Comparative Analysis of Non-Linear Growth Models under Error Assumptions using a COVID-19 Mortality Data in Nigeria

Accurate modelling of mortality dynamics during epidemic outbreaks is essential for effective public health planning and response. Nonlinear growth models have been widely applied in epidemiology to capture complex population-level patterns; however, model performance can be substantially influenced by underlying error assumptions. This study presents a comparative analysis of four nonlinear growth models—Mitscherlich, Gompertz, Richards, and Weibull—under additive and multiplicative error structures using COVID-19 mortality data from Nigeria. Mortality data covering the 2020–2021 pandemic period were obtained from the Nigeria Centre for Disease Control (NCDC). Model parameters were estimated using the modified Levenberg–Marquardt algorithm implemented in the R programming environment. Model adequacy and performance were assessed using information-theoretic criteria and likelihood-based model probabilities. Results indicate notable differences in parameter stability and goodness-of-fit across models and error assumptions. Among the competing specifications, the Mitscherlich growth model under the additive error assumption demonstrated superior performance, exhibiting the lowest information criterion values and the highest model probability. These findings highlight the importance of jointly considering model structure and error formulation in mortality modelling. The study provides empirical evidence to guide model selection for epidemic forecasting and contributes to improved understanding of nonlinear growth behaviour in human mortality data within the Nigerian context.