A Mathematical Model for the Dynamics of Tomato Yellow Leaf Curl Disease in Tanzania.

Abstract

Tomato yellow leaf curl virus (TYLCV) is among the greatest destructive pathogens of tomato. TYLCV is transmitted from whitefly vector to the host plant and vice versa. A mathematical model has been developed and analysed for the interaction between tomato yellow leaf curl disease (TYLCD) and tomato plants under the influence of bemisia tabaci. Positivity and boundedness of the solution has been checked to ensure our model being well posed and then the basic reproductive number (R0) were computed using the next generation matrix method. The stability analysis of our model equilibria were done using various methods. Local and global disease free equilibrium points were analysed using Routh-Hurwitz criteria and the method proposed by Castillo-Chavez et al. (2002) respectively while local and global endemic equilibrium points were analysed using Routh-Hurwitz criteria and Lyapunov direct method respectively. Wecomputed the sensitivity indices of the each parameter in relating to R0 of the model. Numerical simulations were done to validate our theoretical results, and the epidemiological meaning of the key outcomes were briefly discussed. Results indicate that the increase of number of vectors around the field lead to decrease of amount of tomato yield in that field due to TYLCV also as transmission rates decrease, the TYLCD incidence and prevalence also decrease. This study recommends, providing seminars, mass education and other different ways to farmers on transmission and spread of TYLCD and advise them proper method of controlling it.