In the present article we propose a Partial Integro-Differential Equation(PIDE)model to approximate a stochastic SIS compartmental model for viral infection spread.First,an appropriate set of reactions is considered,a...In the present article we propose a Partial Integro-Differential Equation(PIDE)model to approximate a stochastic SIS compartmental model for viral infection spread.First,an appropriate set of reactions is considered,and the corresponding Chemical Master Equation(CME)that describes the evolution of the reaction network as a stochastic process is posed.In this way,the inherent stochastic behaviour of the infection spread is incorporated in the modelling approach.More precisely,by considering that infection is propagated in bursts we obtain the PIDE model as the continuous counterpart to approximate the CME.In this way,the model takes into account that one infectious individual can be in contact with more than one susceptible person at a given time.Moreover,an appropriate semi-Lagrangian numerical method is proposed to efficiently solve the PIDE model.Numerical results and computational times for CME and PIDE models are compared and discussed.We also include a comparison of the main statistics of the PIDE model with the deterministic ODE model.Moreover,we obtain an analytical expression for the stationary solution of the proposed PIDE model,which also allows us to study the disease persistence.The methodology presented in this work is also applied to a real scenario as the COVID-19 pandemic.展开更多
A non-local abstract Cauchy problem with a singular integral is studied, which is a closed system of two evolution equations for a real-valued function and a function-valued function. By proposing an appropriate Banac...A non-local abstract Cauchy problem with a singular integral is studied, which is a closed system of two evolution equations for a real-valued function and a function-valued function. By proposing an appropriate Banach space, the well-posedness of the evolution system is proved under some boundedness and smoothness conditions on the coefficient functions. Furthermore, an isomorphism is established to extend the result to a partial integro-differential equation with a singular convolution kernel, which is a generalized form of the stationary Wigner equation. Our investigation considerably improves the understanding of the open problem concerning the well-posedness of the stationary Wigner equation with in ow boundary conditions.展开更多
We present a probabilistic construction of R^(d)-valued non-linear affine processes with jumps.Given a setΘof affine parameters,we define a family of sublinear expectations on the Skorokhod space under which the cano...We present a probabilistic construction of R^(d)-valued non-linear affine processes with jumps.Given a setΘof affine parameters,we define a family of sublinear expectations on the Skorokhod space under which the canonical process X is a(sublinear)Markov process with a non-linear generator.This yields a tractable model for Knightian uncertainty for which the sublinear expectation of a Markovian functional can be calculated via a partial integro-differential equation.展开更多
基金support from grant FJC2019-041397-I funded by MCIN/AEI/10.13039/501100011033MP and CV acknowledge funding from the Spanish Ministry of Science and Innovation(grant PID2022-141058OB-I00)+1 种基金from the Galician Government(grants ED431C 2022/047 and ED431G 2023/01,both including FEDER financial support)IOM acknowledges support from grant GAIN Opportunius Xunta de Galicia 2021.
文摘In the present article we propose a Partial Integro-Differential Equation(PIDE)model to approximate a stochastic SIS compartmental model for viral infection spread.First,an appropriate set of reactions is considered,and the corresponding Chemical Master Equation(CME)that describes the evolution of the reaction network as a stochastic process is posed.In this way,the inherent stochastic behaviour of the infection spread is incorporated in the modelling approach.More precisely,by considering that infection is propagated in bursts we obtain the PIDE model as the continuous counterpart to approximate the CME.In this way,the model takes into account that one infectious individual can be in contact with more than one susceptible person at a given time.Moreover,an appropriate semi-Lagrangian numerical method is proposed to efficiently solve the PIDE model.Numerical results and computational times for CME and PIDE models are compared and discussed.We also include a comparison of the main statistics of the PIDE model with the deterministic ODE model.Moreover,we obtain an analytical expression for the stationary solution of the proposed PIDE model,which also allows us to study the disease persistence.The methodology presented in this work is also applied to a real scenario as the COVID-19 pandemic.
基金National Natural Science Foundation of China (Grant Nos. 1167103& 91630130, 91434201, 11421101).
文摘A non-local abstract Cauchy problem with a singular integral is studied, which is a closed system of two evolution equations for a real-valued function and a function-valued function. By proposing an appropriate Banach space, the well-posedness of the evolution system is proved under some boundedness and smoothness conditions on the coefficient functions. Furthermore, an isomorphism is established to extend the result to a partial integro-differential equation with a singular convolution kernel, which is a generalized form of the stationary Wigner equation. Our investigation considerably improves the understanding of the open problem concerning the well-posedness of the stationary Wigner equation with in ow boundary conditions.
文摘We present a probabilistic construction of R^(d)-valued non-linear affine processes with jumps.Given a setΘof affine parameters,we define a family of sublinear expectations on the Skorokhod space under which the canonical process X is a(sublinear)Markov process with a non-linear generator.This yields a tractable model for Knightian uncertainty for which the sublinear expectation of a Markovian functional can be calculated via a partial integro-differential equation.
