The typical way to analyse the closed system is direct numerical integration; however, some analytic traction can be gained. One example is the use of a linearising Ansatz to derive the early asymptotic behaviour of the dynamical system. Interestingly, when this is done for φ = 0 (such that there are no triangular loops in the network) as in Eames and Keeling [96] , the result for the early asymptotic growth rate agrees with the exact result of (10). In [95] , the differential equations for an n-regular graph were also manipulated to give an expression for final size that agreed with the exact result (12) Equation (22), however, is not the only possible network moment closure regime: Boots and Sasaki [131] and Bauch [132] considered regimes in which closure depended on the disease state (i.e., triples composed of different arrangements of susceptibles and infecteds close differently) to deal with spatial lattice-based systems and early disease invasion respectively. For example Boots and Sasaki [131] 