In infectious disease modelling, a who acquires infection from whom (WAIFW) matrix is a matrix that describes the rate of transmission of infection between different groups in a population, such as people of different ages.[1] Used with an SIR model, the entries of the WAIFW matrix can be used to calculate the basic reproduction number using the next generation operator approach.[2]
The
2 x 2
\begin{bmatrix}\beta11&\beta12\ \beta21&\beta22\end{bmatrix}
\betaij
i
j
Assortative mixing occurs when those with certain characteristics are more likely to mix with others with whom they share those characteristics. It could be given by
\begin{bmatrix}\beta&0\ 0&\beta\end{bmatrix}
2 x 2
\beta11,\beta22>\beta12,\beta21
\beta11,\beta22<\beta12,\beta21
Homogenous mixing, which is also dubbed random mixing, is given by
\begin{bmatrix}\beta&\beta\ \beta&\beta\end{bmatrix}
It need not be the case that
\betaij=\betaji
\begin{bmatrix}\beta1&\beta2\ \beta1&\beta2\end{bmatrix}\begin{bmatrix}\beta1&\beta1\ \beta2&\beta2\end{bmatrix} \begin{bmatrix}0&\beta1\ \beta2&0\end{bmatrix}
The social contact hypothesis was proposed by, Peter Teunis, and Mirjam Kretzschmar in 2006. The hypothesis states that transmission rates are proportional to contact rates,
\betaij\proptocij