In this paper, we propose random fluctuation on contact and recovery rates in deterministic SIR model with disease deaths in nonparametric manner and derive a new stochastic SIR model with distributed time delay and g...In this paper, we propose random fluctuation on contact and recovery rates in deterministic SIR model with disease deaths in nonparametric manner and derive a new stochastic SIR model with distributed time delay and general diffusion coefficients. By analysis of the introduced model, we obtain the sufficient conditions for the regularity, existence and uniqueness of a global solution by means of Lyapunov function. Moreover, we also investigate the stochastic asymptotic stability of disease free equilibria and endemic equilibria of this model. Finally, we illustrate our general results by applications.展开更多
Development of a biostable and biosafe vitreous substitute is highly desirable,but remains a grand challenge.Herein,we propose a novel strategy for constructing a readily administered vitreous substitute based on a th...Development of a biostable and biosafe vitreous substitute is highly desirable,but remains a grand challenge.Herein,we propose a novel strategy for constructing a readily administered vitreous substitute based on a thiol-acrylate clickable polyzwitterion macromonomer.A biocompatible multivinyl polycarboxybetaine(PCB-OAA)macromonomer is designed and synthesized,and mixed with dithiothreitol(DTT)via a Michael addition reaction to form a hydrogel in vitreous cavity.This resultant PCB-OAA hydrogel exhibits controllable gelation time,super anti-fouling ability against proteins and cells,excellent biocompatibility,and approximate key parameters to human vitreous body including equilibrium water content,density,optical properties,modulus.Remarkably,outperforming clinically used silicone oil in biocompatibility,this rapidly formed hydrogel in the vitreous cavity of rabbit eyes remains stable in vitreous cavity,showing an appealing ability to prevent significantly inflammatory response,fibrosis and complications such as raised intraocular pressure(IOP),and cataract formation.This zwitterionic polymer hydrogel holds great potential as a vitreous substitute.展开更多
文摘In this paper, we propose random fluctuation on contact and recovery rates in deterministic SIR model with disease deaths in nonparametric manner and derive a new stochastic SIR model with distributed time delay and general diffusion coefficients. By analysis of the introduced model, we obtain the sufficient conditions for the regularity, existence and uniqueness of a global solution by means of Lyapunov function. Moreover, we also investigate the stochastic asymptotic stability of disease free equilibria and endemic equilibria of this model. Finally, we illustrate our general results by applications.
基金We are thankful for the financial support of the National Natural Science Foundation(Grant Nos.51733006,52073203,31771030).
文摘Development of a biostable and biosafe vitreous substitute is highly desirable,but remains a grand challenge.Herein,we propose a novel strategy for constructing a readily administered vitreous substitute based on a thiol-acrylate clickable polyzwitterion macromonomer.A biocompatible multivinyl polycarboxybetaine(PCB-OAA)macromonomer is designed and synthesized,and mixed with dithiothreitol(DTT)via a Michael addition reaction to form a hydrogel in vitreous cavity.This resultant PCB-OAA hydrogel exhibits controllable gelation time,super anti-fouling ability against proteins and cells,excellent biocompatibility,and approximate key parameters to human vitreous body including equilibrium water content,density,optical properties,modulus.Remarkably,outperforming clinically used silicone oil in biocompatibility,this rapidly formed hydrogel in the vitreous cavity of rabbit eyes remains stable in vitreous cavity,showing an appealing ability to prevent significantly inflammatory response,fibrosis and complications such as raised intraocular pressure(IOP),and cataract formation.This zwitterionic polymer hydrogel holds great potential as a vitreous substitute.
