Impact of water stress on plants production: A study case of banana-plantain

This paper has been motivated by the following ecological question: how influential is the water stress on plants production? The aim of this paper is to investigate the impact of water stress and irrigation 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, the absorption of water by plants, water stress, the plants production and the plants compensation. We present the theoretical analysis of the model. More precisely, we show that the model is well-posed. We also compute trivial equilibria and derive a threshold parameter that determines the outcome of water stress within a plantation. Further, we perform a numerical simulation in the case of banana-plantain plant to support and valid theoretical results. 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. We found that the water stress can cause about 62.57% tons of loss of banana-plantain production within a plantation with 1600 rejects initially planted. We also consider the irrigation as a control parameter of water stress. We found that the irrigation increases the stressed plant production to more than 60% for 1600 rejects initially planted. This suggests that climate change may play a detrimental role on banana-plantains production. We also investigate the role of the type of soil in banana-plantain production. Our finding suggests that the Fine Sandy Loam soil is more resilient to water stress than Silty Clay and Loamy soils.