Human-Wildlife interactions in a tropical forest context: modeling, analysis and simulations

TL;DR

This work develops and analyzes a two-zone human-wildlife model capturing migration between a domestic village and a tropical forest, where hunting and habitat anthropisation influence wildlife dynamics. By combining a quasi-steady state approach and monotone (competitive) system theory, the authors derive conditions under which extinction, coexistence, or periodic oscillations arise, highlighting how immigration and anthropisation shift these thresholds. They establish global boundedness, local and global stability results, and compare reduced and full models, revealing the limits of QSSA for finite-time dynamics. Numerical simulations and bifurcation analyses contextualize the ecological implications for conservation and human livelihoods in South Cameroon, emphasizing the need to control hunting and habitat disturbance to sustain wildlife populations. The work also demonstrates how reformulations to competitive frameworks enable powerful, globally applicable insights into complex ecological interactions under human pressure.

Abstract

Anthropisation and excessive hunting in tropical forests threaten biodiversity, ecosystem maintenance and human food security. In this article, we focus on the issue of coexistence between humans and wildlife in an anthropised environment. Assuming that the human population moves between its residential area and the surrounding forest to hunt, we study a resource-consumer model with consumer migration. A comprehensive analysis of the system is carried out using classical theory and monotone systems theory. We show that the possibilities for long-term coexistence between human populations and wildlife populations are determined by hunting rate thresholds. Depending on the level of anthropisation and the hunting rate, the system may converge towards a limit cycle or a co-existence equilibrium. However, the conditions for coexistence become more difficult as anthropisation increases. Numerical simulations are provided to illustrate the theoretical results.

Figures (10)

• Figure 1: System flow chart.
• Figure 2: Orbits of systems \ref{['equation:HDFW']} and \ref{['equation:HDFWHW']} for $\epsilon = 0.1$, $\epsilon = 1/365$ and $\epsilon = 10^{-4}$ in the $H_D - F_W$ plane. In the two first cases, the non-reduced system \ref{['equation:HDFWHW']} converges towards a limit cycle while for $\epsilon = 10^{-4}$ it converges towards $EE^{HF_W}$, as does the reduced system \ref{['equation:HDFWHW']}. Parameters values: $\mathcal{I} = 0$, $\beta = 0$, $r_F = 0.6$, $K_F = 7250$, $\alpha = 0.1$, $\lambda_{F} = 0.015$, $e = 0.2$, $\mu_D = 0.02$, $f_D = 0.0$, $\tilde{m}_D = 0.0019$, $\tilde{m}_W = 0.0066$.
• Figure 3: Bifurcation diagram when $\mathcal{I} = 0$ and $\beta = 0$.
• Figure 4: Bifurcation diagram when $\mathcal{I} = 0.1$ and $\beta = 0$.
• Figure 5: Bifurcation diagram when $\mathcal{I} = 1$ and $\beta = 0$.

Theorems & Definitions (61)

• Remark 1
• Proposition 2
• proof
• Proposition 3
• proof
• Proposition 4
• proof
• Proposition 5
• Remark 6
• proof