In this paper we put forward a viral propagation model with a nonlinear infection rate and free boundaries and investigate the dynamical properties.This model is composed of two ordinary differential equations and one...In this paper we put forward a viral propagation model with a nonlinear infection rate and free boundaries and investigate the dynamical properties.This model is composed of two ordinary differential equations and one partial differential equation,in which the spatial range of the first equation is the whole space R,and the last two equations have free boundaries.As a new mathematical model,we prove the existence,uniqueness and uniform estimates of the global solution,and provide the criteria for spreading and vanishing,and the long time behavior of the solution components u,v and w.Comparing this model with the corresponding ordinary differential systems,the basic reproduction number R_(0) plays a different role.We find that when R_(0)≤1,the virus cannot spread successfully;when R_(0)>1,the successful spread of the virus depends on the initial value and varying parameters.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11771110 and 11971128)。
文摘In this paper we put forward a viral propagation model with a nonlinear infection rate and free boundaries and investigate the dynamical properties.This model is composed of two ordinary differential equations and one partial differential equation,in which the spatial range of the first equation is the whole space R,and the last two equations have free boundaries.As a new mathematical model,we prove the existence,uniqueness and uniform estimates of the global solution,and provide the criteria for spreading and vanishing,and the long time behavior of the solution components u,v and w.Comparing this model with the corresponding ordinary differential systems,the basic reproduction number R_(0) plays a different role.We find that when R_(0)≤1,the virus cannot spread successfully;when R_(0)>1,the successful spread of the virus depends on the initial value and varying parameters.
