A Mathematical Modelling and Data-Driven Approach for Understanding the Effects of Climate Change on Cocoa Farming in Nigeria

: Time-delayed modelling

Abstract

Cocoa crops are major export crop in West Africa, but the farming process faces significant challenges, including climate variability. To gain a comprehensive understanding of the effects of change in climate on cocoa production, we conducted a research utilising mathematical modelling and data-driven approaches. This work investigates the impact of climate change on cocoa farming in Nigeria by employing both delay differential equations (DDE) and stochastic delay differential equations (SDDE), along with statistical modelling using the Autoregressive Integrated Moving Average (ARIMA) method.
In our investigation, we developed a time-delayed model to capture the growth dynamics of cocoa from flowering to pod formation and harvesting stages. To account for the seasonal variations in climate, we introduced a periodic forcing function into the model. This resulted in a nonlinear parametrically forced ordinary differential equation (ODE) for the flowering stage, coupled with a DDE for pod formation and harvesting. Through the analysis of the system, we discovered that the cocoa flowering exhibits periodic behaviour when subjected to periodic forcing, where the result suggests that the climatic condition is a significant driving force in the crop dynamic. Furthermore, we investigated the significance of random disturbances in cocoa growth dynamics by extending the model using a system of stochastic delay differential equation. This enabled us to simulate the impact of noise on cocoa production and explore the dynamics of the solution under varying conditions. By employing numerical techniques and simulations, we identified the variability in the crop dynamics with respect to the noise which enable us to gain valuable insights into the behaviour of the system and the consequences of climate variability on cocoa production. Additionally, we examined the statistical modelling of the crop production through the ARIMA model which enhance reasonably forecast of the future production trend. Overall, this research contributes towards a deeper understanding of the complex dynamics of cocoa production in Nigeria and the implications of climate variability on the farming process. The findings hold relevance for policymakers, researchers, and cocoa farmers, as it provide guidance for developing strategies to mitigate the impact of climate variability on cocoa production.

Date of Award	4 Dec 2023
Original language	English
Awarding Institution	University of Bath
Supervisor	Chris Budd (Supervisor) & Ben Adams (Supervisor)