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Table 1 Expressions for derivatives in all models

From: A comparison of five malaria transmission models: benchmark tests and implications for disease control

 

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)