The Effects of Climate Variation on Cocoa Farming in Ghana

多年来，常微分方程式一直是用来模拟几种物理现象的基本工具。尽管这些模型产生了一些合理的结果，但人们注意到，这些模型在应用时没有考虑到一些事件的现实情况。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，这导致了时滞微分方程的诞生。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有助于解释响应中延迟的影响的延迟项。因此，这使得该方程更适合于反应延迟或时间滞后的事件--特别是与流行病、自动化、交通流量有关的事件，特别是在农业实践中，在产量和收获过程之前可以观察到时间滞后。因此，为了这项研究的目的，将使用延迟微分方程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，反应的延迟可以在可可豆在收获前成熟的时间段发现。因此，这项研究的目的是使用延迟微分方程建立一个数学模型--该模型将与可可生产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。这项研究将实际应用于一家巧克力公司，该公司需要有弹性的可可供应链来应对未来的巧克力生产。这项研究将为农民提供关于耕作过程、地点和时期的充分信息，以确保在收获阶段实现最大产量。因此，这将导致作物持续用于工业用途的可持续性。

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.