Table 1.

Model variables and parameters used in the simulations of the model equations (1) – (6)

Symbol	Description	Units	Initial Condition
S	Free/extracellular anthrax spores	spores	variable
A	Alveolar phagocyte population (Set to quasi-steady state)	Cells	n/a
H	Alveolar host cell; assume that there are nS spores per H	Cells	0.0
E	Resident immune cells in MLN (Early response in MLN)	Cells	2×109
Be	Extracellular bacteria	CFU	0.0
N	Neutrophils	Cells	0.0
TA	Anthrax Toxins	TA-units	0.0

Name	Description	Value Used	Sources/Ranges/Explanations
BeMAX	Carrying capacity for the Be population;	5×1011 Be	Estimated; (Hanna, 1999) reports that bacterial levels in the blood can reach as high as 108/ml. We assume a (0–1) mL volume for a mediastinal lymph node and approximately 20–50 mediastinal lymph nodes (MLN) (Dietrich, 1998; Schmidt, 2007), giving a range of (0–50) mL for total MLN volume. Using Hanna’s number and 50 mL volume, this gives 5×109 bacteria total and we assume that greater numbers of bacteria can pack into the lymph node tissues than in the blood and thus increase this number to 5×1011
ct1, ct2,ct3	Controls the effectiveness of the anthrax toxins, TA, to inhibit neutrophil processes (phagocytosis/killing, recruitment and chemotaxis)	1 TA-units	Estimated; The inhibition is at 50% when the anthrax toxin reaches its maximum level of 1 TA-unit;
ctb	Saturation of the production of anthrax toxin by bacteria	1000 Be	Estimated;
C	Ciprofloxacin antibiotic treatment amount	0.675	Estimated such that its effects on bacteria would not be negligible nor unrealistically successful in all scenarios
D	Doxycycline antibiotic treatment amount	1.23	Estimated such that its effects on bacteria would not be negligible nor unrealistically successful in all scenarios
k1	Rate of apoptosis of resident immune cells in MLN after interaction with Be (i.e. via intracellular anthrax toxin, not specifically modeled)	10−5 /Be per hr	Estimated; (DeLeo, 2004)
k2	Rate at which resident lung cells (which we call host cells), H, phagocytose anthrax spores	10−10/H per hr	Estimated; when all the spores are taken up, there should be S/ns # of infected host cells. k2 determines how quickly/slowly that happens. that k2=10–10 has all spores taken up by resident lung cells around 10 hours.
k3	Rate at which spore-containing host cells migrate to MLN and release vegetative bacteria (which came about from the germinated spores inside the host cell – we assume that some intra-cellular growth has occurred)	0.05/hr	Estimated (Hanna, 1993; Hanna, 1998; Hanna, 1999; Shetron-Rama, 2010). This is computed from simulations such that all infected host cells are gone from the lung compartment by 4 days, for initial spore counts ≤ 2×104. (See paper for more details.)
k4	Rate of production of anthrax toxins by bacteria	2 TA-units per hr	Estimated;
k5	Growth rate of extracellular bacteria, Be	0.8/hr	Doubling time =0.78 hour → growth rate of 0.88865/hr (Kalns, 2002). We took the growth rate to be slightly smaller since under normal circumstances growth conditions are not ideal.
k6	Rate at which resident immune cells in MLN kill Be	5×10−10/E per hr	Estimated; Figure 9 in (Cote, 2006) implies there exists other mechanisms other than neutrophils that are involved in killing anthrax but that these are overwhelmed with larger initial spore counts.
k8	Rate of phagocytosis and killing of Be by N	6×10−10/N per hr	Estimated; (Hampton, 1994)
k9	Rate at which resting neutrophils are activated by Be	5×10−10/BeE per hr	Estimated
k10	Rate at which resting neutrophils are activated by already activated neutrophils	1×10−5/N per hr	Estimated
N0	Source of resting neutrophils	5500 N	Estimated such that maximum neutrophil infiltration is not greater than 2.5×109. We assume that a maximum of 5×107 neutrophils can occupy a milliliter of volume. Assuming a volume of 50mL of lymph nodes (See explanation in BeMAX), gives a maximum neutrophil capacity of 2.5×109.
nb	Number of bacteria (on average) inside a host cell after migration of the cell to the MLN and after anthrax spores have germinated, become vegetative bacteria and grown intracellularly before lysing the cell.	5 Be	Estimated
ns	Number of spores (on average) phagocytosed by resident lung host cells	3 S	Estimated
sA	Source of resident lung host cells (like alveolar macrophages or dendritic cells, prior to phagocytosing spores)	3×108 H/hr	Previous work: Day, 2009
sE	Source of resident immune cells in MLN	1×108 E/hr	Estimated
μA	Death rate of resident lung host cells (like alveolar macrophages or dendritic cell, prior to phagocytosing spores)	0.05/hr	Previous work: Day, 2009
μE	Death rate of resident immune cells in MLN	0.05/hr	Estimated; based on μA;
μN	Death rate of primed neutrophils;	0.06/hr	Reynolds, 2006; Half-life 1–2 days (24–48 hours) → (0.01444, 0.02888)/hr- Wikipedia; We use a larger value to include other removal mechanisms of neutrophils (e.g. by macrophages)
μTA	Decay of anthrax toxins	2/hr	Estimated; Watson_2007 reports PA half-lives of 10–20 minutes → decay rates of (ln(2)/20)*60 to (ln(2)/10)*60 per hour → (2.07944, 4.15888)