Modeling the dynamics and control of cassava mosaic disease

Abstract

Cassava mosaic disease (CMD) is caused by cassava mosaic virus (CMV) and is transmitted by the whitefly vector called Bemisia tabaci. In this study, the deterministic model for transmission dynamics of CMD is formulated by considering the whitefly vector, cassava resistant and sus- ceptible breeds, and infected cassava. The basic reproduction number R0 and sensitivity index for each parameter with respect to basic reproduction number R0 are computed to determine which parameters are sensitive to the dynamics of cassava mosaic disease. Analysis shows that the death rate of whitefly vectors, infection rate for susceptible vectors, the number of vectors that can be supported and recruitment rate of whitefly are most sensitive parameters to the dy- namics of cassava mosaic disease. The disease stability at cassava mosaic free equilibrium was investigated by using metzler matrix (box invariance). We found that disease free equilibrium is asymptotically stable when R0 < 1. By using Lyapunovs direct method and LaSalles invariant principle, endemic equilibrium is asymptotically stable when R0 > 1. Numerical simulation in- dicates that, cassava new infections increase as many whitefly vectors are recruited and acquire cassava mosaic disease. When controls are not considered, the susceptible breed and cassava resistant breed will be wiped out after five and ten months respectively. To control the disease interventions which target whitefly vectors, farmers are encouraged to apply control strategies such as spraying of insecticide, using of vector-resistant varieties, phytosanitation which in- volves the removal of infected cassava plants from the farm, crop hygiene and the use of free stem cutting method. Analysis shows that spraying of insecticide and the death of whitefly vec- tor plays the most important role in the eradication of CMD. This study concludes that, spraying of insecticide is the possible way to get rid of both infected and susceptible vector as well as the removal of infected cassava plants from the farm will help to reduce the contact rate between plants and vectors.