## 2 Method
### Transfer of Oil Contamination  
The concentration of oil contamination for each state in state space \(S\) at different times is calculated according to the principle of mass conservation. The transfer of oil contamination can be described using the discrete-time Markov chain following the research on the transmission of the SARS virus in a hospital by [PERSON] et al. [28]. The quantity of oil contamination on workbenches and gloves is calculated according to Equations (2) and (3). Here, the transfer process does not consider the influence of MWF type and other factors. \[N_{s}^{\prime}=\tau_{hs}\frac{N_{h}}{A_{h}}A_{c}-\tau_{sh}\frac{N_{s}}{A_{s}}A _{c}+N_{s}=\frac{A_{c}}{A_{h}}\tau_{hs}N_{h}+\left(1-\frac{A_{c}}{A_{s}}\tau_{ sh}\right)N_{s} \tag{2}\]  
\[N_{h}^{\prime}=\tau_{sh}\frac{N_{s}}{A_{s}}A_{c}-\tau_{hs}\frac{N_{h}}{A_{h}}A _{c}+N_{h}=\frac{A_{c}}{A_{s}}\tau_{sh}N_{s}+\left(1-\frac{A_{c}}{A_{h}}\tau_{ hs}\right)N_{h} \tag{3}\]  
In the contact transmission model, oil contamination is considered to be evenly distributed on the surface. Equations (4) and (5) are used to calculate the oil contamination concentration in various states. \[C_{s}^{\prime}=\frac{\left[\frac{A_{c}}{A_{h}}\tau_{hs}C_{h}A_{h}+(1-\frac{A _{c}}{A_{s}}\tau_{sh})C_{s}A_{s}\right]}{A_{s}}=(1-\frac{A_{c}}{A_{s}}\tau_{ sh})C_{s}+\frac{A_{c}}{A_{s}}\tau_{hs}C_{h} \tag{4}\]  
\[C_{h}^{\prime}=\frac{\left[\frac{A_{c}}{A_{s}}\tau_{sh}C_{s}A_{s}+(1-\frac{A _{c}}{A_{h}}\tau_{hs})C_{h}A_{h}\right]}{A_{h}}=\frac{A_{c}}{A_{h}}\tau_{sh}C_ {s}+(1-\frac{A_{c}}{A_{h}}\tau_{hs})C_{h} \tag{5}\]  
By using matrix notations, Equations (4) and (5) can be written in compact form as follows:  
\[\left[ \begin{array}{cc}C_{s}^{\prime}&C_{h}^{\prime}\end{array} \right]= \left[ \begin{array}{cc}C_{s}&C_{h}\end{array} \right]\left[ \begin{array}{cc }1-\frac{A_{c}}{A_{s}}\tau_{sh}&\frac{A_{c}}{A_{h}}\tau_{sh}\\ \frac{A_{c}}{A_{s}}\tau_{hs}&1-\frac{A_{c}}{A_{h}}\tau_{hs}\end{array} \right] \tag{6}\]where \(C_{s}^{\prime}\) and \(C_{h}^{\prime}\) represent the oil contamination concentration on workbenches and gloves after one touching behavior, and \(C_{s}\) and \(C_{h}\) represent the oil contamination concentration before touching. According to Equations (2)-(5), oil contamination on surfaces after one touching action only depends on the state before the action rather than the sequence of states that precede it, which conforms to the definition of Markov chains. Therefore, each behavior consisting of a series of touching actions can be regarded as a discrete-time Markov chain, while the surfaces of workbenches and gloves can be regarded as different states in the Markov chain. The square matrix in Equation (6) can be regarded as a simple transition matrix for the Markov chain. For the entire workshop, we assume the presence of \(m+q\) representative surfaces, including the workbench and glove surfaces. For one type of behavior, including \(n\) touching actions, the final conditions can be obtained as follows:  
\[\mathbf{C}^{(n)}=\mathbf{C}^{(n-1)}\mathbf{P}^{(n)}\mathbf{E} \tag{7}\]  
with \(\mathbf{C}^{(k)}=\)\(\left[C_{1}^{(k)},\ C_{2}^{(k)},\ \ldots,\ C_{m+q}^{(k)}\right]\), \(k\) numbers from 0 to \(n\), \(\mathbf{P}^{(n)}=\)\(\left[ \begin{array}{ccc}1-\frac{A_{c(i)}}{A_{i}}\tau_{ij}&\cdots&\frac{A_{c(i)}}{A_{i}} \tau_{ij}\\ \vdots&\ddots&\vdots\\ \frac{A_{c(i)}}{A_{j}}\tau_{ii}&\cdots&1-\frac{A_{c(i)}}{A_{j}}\tau_{ij}\end{array}