A Predator-Prey Model With Cross-Species Infectious Diseases Transmitted Through Predation

Generally in a predator-prey system,cross-species infectious diseases are mainly transmitted through contact or predation,and this paper focuses on a system of cross-species infectious diseases spreading through predation routes,since in this system not only can the disease affect the stability of a predator-prey system,but predation can also play a role in limiting the spread of disease.Combined with other scholars' research,this paper establishes a predator-prey system with infectious diseases.Individuals in the system can be classified as healthy predators,infected predators,healthy predators,and predator,and it is assumed that the disease spreads through the contact in the predator population and in the prey population,but only can be transmitted through predation cross the species,that is,the case that contact happened but not predation,no cross-infection occurs.First,in order to discuss the time dynamics of the population,the dynamics of the population scale with time is obtained by numerical simulation.It is found that the system will stabilize after enough time steps,but under different parameters,the composition of surviving species is different.Furthermore,through traversal of the different grouped parameters,the corresponding region segmentation is obtained.And,the parameter thresholds corresponding to different states are obtained.By observing the number and the area of the region segmentation,the influence of different parameters are obtained.It is found that the predation rate is the key parameter to control the extinction of the disease.And under the combined effect of the predation rate and the contact infection rate of the predator and the predator,the disease can completely be eliminated.Finally,the local stability condition is obtained by the stability analysis,and the global stability sufficient condition of the corresponding equilibrium point is obtained.The corresponding conditions for global stability are thinner compared with that of the local stability.