Theory and Modern Applications
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 |