Table 1 Illustrates latent modification to the model’s process.
From: Computational analysis of a mathematical model of hookworm infection
Transition | Probabilities |
|---|---|
\(\:{\left(\varDelta\:\mathbf{U}\right)}_{1}={\left[\begin{array}{cccccccc}1&\:0&\:0&\:0&\:0&\:0&\:0&\:0\end{array}\right]}^{\mathbf{T}}\) | \(\:{\text{P}}_{1}=\left(\pi\:\right)\varDelta\:\text{t}\) |
\(\:{\left(\varDelta\:\mathbf{U}\right)}_{2}={\left[\begin{array}{cccccccc}-1&\:1&\:0&\:0&\:0&\:0&\:0&\:0\end{array}\right]}^{\mathbf{T}}\) | \(\:{\text{P}}_{2}=\left(\lambda\:S{L}_{2}{e}^{-\mu\:\tau\:}\right)\varDelta\:\text{t}\) |
\(\:{\left(\varDelta\:\mathbf{U}\right)}_{3}={\left[\begin{array}{cccccccc}-1&\:0&\:0&\:0&\:0&\:0&\:0&\:0\end{array}\right]}^{\mathbf{T}}\) | \(\:{\text{P}}_{3}=\left(\mu\:S\left(t\right)\right)\varDelta\:\text{t}\) |
\(\:{\left(\varDelta\:\mathbf{U}\right)}_{4}={\left[\begin{array}{cccccccc}1&\:0&\:0&\:0&\:-1&\:0&\:0&\:0\end{array}\right]}^{\mathbf{T}}\) | \(\:{\text{P}}_{4}=\left(\gamma\:R\left(t\right)\right)\varDelta\:\text{t}\) |
\(\:{\left(\varDelta\:\mathbf{U}\right)}_{5}={\left[\begin{array}{cccccccc}0&\:-1&\:0&\:0&\:0&\:0&\:0&\:0\end{array}\right]}^{\mathbf{T}}\) | \(\:{\text{P}}_{5}=\left(\mu\:E\right)\varDelta\:\text{t}\) |
\(\:{\left(\varDelta\:\mathbf{U}\right)}_{6}={\left[\begin{array}{cccccccc}0&\:-1&\:0&\:1&\:0&\:0&\:0&\:0\end{array}\right]}^{\mathbf{T}}\) | \(\:{\text{P}}_{6}=\left(\epsilon\:\sigma\:E\right)\varDelta\:\text{t}\) |
\(\:{\left(\varDelta\:\mathbf{U}\right)}_{7}={\left[\begin{array}{cccccccc}0&\:-1&\:1&\:0&\:0&\:0&\:0&\:0\end{array}\right]}^{\mathbf{T}}\) | \(\:{\text{P}}_{7}=\left(\left(1-\epsilon\:\right)\sigma\:E\right)\varDelta\:\text{t}\) |
\(\:{\left(\varDelta\:\mathbf{U}\right)}_{8}={\left[\begin{array}{cccccccc}0&\:0&\:-1&\:1&\:0&\:0&\:0&\:0\end{array}\right]}^{\mathbf{T}}\) | \(\:{\text{P}}_{8}=\left({\tau\:}_{1}{I}_{1}\right)\varDelta\:\text{t}\) |
\(\:{\left(\varDelta\:\mathbf{U}\right)}_{9}={\left[\begin{array}{cccccccc}0&\:0&\:-1&\:0&\:1&\:0&\:0&\:0\end{array}\right]}^{\mathbf{T}}\) | \(\:{\text{P}}_{9}=\left({\theta\:}_{1}{I}_{1}\right)\varDelta\:\text{t}\) |
\(\:{\left(\varDelta\:\mathbf{U}\right)}_{10}={\left[\begin{array}{cccccccc}0&\:0&\:-1&\:0&\:0&\:0&\:0&\:0\end{array}\right]}^{\mathbf{T}}\) | \(\:{\text{P}}_{10}=\left(\mu\:{I}_{1}\right)\varDelta\:\text{t}\) |
\(\:{\left(\varDelta\:\mathbf{U}\right)}_{11}={\left[\begin{array}{cccccccc}0&\:0&\:0&\:-1&\:0&\:0&\:0&\:0\end{array}\right]}^{\mathbf{T}}\) | \(\:{\text{P}}_{11}=\left(\delta\:{I}_{2}\right)\varDelta\:\text{t}\) |
\(\:{\left(\varDelta\:\mathbf{U}\right)}_{12}={\left[\begin{array}{cccccccc}0&\:0&\:0&\:-1&\:1&\:0&\:0&\:0\end{array}\right]}^{\mathbf{T}}\) | \(\:{\text{P}}_{12}=\left({\theta\:}_{2}{I}_{2}\right)\varDelta\:\text{t}\) |
\(\:{\left(\varDelta\:\mathbf{U}\right)}_{13}={\left[\begin{array}{cccccccc}0&\:0&\:0&\:-1&\:0&\:0&\:0&\:0\end{array}\right]}^{\mathbf{T}}\) | \(\:{\text{P}}_{13}=\left(\mu\:{I}_{2}\right)\varDelta\:\text{t}\) |
\(\:{\left(\varDelta\:\mathbf{U}\right)}_{14}={\left[\begin{array}{cccccccc}0&\:0&\:0&\:0&\:-1&\:0&\:0&\:0\end{array}\right]}^{\mathbf{T}}\) | \(\:{\text{P}}_{14}=\left(\left(\mu\:+\gamma\:\right)R\right)\varDelta\:\text{t}\) |
\(\:{\left(\varDelta\:\mathbf{U}\right)}_{15}={\left[\begin{array}{cccccccc}0&\:0&\:0&\:0&\:0&\:-1&\:1&\:0\end{array}\right]}^{\mathbf{T}}\) | \(\:{\text{P}}_{15}=\left(\omega\:F\right)\varDelta\:\text{t}\) |
\(\:{\left(\varDelta\:\mathbf{U}\right)}_{16}={\left[\begin{array}{cccccccc}0&\:0&\:0&\:0&\:0&\:-1&\:0&\:0\end{array}\right]}^{\mathbf{T}}\) | \(\:{\text{P}}_{16}=\left(\psi\:F\right)\varDelta\:\text{t}\) |
\(\:{\left(\varDelta\:\mathbf{U}\right)}_{17}={\left[\begin{array}{cccccccc}0&\:0&\:0&\:0&\:0&\:0&\:-1&\:1\end{array}\right]}^{\mathbf{T}}\) | \(\:{\text{P}}_{17}=\left(\varphi\:{L}_{1}\right)\varDelta\:\text{t}\) |
\(\:{\left(\varDelta\:\mathbf{U}\right)}_{18}={\left[\begin{array}{cccccccc}0&\:0&\:0&\:0&\:0&\:0&\:-1&\:0\end{array}\right]}^{\mathbf{T}}\) | \(\:{\text{P}}_{18}=\left(v{L}_{1}\right)\varDelta\:\text{t}\) |
\(\:{\left(\varDelta\:\mathbf{U}\right)}_{19}={\left[\begin{array}{cccccccc}0&\:0&\:0&\:0&\:0&\:0&\:0&\:-1\end{array}\right]}^{\mathbf{T}}\) | \(\:{\text{P}}_{19}=\left(k{L}_{2}\right)\varDelta\:t\) |
