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Theory and Modern Applications

Table 1 Definition, dimension and parameter values of model (1)

From: Dynamical features of pine wilt disease through stability, sensitivity and optimal control

Parameter

Description

Dimension

Value

\(\lambda _{h}\)

Input rate of pine trees

Trees × year−1

0.601

\(\lambda _{v}\)

Emergence rate of adult pine sawyer

Pine sawyer × year−1

0.948

\(\mu _{h}\)

Felling rate of healthy pine trees

year−1

0.8838

δ

Expolitation rate of infected pine trees

year−1

0.98

\(\mu _{v}\)

Pine sawyer mortality rate

year−1

0.857

α

Transmission rate per contact through maturation feeding

year−1

0.00323

ϕ

Mean number of contacts of adult pine sawyer during maturation feeding

dimensionless

2.44

β

Rate of nematodes’ transmission of pine sawyer through oviposition

year−1

0.427

ψ

Mean number of contacts at ovipostion moment

dimensionless

9.73

θ

The probability of healthy pines not to be tainted through nematode but cease oleoresin naturally

dimensionless

0.443

k

Transition rate of pine trees from the exposed class into the infectious one

year−1

0.814

γ

Possessing rate of nematode of adult vectors at the time of emergence from dead pines

year−1

0.790202

\(\beta _{1}\)

Nematode transmission rate into beetles during mating

year−1

0.8844

ρ

Transition rate of exposed pines to either \(A_{h}\) compartment or to \(I_{h}\) compartment at the per capita rate k

year−1

0.802