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Table 2 List of Model’s Transition Probabilities and Respective Conceptual Interpretations and Sources. Each transition probability represents the probability that a child in a given nutritional state moves to another within one month

From: A mathematical model to estimate the incidence of child wasting in Yemen

Nutrition state transition

Interpretation

Transition probability

Source data/notes

From Healthy state

   

\({Healthy\ to\ Healthy\ (p}_{HH})\)

Remains healthy

1–\({p}_{HM} - 0.000750\)

\({Healthy\ to\ Moderately\ Wasted\ (p}_{HM})\)

Incidence of Moderate Wasting

Unknown

To be estimated

\({Healthy\ to\ Severely\ Wasted\ (p}_{HS}\))

Develops severe wasting from healthy

0

Model assumption 2

\({Healthy\ to\ Severly\ Wasted\ with\ complications\ (p}_{HC})\)

Develops severe wasting w/ complication from healthy

0

\({Healthy\ to\ Deceased\ (p}_{HD})\)

General Under-five Mortality Rate

0.000750

2019 Lahj SMART Survey

From Severely Wasted state

   

\({Severely Wasted to Healthy (p}_{SH})\)

Severe Wasting Spontaneous Recovery

0

Model assumption 4

\({Severely\ Wasted\ to\ Moderately\ Wasted\ (p}_{SM})\)

Untreated severe wasting improves to moderate wasting

0.0914

Single time point follow-up of severely wasted children – India (Sachdev et al.) [17]

\({Severely\ Wasted\ to\ Severely\ Wasted\ (p}_{SS})\)

Severe wasting remains severe wasting

1−\({p}_{S{T}_{S}}-0.0724\)

\({Severly\ Wasted\ to\ Severely\ Wasted\ with\ complications\ (p}_{SC})\)

Untreated severe wasting develops medical complication

0.01026

Nutrition Cluster OTP/TFC Data

\({Severely\ Wasted\ to\ {{\text{Treatm}}{\text{ent}}}_{S}\ (p}_{S{T}_{S}})\)

Admitted to OTP

[0.200,0.678]

Nutrition Cluster OTP Data

\({Severely\ Wasted\ to\ Deceased\ (p}_{SD})\)

Untreated Severe Wasting Case Fatality

0.00872

Hazard ratios from pooled analysis (Olofin et al.) [16]

From Moderately Wasted State

   

\({Moderately\ Wasted\ to\ Healthy\ (p}_{MH})\)

Moderate Wasting Spontaneous Recovery

0.07814

Randomized controlled trial—Burkina Faso (Nikièma et al.) [18]

\({Moderately\ Wasted\ to\ Severely\ Wasted\ (p}_{MS})\)

Untreated moderate wasting progresses to severe wasting (severe wasting incidence)

Unknown

To be estimated

\({Moderately\ Wasted\ to\ Moderately\ Wasted\ (p}_{MM})\)

Moderate wasting remains moderate wasting

1−\({p}_{MS}\)\({p}_{M{T}_{m}}\)\(0.0807\)

\({Moderately\ Wasted\ to\ {\text{Treatment}}_{M}\ (p}_{M{T}_{m}})\)

Admitted to TSFP

[0.0529,0.176]

Nutrition Cluster TSFP Data

\({Moderately\ Wasted\ to\ Deceased\ (p}_{MD})\)

Untreated Moderate Wasting Case Fatality

0.00260

Hazard ratios from pooled analysis (Olofin et al.) [16]

From Severely Wasted with complications state

   

\({Severely\ Wasted\ with\ complications\ to\ Severely\ Wasted\ with\ complications\ (p}_{CC})\)

Severely wasted w/ complications remains severely wasted w/ complications

1−\({p}_{C{T}_{C}}-\)0.00260

\({Severely\ Wasted\ with\ complications\ to\ {\text{Treatment}}_{SC}\ (p}_{C{T}_{C}})\)

Admitted to TFC

[0.0,0.229]

