The Effects of Climate Variation on Cocoa Farming in Ghana

多年来，常微分方程一直是用于模拟多种物理现象的重要工具。尽管这些模型产生了一些合理的结果，但据观察，这些模型在应用时没有考虑到许多事件的现实。这方面的一个很好的例子是将这些模型应用于人口动态-可以观察到人口对环境变化的反应有停顿。因此，人们寻求一种更现实的模型来描述许多物理事件，这导致了延迟微分方程的诞生。延迟微分方程区别于常微分方程的一个主要特征是包含了延迟项，这有助于解释响应中延迟的影响。因此，这使得方程更适合于在响应中经历延迟或时滞的事件-特别是与流行病、自动化、交通流量以及特别是在产量和收获过程之前可以观察到时滞的农业实践有关的事件。因此，为了这项研究的目的，延迟微分方程将被用来构建一个数学模型，以确定气候变化对加纳可可种植的影响。在这种情况下，可以在收获前可可豆荚成熟的时间段内发现响应延迟。因此，本研究的目的是使用延迟微分方程建立一个数学模型，该模型将与可可产量和当地气候变化的数据联系起来。这一模型将应用于可可生产，以了解影响可可生产时空变化的气候因素。本研究将实际应用于一家巧克力公司，该公司未来的巧克力生产需要一个清洁的可可供应链。这项研究将为农民提供有关种植过程、地点和时期的充分信息，以确保收获阶段的最大产量。因此，这将导致作物的可持续性，以供连续的工业使用。

For many years, Ordinary Differential Equations have been an essential tool used in the modelling of several physical phenomena. Even though these model produce some reasonable results, it is observed that the models do not take into account the reality of a number of events when being applied. A good example of this is in applying these models to population dynamics- where it can be observed that there are pauses in the population's response to change in the environment. As such, a more realistic model is sought after to describe many physical events and this has led to the birth of the Delay Differential Equation. A major characteristic that differentiates the Delay Differential Equation from the Ordinary Differential Equation is the inclusion of the delay term that helps to account for the effect of delays in responses. This therefore, makes the equation more suitable for the event which experiences delay or time lag in responses- especially in relation to epidemics, automation, traffic flow and particularly agricultural practices where a time lag can be observed before the yield and harvesting process. Hence, for the purpose of this research, the Delay Differential Equation will be used to construct a mathematical model to determine the effect of climate variation on cocoa farming in Ghana. In this case, the delay in response can be found in the period of time that the cocoa pods are ripening before harvest. The objective of this research therefore, is to use the Delay Differential Equation to build a mathematical model- which will be linked with the data on cocoa production and local climate variation. This model will be applied in the context of cocoa production in order to understand the climatic factors that influence the temporal and spatial variation of cocoa production. This research will be practically applied in a chocolate company which requires a resiliant cocoa supply chain for the future of chocolate production. This research will provide farmers with adequate information about the farming process, location and period which the growing should be implemented to ensure maximum yield during the harvesting phase. This will therefore, lead to sustainability of the crop for continuous industrial use.