# Table 1 Expressions for derivatives in all models

Ross Macdonald McKenzie
S h - - q R h (t)-h I m (t)S h (t)
e h ,E h - - h I m (t)S h (t)-k E h (t)
i h ,I h a b m i m (t)(1-i h (t)) a b m i m (t)(1-i h (t)) k E h (t)-p I h (t)
- -r i h (t) -r i h (t)
r h ,R h - - p I h (t)-q R h (t)
S m - - f-h I h (t)S m (t)-d S m (t)
e m ,E m - a c i h (t)(1-e m (t)-i m (t))-μ2e m (t) h I h (t)S m (t)-g E m (t)-d E m (t)
- - $- aci h (t- τ m ) 1- e m (t- τ m )- i m (t- τ m ) e - μ 2 τ m$
i m ,I m a c i h (t)(1-i m (t)) a c i h (t-τ m )(1-e m (t-τ m )-μ2i m (t) g E m (t)-d I m (t)
-   $- i m (t- τ m ) e - μ 2 τ m$
Anderson/May
e h ,E h   $- abmi m (t- τ h ) 1- e h (t- τ h )- i h (t- τ h ) e - τ h ( r + μ 1 ) )$
i h ,I h   a b m i m (t-τ h )(1-e h (t-τ h )
$- i h (t- τ h ) e - τ h ( r + μ 1 ) - ri h (t)- μ 1 i h (t)$
e m ,E m   a c i h (t)(1-e m (t)-i m (t))-μ2e m (t)
-   $- aci h (t- τ m ) 1- e m (t- τ m )- i m (t- τ m ) e - μ 2 τ m$
i m ,I m   a c i h (t-τ m )(1-e m (t-τ m )-μ2i m (t)
-   $- i m (t- τ m ) e - μ 2 τ m$
Chitnis
S h   q R h (t)
-h I m (t)S h (t)
e h ,E h   $σ m σ h N m ( t ) b hm i m ( t ) σ m N m ( t ) + σ h N h ( t ) 1- e h (t)- i h (t)- r h (t)$
$- ν h + ψ h + Λ h N h ( t ) e h (t)+ δ h i h (t) e h (t)$
i h ,I h   $ν h e h (t)- γ h + δ h + ψ h + Λ h N h ( t ) i h (t)$
+δ h i h (t)2
r h ,R h   $γ h i h (t)- ρ h + ψ h + Λ h N h ( t ) r h (t)+ δ h i h (t) r h (t)$
N h   Λ h +ψ h N h (t)-(μ1h+μ2hN h (t))N h (t)-δ h i h (t)N h (t)
e m ,E m   $σ m σ h N h ( t ) σ m N m ( t ) + σ h N h ( t ) b mh i h (t)+ b ~ mh r h (t) 1- e m (t)- i m (t)$
i m ,I m   ν m e m (t)-ψ m i m (t)
N m   ψ m N m (t)-(μ1m+μ2mN m (t))N m (t)