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Table 3 Transitions between the states of the stochastic model

From: Identifying conditions for elimination and epidemic potential of methicillin-resistant Staphylococcus aureus in nursing homes

Event

Transition

Rate Constant

Rate

Admission of susceptible residents

 → S

(1 − λ

(1 − λ

Discharge of susceptible residents

S → 

γ S

γ S S

Admission of colonized with non-USA300

 → I 1

(w 1 λ

(w 1 λ

Discharge of colonized with non-USA300

I 1 → 

w 1 γ I

(w 1 γ I )I

Transmission of non-USA300 from colonized with non-USA300 to susceptible

S + I 1 → 2I 1

\( \frac{b_{1n}}{N} \)

\( \frac{b_{1n}}{N}S{I}_1 \)

Transmission of non-USA300 from co-colonized to susceptible

S + I b  → I 1 + I b

\( \frac{b_{1n}}{N} \)

\( \frac{b_{1n}}{N}S{I}_b \)

Clearance of colonized with non-USA300

I 1 → S

g n1

g n1 I 1

Admission of colonized with USA300

 → I 3

(w 3 λ

(w 3 λ

Discharge of colonized with USA300

I 3 → 

w 3 γ I

(w 3 γ I )I

Transmission of USA300 from colonized with USA300 to susceptible

S + I 3 → 2I 3

\( \frac{b_{3n}}{N} \)

\( \frac{b_{3n}}{N}S{I}_3 \)

Transmission of USA300 from co-colonized to susceptible

S + I b  → I 3 + I b

\( \frac{b_{3n}}{N} \)

\( \frac{b_{3n}}{N}S{I}_b \)

Clearance of colonized with USA300

I 3 → S

g n3

g n3 I 3

Admission of co-colonized with both strains

 → I b

(w b λ

(w b λ

Discharge of co-colonized with both strains

I b  → 

w b γ I

(w b γ I )I

Transmission of USA300 from co-colonized to colonized with non-USA300

I 1 + I b  → 2I b

\( \frac{b_{3n}}{N} \)

\( \frac{b_{3n}}{N}{I}_1{I}_b \)

Transmission of USA300 from colonized with USA300 to colonized with non-USA300

I 1 + I 3 → I b  + I 3

\( \frac{b_{3n}}{N} \)

\( \frac{b_{3n}}{N}{I}_1{I}_3 \)

Transmission of non-USA300 from co-colonized to colonized with USA300

I 3 + I b  → 2I b

\( \frac{b_{1n}}{N} \)

\( \frac{b_{1n}}{N}{I}_3{I}_b \)

Transmission of non-USA300 from colonized with non-USA300 to colonized with USA300

I 1 + I 3 → I 1 + I b

\( \frac{b_{1n}}{N} \)

\( \frac{b_{1n}}{N}{I}_3{I}_1 \)

Clearance of co-colonized from USA300

I b  → I 1

g n3

g n3 I b

Clearance of co-colonized from non-USA300

I b  → I 3

g n1

g n1 I b