Approximate disease dynamics in household-structured populations: supplementary information

The subset of yij relevant to computing the correction term are those strictly bounded by the axes (see diagram Fig.1(a)). The differential equation for a variable referring to a given point on this diagram will involve the variable itself, the variable for the point diagonally down and right (via δ and β), and the variable associated with the point vertically above (via ν) see diagram Fig.1(b). A closed set of differential equations for the variables involved in the correction is therefore obtained by appending the variables y2,0 up to yn−1,0 (see diagram Fig.1(a)). This set of variables obey a differential equation of the form