The derivation of such conditions was presented before (Provatas & Elder, 2010; Pego, 1989; Dai & Du, 2012; Elder et al., 2001; Fife, 1992; Emmerich, 2008; Garcke et al., 2004; Ahmed et al., 2016; Caginalp, 1989), and hence we only summarize the final relations here.
We plotted the final relations between the logarithm of mortality rate in under 5s and the variables included in the final generalised additive mixed model.
In the absence of the plasma the dispersion relation reduce to the final dispersion relation in the Ref. [18, 19].
However, this mode had contributions to the final dispersion relation of the same order as those came from the Alfvén mode itself.
To obtain the final dispersion relation we must employ the discontinuity conditions in the axial and azimuthal magnetic fields due to the helix current sheet as follows δ B θ R h + ε - δ B θ R h - ε = 4 π c δ J ll Δ R h sin φ and δ B ^ z R h - ε - δ B ^ z R h + ε = 4 π c δ J ^ ll Δ R h cos φ, (8).
To obtain the final dispersion relation, we must employ the discontinuity conditions in the axial and azimuthal magnetic fields due to the helix current sheet as follows: 1 δ B ^ z, l, m R h - ε - δ B ^ z, l, m R h + ε = 4 π c δ J ^ ‖ Δ R h cos φ, (133) 2 δ B θ, l, m R h + ε - δ B θ, l, m R h - ε = 4 π c δ J ‖ Δ R h sin φ, (134 where, δJ∥ is the surface current density parallel to the helix [18].
If an intervention is focused only on a portion of cases or if disease-induced deaths occur in non-negligible order, not only the variance but also the formulae for the final size relation (our equation (1)) have to be reassessed [58] [60].
However, the final size relation for multi-strain models, such as the one considered in this study, may be difficult to obtain.
