New Advanced Trigonometric Modeling of COVID-19 Cases in Saudi Arabia

Background: COVID-19 has posed substantial challenges to healthcare systems globally, emphasizing the need for robust epidemiological tracking, particularly in regions like Saudi Arabia where distinct variations in case rates necessitate specialized public health strategies.Aims and Objectives: This study aims to identify the most effective model for predicting COVID-19 trends by analyzing daily time-to-event case data across six Saudi regions. The goal is to enhance resource allocation and intervention strategies by gaining a deeper understanding of the epidemic’s dynamics and developing a reliable method for early detection of trend changes to prompt timely public health actions.Research Gap: Previous studies have predominantly utilized simpler statistical models such as log-normal, Gamma, and Weibull distributions, which often fall short in accurately describing the complex behaviors of COVID-19 case distributions, particularly during peak times and periods of periodicity. This study addresses these shortcomings by employing advanced trigonometrically enhanced models.Methodology: To model daily time-to-event COVID-19 case data from various regions in Saudi Arabia spanning 2020 to 2023, we employed the new trigonometric Weibull distribution from the new trigonometric-generated P-class of distributions. Our methodological approach included a comprehensive model validation process, utilizing a comparative analysis across seven distinct estimation techniques. Maximum likelihood estimation proved to be the most effective overall. We also adapted specific classical estimation techniques to fit the unique epidemiological characteristics of each region: Cramer von Mises estimation for Abu ‘Urwah, Al-Aridah, and Al Bada’I; Anderson–Darling estimation for Abha; maximum product spacing estimation for Ad Dammam; and maximum likelihood estimation for Abu ‘Arish. This tailored approach allowed for a detailed analysis of regional data, enhancing the accuracy and relevance of our modeling outcomes.Conclusions: The new trigonometric Weibull distribution effectively modeled daily COVID-19 cases across various regions in Saudi Arabia, demonstrating superior fit and capturing complex epidemic dynamics. This study highlights the new trigonometric Weibull distribution distribution’s capability to detect significant trends and periodic fluctuations, enhancing public health response strategies. Its successful application underscores the value of advanced trigonometric models in epidemiological research and pandemic management.