Linear Time-Variant Logistic Models with a Shape Parameter

Evaluates and fits the Linear Time-Variant Logistic Model with Shape Parameter (LTVLMS) for dynamic growth processes. The model combines a linearly time-varying growth rate with a shape parameter for asymmetric trajectories and includes numerically stable prediction utilities. Methodological details are provided by Betrouni and Kernane (2026) "Linear Time-Varying Logistic Model With Shape Parameter for Dynamic Epidemic Modeling" .

ltvlms

ltvlms is an R package for evaluating, fitting, comparing, and validating four nonlinear growth curves:

• Logistic
• Gompertz
• Richards
• Linear Time-Variant Logistic Model with Shape Parameter (LTVLMS)

The package accompanies the article Linear Time-Varying Logistic Model With Shape Parameter for Dynamic Epidemic Modeling by Redouane Betrouni and Tewfik Kernane (doi:10.1155/jama/4928447). Bander Hussein is the third package author and package maintainer.

What the proposed model changes

An ordinary logistic curve uses one constant growth rate. LTVLMS instead uses

r(t) = r0 + r1 * t

and adds a positive shape parameter nu. This permits asymmetric trajectories and, when r1 is negative, a transition from increasing to decreasing growth pressure.

Installation

The initial CRAN release is under review. For the reviewed source archive, run:

install.packages(file.choose(), repos = NULL, type = "source")
library(ltvlms)

Select ltvlms_0.1.0.tar.gz when prompted. After the package is available on CRAN, installation will use:

install.packages("ltvlms")

When this repository is public, the development version can be installed with:

install.packages("remotes")
remotes::install_github("bshussein/ltvlms")

First analysis

library(ltvlms)
data(south_africa_hiv)

fit <- fit_growth_model(
  time = south_africa_hiv$year,
  response = south_africa_hiv$prevalence,
  model = "ltvlms",
  n_starts = 50,
  seed = 42
)

fit
coef(fit)
metrics(fit)
plot(fit, xlab = "Year", ylab = "HIV prevalence (%)")
predict(fit, newdata = 2024:2026)

Compare all four models

comparison <- compare_growth_models(
  south_africa_hiv$year,
  south_africa_hiv$prevalence,
  n_starts = 50,
  seed = 42
)

comparison
plot(comparison, xlab = "Year", ylab = "HIV prevalence (%)")

Cross-validation

Random folds evaluate interpolation among observed years:

cross_validate_growth(
  south_africa_hiv$year,
  south_africa_hiv$prevalence,
  model = "ltvlms",
  method = "random"
)

Forward folds evaluate prediction of later years from earlier years:

cross_validate_growth(
  south_africa_hiv$year,
  south_africa_hiv$prevalence,
  model = "ltvlms",
  method = "forward"
)

These answer different questions and should not be treated as interchangeable.

Included data

• south_africa_hiv: 34 annual South Africa observations, 1990-2023.
• hiv_prevalence_63: 2,142 observations for 63 countries and regions.

The prevalence values are UNAIDS estimates for adults aged 15-49, not raw diagnosis counts. The package's MIT license covers the software, not the UNAIDS-derived data. The data source and applicable UNAIDS terms are recorded in inst/COPYRIGHTS and the dataset documentation.

Reproducibility and safeguards

• Model functions do not depend on hidden global variables.
• Exponential calculations use stable log-scale forms and conservative clipping.
• Parameter bounds, successful starts, and boundary estimates are retained.
• Failed model comparisons and cross-validation folds remain visible.
• Seeds are explicit and do not permanently alter the user's random-number state.
• Standard information criteria and manuscript-compatible formulas are labeled separately.

The current implementation follows the published equation and its reported South Africa parameter scale. The article is the authoritative scientific source for this release; earlier analysis scripts are not treated as the release specification. See the reproduction guide below for verified results and transparent notes about the article tables.

Guides

• Getting started: beginner tutorial
• Reproducing the paper: South Africa reproduction
• Methodological notes: assumptions, validation, and limitations

Citation

Run the following command for the package and article citations:

citation("ltvlms")

License

MIT License.