Analysis and optimal control measures of diseases in cassava population

Cassava amongst other crops is ranked currently as the third most essential source of carbohydrate in the tropics and a major food source in Africa. In spite of these gains, cassava production is highly threatened by pathogen-causing diseases. In this study, a deterministic compartmental model is developed to investigate the effect of these diseases on cassava production. The local and global stabilities of the disease free and endemic equilibrium states of the model without control are analyzed. The model is extended to incorporate control techniques necessary in eradicating cassava diseases. Optimal control theory is applied on the control model to explore the impact of the introduction of resistant cassava plant, the use of all other traditional practices and the application of pesticides in the prevention and eradication of diseases in cassava production. Numerical simulation of the models are carried out and results obtained indicates that introduction of control measures should be done largely at the onset of cassava planting by introducing resistant cassava stems to reduce the spread of the disease and also maintain minimum cost for production and thereby maximize profit from its yield. The cost effectiveness analysis agreed with our earlier analysis and shows that the best and effective control is the use of resistant cassava stem together with the IPM approach.