Stationary distribution and global stability of stochastic predator-prey model with disease in prey population

Abstract

In this paper, a new stochastic four-species predator-prey model with disease in the first prey is proposed and studied. First, we present the stochastic model with some biological assumptions and establish the existence of globally positive solutions. Moreover, a condition for species to be permanent and extinction is provided. The above properties can help to save the dangered population in the ecosystem. Through Lyapunov functions, we discuss the asymptotic stability of a positive equilibrium solution for our model. Furthermore, it is also shown that the system has a stationary distribution and indicating the existence of a stable biotic community. Finally, our results of the proposed model have revealed the effect of random fluctuations on the four species ecosystem when adding the alternative food sources for the predator population. To illustrate our theoretical findings, some numerical simulations are presented.

Keywords:

• Predator-prey system
• stochastically permanent
• extinction
• stochastic stability
• stationary distribution

2020 Mathematics Subject Classifications:

• 60H10
• 60H30
• 92D30
• 93E15

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Our paper contains numerical experimental results, and values for these experiments are included in the paper. The data is freely available.

Additional information

Funding

The work of first author is supported by the DST-INSPIRE Fellowship [grant number DST/INSPIRE Fellowship/2017/IF170244], Department of Science and Technology, New Delhi. The second author is thankful to the DST-FIST [grant number SR/FST/MSI-115/2016(Level-I)], Department of Science and Technology, New Delhi for providing financial support. The last author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) [grant number 2021R1F1A1048937].