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In our model the density of the parasite, 
, depends on two factors – its own replication (at rate 
) and its clearance by activated innate immune cells 
at rate 
. The total number of innate immune cells equals 
and they can be either in a resting or activated state. Since 
is the number of activated cells, the number of resting cells equals 
. Resting innate immune cells are activated at rate 
, and revert back to the inactive state at exponential rate 
.
