Table 2 Intervention policies

No intervention

No food or ITN

\(\phi _0^c\) fixed, \(\phi _t^{(1)} = \phi _t^{(2)} = 0\),

\(\phi _a^1 = \frac{\alpha }{1-\alpha } \phi _0^c, \phi _N = 2\alpha \phi _0^c\),

Targeted food

Food if WAZ \(< \theta \)

\(p_I=1\), \(\phi _0^c\) fixed, \(\phi _t^{(1)} = \phi _t^{(2)} = P(Z<\theta )\),

\(\phi _a^1 = \frac{\alpha }{1-\alpha } \phi _0^c, \phi _N = 2\alpha \phi _0^c\),

\(P(G=11|Z=z, G_0 =1)= 1_{\{z>\theta \}}\),

\(P(G=12|Z=z, G_0 =1)= 1_{\{z<\theta \}}\),

\(P(G=21|Z=z, G_0 =2)= 1_{\{z>\theta \}}\),

\( P(G=22|Z=z,G_0=2)=1_{\{z<\theta \}}\)

Untargeted ITN

ITN with probability \(\phi \) if unprotected

\(p_I = p, \phi _0^c\) fixed, \(\phi _t^{(1)} = \phi , \phi _t^{(2)} = 0, f_A(a)=\delta (a)\),

\(\phi _a^1 = \frac{\alpha }{1-\alpha } (\phi _0^c + (1 - \phi _0^c)\phi ), \phi _N = 2\alpha (\phi _0^c + (1 - \phi _0^c)\phi )\),

\(P(G=11|Z=z, G_0 =1)= 1 - \phi \),

\(P(G=12|Z=z, G_0 =1)= \phi \),

\(P(G=21|Z=z, G_0 =2)= 1\),

\( P(G=22|Z=z,G_0=2)= 0\)

Targeted ITN

ITN if WAZ \(< \theta \) and unprotected

\(p_I = p, \phi _t^{(1)}=P(Z<\theta ), \phi _t^{(2)} = 0\), \(\phi _0^c\) fixed, \(f_A(a)=\delta (a)\),

\(\phi _a^1 = \frac{\alpha }{1-\alpha } (\phi _0^c + (1 - \phi _0^c)\phi _t^{(1)}), \phi _N = 2\alpha (\phi _0^c + (1 - \phi _0^c)\phi _t^{(1)})\),

\(P(G=11|Z=z, G_0 =1)= 1_{\{z>\theta \}}\),

\(P(G=12|Z=z, G_0 =1)= 1_{\{z<\theta \}}\),

\(P(G=21|Z=z, G_0 =2)= 1\),

\( P(G=22|Z=z,G_0=2)= 0\)

Targeted food and

food if WAZ \(< \theta \),

\(p_I = p, \phi _t^{(1)}= \phi _t^{(2)} = P(Z<\theta )\), \(\phi _0^c\) fixed,

Targeted ITN

ITN if WAZ \(< \theta \) and unprotected

\(\phi _a^1 = \frac{\alpha }{1-\alpha } (\phi _0^c + (1 - \phi _0^c)\phi _t^{(1)}),\, \phi _N = 2\alpha (\phi _0^c + (1 - \phi _0^c)\phi _t^{(1)})\),

\(P(G=11|Z=z, G_0 =1)= 1_{\{z>\theta \}}\),

\(P(G=12|Z=z, G_0 =1)= 1_{\{z<\theta \}}\),

\(P(G=21|Z=z, G_0 =2)= 1_{\{z>\theta \}}\),

\( P(G=22|Z=z,G_0=2)=1_{\{z<\theta \}}\)