Modelling the dynamics of Cassava Mosaic Disease with non-cassava host plants
Bahati Erick, Maranya Mayengo
Abstract
Cassava Mosaic Disease (CMD) is the prominent cassava disease which compromises cassava production in Africa, both qualitatively and quantitatively for many years. In this study, the mathematical model for the dynamics of CMD with Non-cassava host plant population is formulated and analyzed. The analysis of basic model properties confirmed the positive boundedness of the model solution for all time t≥0. Utilizing the next generation matrix the basic reproduction number R0 is derived and stability analysis is analyzed. Analytical results confirmed that, the disease–free equilibrium point (DFE) is locally asymptotically stable whenever R0<1 and unstable otherwise. The sensitivity index analysis identified mortality rate and the carrying capacity of whiteflies as the most sensitive parameters of model. This implies that, any deliberate efforts towards controlling CMD should be directed into increasing the mortality rate of whiteflies and/or reducing their carrying capacity. In view of this, it is clear that deliberate measures such as the use of pesticides and entomopathogenic fungi which increases the parameter value of ω, and removing non-cassava host plants which will eventually decrease the parameter value of κw may bring significant results in combating CMD compared to the control of other model parameters. The decision regarding the best approach out of the two requires optimal control and cost–effective analysis of available control strategies. Furthermore, the numerical simulation results suggested that Cassava Mosaic Disease (CMD) can be controlled by increasing mortality rate of whiteflies, and the decreasing in the carrying capacity of whiteflies.