Global dynamic analysis of a vector-borne plant disease model

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 1 Dimensionless variables and parameters (with illustrative parameter values) in system ( 1 )

Parameter	Description	Default value
S	number of the susceptible plant hosts	-
I	number of the infected plant hosts	-
R	number of the recovered plant hosts	-
K	sum of the total plant hosts	50-1,000
X	density of the susceptible insect vectors	-
Y	density of the infected insect vectors	-
N	sum of the total insect vectors density	50-100
$β_{1}$	infection ratio between infected hosts and susceptible vectors	0.01-0.02
$β_{p}$	biting rate of an infected vector on the susceptible host plants	0.01-0.02
$β_{s}$	infection incidence between infected and susceptible hosts	0.01-0.02
$α_{1}$	determines the level at which the force of infection saturates	0.1
$α_{p}$	determines the level at which the force of infection saturates	0.2
$α_{s}$	determines the level at which the force of infection saturates	0.2
γ	the conversion rate of infected hosts to recovered hosts	0-0.25
μ	natural death rate of plant hosts	0-0.1
Λ	birth or immigration of insect vectors	5
m	natural death rate of insect vectors	0-0.5
d	disease-induced mortality of infected hosts	0.1