Weibull distributions¶

The following parameters use a Weibull distribution.

Note

Parameters are case-sensitive. For Boolean parameters, set to 1 for true or 0 for false. Minimum, maximum, or default values of “NA” indicate that those values are not applicable for that parameter.

EMOD does not use true defaults; that is, if the dependency relationships indicate that a parameter is required, you must supply a value for it. However, many of the tools used to work with EMOD will use the default values provided below.

JSON format does not permit comments, but you can add “dummy” parameters to add contextual information to your files. Any keys that are not EMOD parameter names will be ignored by the model.

Parameter

Data type

Minimum

Maximum

Default

Description

Example

CD4_At_Death_LogLogistic_Heterogeneity

float

0

100

0

The inverse shape parameter of a Weibull distribution that represents the at-death CD4 cell count.

{
"CD4_At_Death_LogLogistic_Heterogeneity": 0.7
}


CD4_At_Death_LogLogistic_Scale

float

1

1000

31.63

The scale parameter of a Weibull distribution that represents the at-death CD4 cell count.

{
"CD4_At_Death_LogLogistic_Scale": 2.96
}


CD4_Post_Infection_Weibull_Heterogeneity

float

0

100

0.275642

The inverse shape parameter of a Weibull distribution that represents the post-acute-infection CD4 cell count.

{
"CD4_Post_Infection_Weibull_Heterogeneity": 0
}


CD4_Post_Infection_Weibull_Scale

float

1

1000

560.432

The scale parameter of a Weibull distribution that represents the post-acute-infection CD4 cell count.

{
"CD4_Post_Infection_Weibull_Scale": 550
}


Days_Between_Symptomatic_And_Death_Weibull_Heterogeneity

float

0.1

10

1

The time between the onset of AIDS symptoms and death is sampled from a Weibull distribution; this parameter governs the heterogeneity (inverse shape) of the Weibull.

{
"Days_Between_Symptomatic_And_Death_Weibull_Heterogeneity": 0.5
}


Days_Between_Symptomatic_And_Death_Weibull_Scale

float

1

3650

183

The time between the onset of AIDS symptoms and death is sampled from a Weibull distribution; this parameter governs the scale of the Weibull.

{
"Days_Between_Symptomatic_And_Death_Weibull_Scale": 618.3
}


float

0.001

1000

21.182

This parameter determines the intercept of the scale parameter, ?, for the Weibull distribution used to determine HIV survival time.

Survival time with untreated HIV infection depends on the age of the individual at the time of infection, and is drawn from a Weibull distribution with shape parameter (see HIV_Adult_Survival_Shape_Parameter) and scale parameter, ?. The scale parameter is allowed to vary linearly with age as follows:

$$\lambda$$ = HIV_Adult_Survival_Scale_Parameter_Intercept + HIV_Adult_Survival_Scale_ Parameter_Slope * Age (in years).

{
}


float

-1000

1000

-0.2717

This parameter determines the slope of the scale parameter, ?, for the Weibull distribution used to determine HIV survival time.

Survival time with untreated HIV infection depends on the age of the individual at the time of infection, and is drawn from a Weibull distribution with shape parameter (see HIV_Adult_Survival_Shape_Parameter) and scale parameter, ?. The scale parameter is allowed to vary linearly with age as follows:

$$\lambda$$ = HIV_Adult_Survival_Scale_Parameter_Intercept + HIV_Adult_Survival_Scale_ Parameter_Slope * Age (in years).

Because survival time with HIV becomes shorter with increasing age, HIV_Adult_Survival_Scale_ Parameter_Slope should be set to a negative number.

{
}


float

0.001

1000

2

This parameter determines the shape of the Weibull distribution used to determine age-dependent survival time for individuals infected with HIV.

{
}


HIV_Child_Survival_Slow_Progressor_Scale

float

0.001

1000

16

The Weibull scale parameter describing the distribution of HIV survival for children who are slower progressors.

{
"HIV_Child_Survival_Slow_Progressor_Scale": 16.0,
"HIV_Child_Survival_Slow_Progressor_Shape": 2.7
}


HIV_Child_Survival_Slow_Progressor_Shape

float

0.001

1000

2.7

The Weibull shape parameter describing the distribution of HIV survival for children who are slower progressors.

{
"HIV_Child_Survival_Slow_Progressor_Scale": 16.0,
"HIV_Child_Survival_Slow_Progressor_Shape": 2.7
}


Sexual_Debut_Age_Female_Weibull_Heterogeneity

float

0

50

20

The inverse shape of the Weibull distribution for female debut age.

{
"Sexual_Debut_Age_Female_Weibull_Heterogeneity": 0.05
}


Sexual_Debut_Age_Female_Weibull_Scale

float

0

50

16

The scale term of the Weibull distribution for female debut age.

{
"Sexual_Debut_Age_Female_Weibull_Scale": 15.919654846191
}


Sexual_Debut_Age_Male_Weibull_Heterogeneity

float

0

50

20

The inverse shape of the Weibull distribution for male debut age.

{
"Sexual_Debut_Age_Male_Weibull_Heterogeneity": 0.05
}


Sexual_Debut_Age_Male_Weibull_Scale

float

0

50

16

The scale term of the Weibull distribution for male debut age.

{
"Sexual_Debut_Age_Male_Weibull_Scale": 16.946729660034
}


Sexual_Debut_Age_Min

float

0

3.40E+38

13

The minimum age at which individuals become eligible to form sexual relationships.

{
"Sexual_Debut_Age_Min": 13
}