Threshold Dynamics Of Ecological Viral Systems With Impulsive Effects On Varying Domain

Based on the theory of impulse differential equation,the current paper will study the threshold dynamics of ecological viral systems with impulsive effects on varying domain,and investigate the plants-pollinators system and the virus infection system respectively.Specifically,the current paper will be discussed from the following two aspects.On the one hand,in order to reveal the population dynamics mechanism caused by the combination of impulsive effects and domain evolution,the second chapter will pass the theory of periodic principal eigenvalue,the properties of impulse function,the estimation of upper and lower bounds,the construction of upper and lower solutions,the montonic iterative theory and other theories and methods,the threshold"ecological reproduction index" of plant-pollinator system with impulsive effects on a periodically evolving domain is defined and its dependence on evolution rate and pulse function are discussed;the extinction-persistence phenomenon of single plant population and the threshold dynamics of plant-pollinator cooperation system are explored successively;the actual impacts of domain evolution and impulsive effects on pollinator propagation are revealed;finally,in the case of plant permanence,the visualized extinction-coexistence results for pollinators with impulsive effects on a periodically evolving domain are obtained by fitting the specific values.On the other hand,in order to explore the impact of pulse vaccination on the virus dynamics,the third chapter will be based on the comparison principle,the construction of upper and lower solutions,monotone iterative theory,Brouwer fixed point theorem,auxiliary functional construction and other methods and theories,by discussing the existence of the infection-free equilibrium point,the immune basic reproduction number of the system is defined;then,the extinction and consistent persistence of the virus are proved by the reproduction number;finally,the existence and global attractivity of the positive steady-state solution of virus infection system are described profoundly.