Effect of Cannibalism on Disease Transmission in Natural Populations

Mengting Yan ； Ning Li

《World Scientific Research Journal》 8卷4期 (2022/04) Pp. 103-121

https://doi.org/10.6911/WSRJ.202204_8(4).0014

摘要

This paper proposes a Leslie‐Gower predator‐prey system with cannibalism and disease in predators. The main purpose of this study is to understand the effect of cannibalism on disease, then we analyzes the cannibalism behavior through the following aspects. Firstly, the local dynamical behaviors of the system near the equilibrium points are studied, then the global dynamical behaviors of the system are analyzed by using the Lyapunov function. Next, the occurrence of Hopf bifurcation around the internal steady state is explored. Moreover, the impact of cannibalism on the stability of population dynamics and whether it can eliminate the disease are investigated. Finally, numerical simulation is carried out and we observe that cannibalism could stabilize the population system and remove disease from the predator population. Thus, in practice, disease can be controlled by regulating cannibalism, which gives a new disease control mechanism.

關鍵字

Leslie‐Gower model ； Cannibalism ； Disease transmission ； Holling type II ； Lyapunov function ； Hopf bifurcation

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