Linear Time-Varying Logistic Model With Shape Parameter for Dynamic Epidemic Modeling

We propose extending the logistic growth model by introducing a Linear Time-Varying Logistic Model with Shape Parameter (LTVLMS). This model incorporates a time-varying linear growth rate function, rt=r0+r1t, along with a shape parameter ν to allow for asymmetry. This approach offers a dynamic model of complex growth processes such as HIV transmission. Unlike traditional logistic models such as the standard logistic growth, Richards curve, and Gompertz model, which assume a fixed growth rate, the LTVLMS adjusts to temporal variations influenced by external factors. Examples of such factors include the introduction of antiretroviral therapy (ART) and the implementation of prevention campaigns. This flexibility allows the LTVLMS to capture trajectories of epidemic curves more accurately. We compare the performance of the LTVLMS against the standard logistic model, the Richards curve, and the Gompertz model. Our analysis highlights the advantages of the LTVLMS through fitting HIV prevalence estimates from the Joint United Nations Program on HIV/AIDS (UNAIDS).