D.A. Zulfiyana, Y. Fuad, B.P. Prawoto
Citrus plant is one of the biggest production fruit plants in the world as well as in Indonesia. Citrus plant can be infected with a disease by virus, such as Citrus Tristeza Virus (CTV) propagated by Toxoptera citricida. Based on the well-known SIR-SI model, it was derived the CTV propagation model of the citrus plant. The obtained model involves citrus plant which consists of subpopulation susceptible, infected, and recovered. While the vector's population were subpopulation susceptible and infected insects. Then two equilibrium points were determined for the model with and without delay, i.e. the disease-free equilibrium and the endemic equilibrium points. Hence the obtained model, which were analysed around two equilibrium points with and without delay, were asymptotic stable. Moreover, the basic reproduction number (p) was determined for obtaining the parameter value m. The numerical simulation with and without delay were demonstrated and the responses of the model were asymptotic stable. By applying time delays, it is concluded that the spread of CTV on citrus plant can be inhibited by accelerating the harvest before it is infected to the virus, so that citrus fruits can be harvested more better than without giving any delay. © Published under licence by IOP Publishing Ltd.
Department of Mathematics, Universitas Negeri Surabaya, Indonesia
