The impact of poaching and regime switching on the dynamics of single-species model

Abstract

It is widely recognized that the criminal act of poaching has brought tremendous damage to biodiversity. This paper employs a stochastic single-species model with regime switching to investigate the impact of poaching. We first carry out the survival analysis and obtain sufficient conditions for the extinction and persistence in mean of the single-species population. Then, we show that the model is positive recurrent by constructing suitable Lyapunov function. Finally, numerical simulations are carried out to support our theoretical results. It is found that: (i) As the intensity of poaching increases, the odds of being at risk of extinction increases for the single-species population. (ii) The regime switching can suppress the extinction of the single-species population. (iii) The white noise is detrimental to the survival of the single-species population. (iv) Increasing the criminal cost of poaching and establishing animal sanctuaries are important ways to protect biodiversity.

Keywords

• stochastic single species model
• poaching
• regime switching
• positive recurrent
• survival analysis