Optimum stratum boundaries and sample sizes for Covid-19 data in Egypt

Area of Science:

• Statistics
• Mathematical Modeling
• Epidemiology

Background:

• Stratified random sampling is crucial for population estimates but sensitive to strata boundary determination and sample allocation.
• Surveys often face budget and time constraints, necessitating efficient resource allocation.
• Optimizing sampling strategies under multiple objectives, including cost and time, remains a challenge.

Purpose of the Study:

• To develop a mathematical goal programming model for determining optimal stratum boundaries in stratified sampling.
• To incorporate cost and time as key objectives in the optimization process for an exponential study variable.
• To evaluate the model's performance using COVID-19 data and compare results with established reports.

Main Methods:

• A mathematical goal programming model was formulated to determine optimum stratum boundaries.
• The model was applied to an exponential study variable under multiple objectives, considering cost and time.
• COVID-19 case data was used to stratify new cases into small, medium, and high categories for model evaluation.

Main Results:

• The goal programming model successfully determined optimal stratum boundaries while considering cost and time.
• Application to COVID-19 data revealed three distinct waves of infection in Egypt between March 2020 and August 2021.
• The model's findings on infection waves align with real-world observations and World Health Organization reports.

Conclusions:

• Mathematical goal programming offers advantages for resource planning and optimization in stratified sampling.
• The proposed model provides an effective method for determining stratum boundaries under practical survey constraints.
• The study demonstrates the model's utility in analyzing epidemiological data, specifically identifying COVID-19 waves.