Nutrition Cluster TFC Data

\({Severely\ Wasted\ with\ complications\ to\ Deceased\ (p}_{CD})\)

Severely Wasted w/ complications Untreated Case Fatality

0.00260

Hazard ratios from pooled analysis (Olofin et al.) [16]

From \({\text{Treatment}}_{S}\) State

   

\({{\text{Treatment}}_{S}\ to\ Healthy\ (p}_{{T}_{S}H})\)

\(\text{Cured at OTP}\)

0.307

Nutrition Cluster OTP Data

\({{\text{Treatment}}_{S}\ to\ Severely\ Wasted\ (p}_{{T}_{S}S})\)

Defaults from OTP

0.0262

Nutrition Cluster OTP Data

\({{\text{Treatment}}_{S}\ to\ {\text{Treatment}}_{M}\ (p}_{{T}_{s}{T}_{m}})\)

\(\text{Referred from OTP to TSFP}\)

0.00503

Nutrition Cluster OTP Data

\({{\text{Treatment}}_{S}\ to\ {\text{Treatment}}_{S}\ (p}_{{T}_{s}{T}_{S}})\)

Remains in OTP

0.657

Nutrition Cluster OTP Data

\({{\text{Treatment}}_{S}\ to\ {\text{Treatment}}_{SC}\ (p}_{{T}_{s}{T}_{C}})\)

Referred from OTP to TFC

0.004204

Nutrition Cluster OTP Data

\({{\text{Treatment}}_{S}\ to\ Deceased\ (p}_{{T}_{S}D})\)

In-treatment (OTP) case fatality

0.000156

Nutrition Cluster OTP Data

From \({\text{Treatment}}_{M}\) State

   

\({{\text{Treatment}}_{M}\ to\ Healthy\ (p}_{{T}_{m}H})\)

Cured at TSFP

0.103

Nutrition Cluster TSFP Data

\({{\text{Treatment}}_{M}\ to\ Moderately\ Wasted\ (p}_{{T}_{m}M})\)

Default from TSFP

0.00442

Nutrition Cluster TSFP Data

\({{\text{Treatment}}_{M}\ to\ {\text{Treatment}}_{M}\ (p}_{{T}_{m}{T}_{m}})\)

Remains in TSFP

0.892

Nutrition Cluster TSFP Data

\({{\text{Treatment}}_{M}\ to\ {\text{Treatment}}_{S}\ (p}_{{T}_{m}{T}_{S}})\)

Referred to OTP from TSFP

0.000918

Nutrition Cluster TSFP Data

\({{\text{Treatment}}_{M}\ to\ Deceased\ (p}_{{T}_{m}D})\)

In-treatment (TSFP) case fatality

0

Nutrition Cluster TSFP Data

From \({\text{Treatment}}_{SC}\) State

   

\({{\text{Treatment}}_{SC}\ to\ Healthy\ (p}_{{T}_{C}H})\)

Cured at TFC

0.792

Nutrition Cluster TFC Data

\({{\text{Treatment}}_{SC}\ to\ {\text{Treatment}}_{M}\ (p}_{{T}_{C}{T}_{m}})\)

Referred from TFC to TSFP

0.0492

Nutrition Cluster TFC Data

\({{\text{Treatment}}_{SC}\ to\ {\text{Treatment}}_{S}\ (p}_{{T}_{C}{T}_{S}})\)

Referred from TFC to OTP

0.158

Nutrition Cluster TFC Data

\({{\text{Treatment}}_{SC}\ to\ {\text{Treatment}}_{SC}\ (p}_{{T}_{C}{T}_{C}})\)

Remains in TFC

0

Nutrition Cluster TFC Data

\({{\text{Treatment}}_{SC}\ to\ Deceased\ (p}_{{T}_{c}D})\)

In-treatment (TFC) case fatality

0

Nutrition Cluster TFC Data

From Deceased state

   

\({Deceased\ to\ Deceased\ (p}_{DD})\)

Deceased state is absorbing

1

Model assumption 6