Analyzing The Stability Of An Avian Epidemic Model Caused By Noise

In the ecosystem,analyzing the persistence and extinction of species is always one of the most concerned topics.In the past few decades,researchers have made extensive explorations on the dynamic properties of different types of deterministic influenza models.However,in the real world,due to the existence of various noise,it becomes quite important to study the random biological influenza models in order to clarify the inevitable impact of different kinds of noise.The existing stochastic influenza models mainly focus on the existence and uniqueness of the corresponding solutions and the various asymptotic behaviors of the system when the time tends to infinity.In this thesis,by introducing two distinct kinds of noise into an avian influenza model,several important dynamic behaviors are demonstrated.Furthermore,the transformation law of the internal stability caused by noise is uncovered by combining the probability optimization method.The main results are as follows:(1)The asymptotic behavior analysis of the avian epidemic SI model with Allee effect.In section two,internal noise is introduced into a mature two-dimensional avian influenza model by assuming that stochastic noise is directly proportional to each population,and the threshold conditions of species persistence and extinction are obtained.In addition,the asymptotic properties are also studied.The results show that different intensity of noise has various effects on the persistence and extinction of species.(2)The effects of stochastic noise on the stability of the system based on the probability optimization method.In order to prove that noise plays a decisive role in the stability of the system,in section three,numerical simulations are carried out to show the complete transformation of the final convergence state of the system caused by the introduction of noise.Through the equivalent approximate solution of the FPK equation of the system when the time tends to infinity,we reveal that the system obtains different probability distribution with different noise intensities.Furthermore,by using the ratio of the probabilities at the two approximate equilibrium points,we explain explicitly the reason of how noise causes stability transformation.(3)The important effects of two certain parameters on the stability of the system.In section three,based on two important parameters of the stochastic model ?a and ?a(?a is the transmission rate from infective avian to susceptible avian and ?a is the natural death rate of the avian population),and given the bifurcation analysis results of the deterministic model,the stability of the stochastic system with different noise intensities is explored.The results reveal that the noise will not only greatly reduce the parameter range of the system to maintain bistability,but also make the system to show almost only monostability,that is,persistence or extinction.In addition,it is also illustrated that the noise can significantly promote persistence.The innovation of this thesis is to emphasize on the exploration of the stability transformation caused by the interference of random noise.Additionally,the introduction of the probability optimization method and the use of FPK equation to observe the influence of the noise on population systems have not been seen in previous studiesThe significance of this thesis is to systemically explain the significant changes to the stability of stochastic system caused by noise,for example,the existence of certain intensity of noise is more conducive to the survival of the species.At the same time,the introduction of a novel analysis method also provides an idea for the analysis of other kind of models.Besides,the important parametric intervals which keep the system persistent provide an effective way and theoretical basis for species protection.