parameter value.In this paper we extend the classic susceptible-infectious-removed(SIR)epidemic model by adding a white noise excitation and then we utilize the large deviation theory to quantitatively study the long-term coexistence exit problem with epidemic.Finally,in order to extend the meaning of parameters in the corresponding deterministic system,we tentatively introduce two new thresholds which then prove rational.
文摘The prediction of the behavior of people in a disaster has a useful role to play in the design of urban structures such as department stores, schools, and office buildings. We focus on using emergency exit signs to effectively guide the evacuation of people on a floor with a dynamically changing layout. A multi-agent simulation is developed to simulate the behavior of evacuees on a floor. A mathematical model is constructed to obtain optimal sign locations to efficiently assist evacuation under the condition that obstacles are dynamically generated on the floor. The optimal sign locations are calculated by the mathematical model. Then, the developed simulation is performed to evaluate the effectiveness of the emergency exit signs and the behavior of evacuees on simple layout models using the calculated optimal sign locations.
