【摘 要】
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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 whic
【机 构】
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School of Mathematics,Harbin Institute of Technology,Harbin 150001,China;School of Science and Engin
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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 R0 plays a different role.We find that when R0 ≤ 1,the virus cannot spread successfully;when R0 ＞ 1,the successful spread of the virus depends on the initial value and varying parameters.
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