Reliable numerical treatment with Adams and BDF methods for plant virus propagation model by vector with impact of time lag and density

Abstract

Plant disease incidence rate and impacts can be influenced by viral interactions amongst plant hosts. However, very few mathematical models aim to understand the viral dynamics within plants. In this study, we will analyze the dynamics of two models of virus transmission in plants to incorporate either a time lag or an exposed plant density into the system governed by ODEs. Plant virus propagation model by vector (PVPMV) divided the population into four classes: susceptible plants [S(t)], infectious plants [I(t)], susceptible vectors [X(t)], and infectious vectors [Y(t)]. The approximate solutions for classes S(t), I(t), X(t), and Y(t) are determined by the implementation of exhaustive scenarios with variation in the infection ratio of a susceptible plant by an infected vector, infection ratio of vectors by infected plants, plants' natural fatality rate, plants' increased fatality rate owing to illness, vectors' natural fatality rate, vector replenishment rate, and plants' proliferation rate, numerically by exploiting the knacks of the Adams method (ADM) and backward differentiation formula (BDF). Numerical results and graphical interpretations are portrayed for the analysis of the dynamical behavior of disease by means of variation in physical parameters utilized in the plant virus models.