MODELING THE TEMPORAL PRIMARY SPREAD OF AFRICAN CASSAVA MOSAIC-VIRUS INTO PLANTINGS

The rate of temporal primary spread of African cassava mosaic virus into cassava plantings has been shown to be dependent on the planting date, P, and on the plant age, t. In this paper, the relationships between the rate of disease progress, P, and t were expressed mathematically. The appropriate functions were chosen, and their parameters were derived by nonlinear regression using a set of experimental data obtained at Adiopodoume (Ivory Coast, West Africa). The resulting equations were incorporated into a monomolecular model with a variable rate r(P) (the product of the change of rate of disease incidence when P was fixed), k, a constant, y, the disease incidence, and t, the time: dy/dt = k.r(P)(t)(1 - y). The modeled disease progress curves were obtained by numerical integration of the differential equation. The close fit between the modeled and the experimental curves showed that the main trends of the epidemics were represented. The model was tested with a set of data obtained in Tanzania (East Africa), and the structure of the model was validated, as there was also a good fit between the observed and modeled disease progress curves. Finally, assumptions were made on the remaining variation around the modeled curves.