A Predator-prey Model Of Cross-species Infectious Diseases Transmitted By Contact

The spread of cross-species infectious diseases at different stages will reflect a different law of transmission.Infectious diseases began to spread among the predators,and through mutation,the virus will be transmitted to the predator,and then as the development of infectious diseases,it can spread in the predator species.The establishment of a mathematical model focus on the propagation of cross-species infectious diseases is of great help in understanding its law of propagation.The first chapter of this paper introduces the prevalence of infectious diseases and model profiles,describes the basic models of infectious diseases.The second chapter introduces the basic predator-prey model.Chapter 3 introduces the general method of the basic reproductive number.In Chapter 4,considering that the virus mutation process mentioned above has occurred,and the infectious disease spreads between species only through contact and can only be transmitted from infected prey to susceptible predators by contact,and this process is irreversible.Combined with the actual situation,the individuals will be divided into the following four categories: susceptible predators,infected predators,susceptible predators and infected predators.Further,regardless of the vertical spread of infectious diseases,individual spatial distribution,environmental capacity constraints,the model is established.Then,by solving the ordinary differential equation,five non-negative equilibrium points are obtained.Based on the biological significance of the basic reproductive number and the stability theory of the ordinary differential equation,the local stability of the equilibrium point is discussed qualitatively and quantitatively,and the conditions for the disappearance of infectious diseases are given.Finally,with a given parameter and the initial value,the time dynamic of the system is observed and discussed,and the final state of the system is obtained.The influence of different parameters on the steady state of the system is discussed.The effects of the infection rate between the predator and the reproductive capacity of the predator on the stability of the system are taken into account.Under different cross-species infection rate,how the infection rate between the predator and between the predator affect the stability of the system is discussed.In addition,the effects of the predators' reproductive capacity and the cross-species infection rate on the stability of the system are discussed as the infection rate among the predators is changing.Moreover,the effect of predation rate coupled with other infection rate on the stability of the system is discussed.