Research On A Hybrid Predator-prey Model And A Multi-species Brucellosis Model With Cross Infection

Population and epidemic dynamic models play an important role in sustainable de-velopment of ecosystems and prevetion and control of infectious diseases,in which many domestic and foreign experts and scholars have studied broadly and deeply,and obtained a number of remarkable results.To study ecological population and brucellosis,a hybrid predator-prey model with general model with general functional response under seasonal succession,a hybrid predator-prey model with general functional response under season-al succession alternating between Gompertz and Logistic growth connected by impulsive pertubations,and a multi-species reaction-diffusion model with brucellosis cross infenc-tion are established in this paper.Global dynamics of which are analyzed,respectively.The main research contents can be arranged as follows:1.In the first section,the relevant research backgrounds and some current and related research achievements about population and epidemic models are briefly introduced in this paper.Finally,main work of this paper is summarized.2.In the second section,a hybrid predator-prey model with general functional re-sponse under seasonal succession is established.The boundedness and permanence of the solution of system are discussed by comparison principle,and the corresponding judgment criteria are given.The availability of the theoretical result is demonstrated by numerical simulation lastly.3.In the third section,a hybrid predator-prey model with general functional response and impulsive perturbations under seasonal succession.By discrete dynamical systems theory and comparison principle of impulsive differential equation and other analytical methods,the ultimately boundedness,permanence and global attractivity of predator-free periodic solution of the system are obtained.The availability of theoretical results are demonstrated by numerical simulation in the end.4.In the fourth section,a multi-species reaction-diffusion with brucellosis cross infection SV EI model is established.Basic reproduction number R₀of the system is obtained.The well-posedness,boundedness of the solution of system are discussed by the theory of reaction diffusion equation.Through parabolic equation comparison principle and other analytical methods,the global asymptotic stability of disease-free steady state and the uniform persistence of positive steady state are obtained.