Modelling the Effect of Incubation and Latent Periods on the Dynamics of Vector-Borne Plant Viral Diseases

Bull Math Biol. 2020 Jul 16;82(7):94. doi: 10.1007/s11538-020-00767-2.

Abstract

Most of the plant viral diseases spread through vectors. In case of the persistently transmitted disease, there is a latent time of infection inside the vector after acquisition of the virus from the infected plant. Again, the plant after getting infectious agent shows an incubation time after the interaction with an infected vector before it becomes diseased. The goal of this work is to study the effect of both incubation delay and latent time on the dynamics of plant disease, and accordingly a delayed model has been proposed. The existence of the equilibria, basic reproductive number ([Formula: see text]) and stability of equilibria have been studied. This study shows the relevance of the presence of two time delays, which may lead to system stabilization.

Keywords: Basic reproduction number; Bifurcation; Stability; Time delay model.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Animals
  • Computer Simulation
  • Disease Vectors
  • Mathematical Concepts
  • Models, Biological*
  • Plant Diseases / prevention & control
  • Plant Diseases / statistics & numerical data
  • Plant Diseases / virology*
  • Time Factors