This work investigates the effect of soil and rainfall on the farm level yield of crops with an emphasis on cocoa crops. Cocoa is an important crop that is predominantly grown in the western part of Africa. However, there have been fluctuations and declining trends in production and many factors have been identified to be responsible. A significant factor is the effect of climate variation and this result in low farm-level yield. To understand the contribution of climate variability on the farm level yield, we construct and analyse a time-delayed model for the effect of soil and rainfall on production. This work uses a system of delay differential equations to model the crop transition from the flowering stage to pod formation and harvesting. We introduce a forcing function into the model to account for the soil-rainfall interaction and then conduct a sensitivity analysis to understand the effect of model parameters. This leads to a novel nonlinear ODE for the flowering with periodically varying coefficients which are coupled to a DDE for the pod formation and harvesting.
Results/Conclusions
We presented a model that accounts for the effect of soil - rainfall interactions on cocoa yields. we studied an approach for investigating the behaviour of the crop in the major stage at the farm level and the formulated time-delayed model adequately captures the transition behaviour of the system from the flowering to harvesting stage. Using the formulated nonlinear parametrically forced delay differential equation enables us to successfully predict the time delay between the pods' formation and harvest. Also, it captures the periodic pattern of the rainfall which leads to the periodic flowering and podding. The growth parameters are obtained through a nonlinear least-squares fit on the rainfall data and it established the rainfall representation which is consistent with a periodic function of a 6-month period. Finally, the model helps to successfully simulate the behaviour of cocoa yield based on rainfall patterns and capture the variation of the shape of the cumulative yield.
