Theoretical Assessment of the Impact of Water Stress on Plants Production: Case of Banana-Plantain

Abstract

The aim of this paper is to investigate the role of water stress on plants production. We propose a mathematical model for the dynamics growth of plants that takes into account the concentration of available water in the soil, water stress, plant production and plants compensation. Sensitivity analysis of the model has been performed in order to determine the impact of related parameters on the dynamics growth of plants. We present the theoretical analysis of the model with and without water stress. More precisely, we show that the full model is well-posedness. For each model, we compute the trivial equilibria and derive two thresholds parameters that determine the outcome of water stress within a plantation. Further, we perform numerical simulation on the case of banana-plantain simulations to support the theory. We found that the Hopf bifurcation occurs for a specific value of the water absorption rate of unstressed plants. The impact of the water stress on the banana-plantain production is also numerically investigated. After, the role of the water stress on the plant production is numerically investigated. We found that the water stress can cause about 68.16% of loss of banana-plantain production within a plantation with 1600 rejets initially planted. This suggests that climate change plays a detrimental role on banana-plantains production.