This paper presents a law of large numbers result,as the size of the population tends to infinity,of SIR stochastic epidemic models,for a population distributed over distinct patches(with migrations between them)and d...This paper presents a law of large numbers result,as the size of the population tends to infinity,of SIR stochastic epidemic models,for a population distributed over distinct patches(with migrations between them)and distinct groups(possibly age groups).The limit is a set of Volterra-type integral equations,and the result shows the effects of both spatial and population heterogeneity.The novelty of the model is that the infectivity of an infected individual is infection age dependent.More precisely,to each infected individual is attached a random infection-age dependent infectivity function,such that the various random functions attached to distinct individuals are i.i.d.The proof involves a novel construction of a sequence of i.i.d.processes to invoke the law of large numbers for processes in,by using the solution of a MacKean-Vlasov type Poisson-driven stochastic equation(as in the propagation of chaos theory).We also establish an identity using the Feynman-Kac formula for an adjoint backward ODE.The advantage of this approach is that it assumes much weaker conditions on the random infectivity functions than our earlier work for the homogeneous model in[20],where standard tightness criteria for convergence of stochastic processes were employed.To illustrate this new approach,we first explain the new proof under the weak assumptions for the homogeneous model,and then describe the multipatch-multigroup model and prove the law of large numbers for that model.展开更多
OBJECTIVE:To investigate the effect of didrovaltrate on L-type calcium current(I Ca-L) in rabbit ventricular myocytes.METHODS:We used the whole cell patch clamp recording technique.RESULTS:Didrovaltrate at concentrati...OBJECTIVE:To investigate the effect of didrovaltrate on L-type calcium current(I Ca-L) in rabbit ventricular myocytes.METHODS:We used the whole cell patch clamp recording technique.RESULTS:Didrovaltrate at concentrations of 30 μg/L and 100 μg/L significantly decreased peak I Ca-L(I Ca-Lmax) from(6.01±0.48) pA/pF to(3.45±0.27) pA/pF and(2.16 ± 0.19) pA/pF(42.6% and 64.1%,n=8,P< 0.01),respectively.Didrovaltrate shifted upwards the current-voltage curves of I Ca-L without changing their active,peak and reverse potentials.Didrovaltrate affected the steady-state inactivation of I Ca-L.The half activation potential(V 1/2) was significantly shifted from(-26 ± 2) to(-36 ± 3) mV(n=6,P<0.05),with a significant change in the slope factor(k)(from 8.8 ± 0.8 to 11.1 ± 0.9,n=6,P<0.05).Didrovaltrate did not affect the activation curve.CONCLUSION:Didrovaltrate blocks I Ca-L in a concentration-dependent manner and probably inhibits I Ca-L in its inactive state,which may contribute to its cardiovascular effect.展开更多
为探讨莲心碱 (liensinine,L ien)对心肌离子流的影响及抗心律失常作用机制。采用全细胞膜片钳技术 ,记录了 L ien对单个豚鼠心肌细胞动作电位 (AP)及纳电流 (INa)与 L -型钙电流 (ICa- L)的影响。 L ien 3～ 30μmol/ L 可剂量依赖性...为探讨莲心碱 (liensinine,L ien)对心肌离子流的影响及抗心律失常作用机制。采用全细胞膜片钳技术 ,记录了 L ien对单个豚鼠心肌细胞动作电位 (AP)及纳电流 (INa)与 L -型钙电流 (ICa- L)的影响。 L ien 3～ 30μmol/ L 可剂量依赖性地降低 AP幅度 (APA)、静息电位 (RP) ,延长 AP时程。 L ien10 ,30 μm ol/ L 分别使 INa及 ICa- L从给药前的 (8.6± 2 .3) n A和 (75 8± 177) p A降至 (5 .4± 1.7)、(2 .2± 1.6 ) n A和 (335± 12 2 )、(137±10 0 ) p A。L ine10 μmol/ L 抑制 INa和 ICa- L的 I- V曲线并使后者的峰值电流电位略右移。结果表明 L ien有钠、L -型钙通道阻滞作用 。展开更多
文摘This paper presents a law of large numbers result,as the size of the population tends to infinity,of SIR stochastic epidemic models,for a population distributed over distinct patches(with migrations between them)and distinct groups(possibly age groups).The limit is a set of Volterra-type integral equations,and the result shows the effects of both spatial and population heterogeneity.The novelty of the model is that the infectivity of an infected individual is infection age dependent.More precisely,to each infected individual is attached a random infection-age dependent infectivity function,such that the various random functions attached to distinct individuals are i.i.d.The proof involves a novel construction of a sequence of i.i.d.processes to invoke the law of large numbers for processes in,by using the solution of a MacKean-Vlasov type Poisson-driven stochastic equation(as in the propagation of chaos theory).We also establish an identity using the Feynman-Kac formula for an adjoint backward ODE.The advantage of this approach is that it assumes much weaker conditions on the random infectivity functions than our earlier work for the homogeneous model in[20],where standard tightness criteria for convergence of stochastic processes were employed.To illustrate this new approach,we first explain the new proof under the weak assumptions for the homogeneous model,and then describe the multipatch-multigroup model and prove the law of large numbers for that model.
基金Supported by the Chinese National Science Foundation (No.81170090)the Science Foundation for Distinguished Young Scholars of Fujian Province(No.2009D015)+1 种基金the Science Foundation for Distinguished Young Scholars of Xiamen(No.3502Z20116009)the Science Foundation of Science and Technology of the Bureau of Xiamen(No. 3502Z20094006)
文摘OBJECTIVE:To investigate the effect of didrovaltrate on L-type calcium current(I Ca-L) in rabbit ventricular myocytes.METHODS:We used the whole cell patch clamp recording technique.RESULTS:Didrovaltrate at concentrations of 30 μg/L and 100 μg/L significantly decreased peak I Ca-L(I Ca-Lmax) from(6.01±0.48) pA/pF to(3.45±0.27) pA/pF and(2.16 ± 0.19) pA/pF(42.6% and 64.1%,n=8,P< 0.01),respectively.Didrovaltrate shifted upwards the current-voltage curves of I Ca-L without changing their active,peak and reverse potentials.Didrovaltrate affected the steady-state inactivation of I Ca-L.The half activation potential(V 1/2) was significantly shifted from(-26 ± 2) to(-36 ± 3) mV(n=6,P<0.05),with a significant change in the slope factor(k)(from 8.8 ± 0.8 to 11.1 ± 0.9,n=6,P<0.05).Didrovaltrate did not affect the activation curve.CONCLUSION:Didrovaltrate blocks I Ca-L in a concentration-dependent manner and probably inhibits I Ca-L in its inactive state,which may contribute to its cardiovascular effect.
