A Fractional Differential Equation Model for the Spread of Potato Leaf Roll Virus (Plrv) on Potatoes

Abstract

Potatoes infected with the PLRV virus will experience a decrease in production up to 90%. In this paper, The PLRV distribution fractional differential equation model with potato and vector populations is reformulated by adding one new parameter, namely the rate of vector death due to predators. The model is divided into susceptible and infected classes. The PLRV dispersion model was developed and converted to a fractional order form for 0<σ ≤ 1. Next, the invariant region, positive solutions, basic reproduction number, equilibrium point, and stability were determined. Based on the stability analysis, it is shown that the stability of the disease-free equilibrium point is locally stable and globally stable if the basic reproduction number (R0)<1, and the stability of the endemic equilibrium point is globally stable if the basic reproduction number (R0)>1. Numerical solutions were also carried out to determine the effect of several parameters on the PLRV distribution model on potatoes. The numerical solution results show that the elimination rate of infected potatoes and the infection rate of potatoes have a significant role in controlling the spread of PLRV in potatoes.