RESEARCH ARTICLE Optimum stratum boundaries and sample sizes for Covid-19 data in Egypt Fatma S. Abo_El.HassanID 1☯ *, Ramadan Hamed 2,3☯ , Elham A. Ismail 1☯ , Safia M. Ezzat 1☯ 1 Statistics Dept, Faculty of Commerce, Al-Azhar University, Girls’ Branch, Cairo, Egypt, 2 Statistics Dept, Faculty of Economics and Political Science, Cairo University, Giza, Egypt, 3 Social Research Center, American University, New Cairo, Egypt ☯ These authors contributed equally to this work. * fatmasayed85@azhar.edu.eg Abstract Stratified random sampling is an effective sampling technique for estimating the population characteristics. The determination of strata boundaries and the allocation of sample size to the strata are two of the most critical factors in maximizing the precision of the estimates. Most surveys are conducted in an environment of severe budget constraints and a specific time is required to finish the survey. So cost and time are two important objectives that are taken under consideration in most surveys. The study suggested Mathematical goal pro- gramming model for determining optimum stratum boundaries for an exponential study vari- able under multiple objectives model when cost and time are under consideration. Compared to other techniques, Goal programming has many advantages in resources plan- ning. Determining the required resources to satisfy the desired goals and the effectiveness of the available resources as well as providing best solutions under different amounts of resources are examples of the advantages of Goal programming. In addition the paper used data on Covid-19 to evaluate the performance of the suggested model for the exponential distribution. The study divided the number of new cases diseases into small, medium and high numbers. It also compared the results with the findings in the reports of the World Health Organization. The suggested mathematical goal programming revealed that Egypt was exposed to three waves of infection during the interval (5/3/2020 to 12/8/2021). These results are identical to the actual reality of covid-19 waves in Egypt. 1 Introduction The basic feature of stratified random sampling is that the internally strata units are homoge- nous, that is, stratum variances should be as small as possible. The equations for determining the optimum stratum boundaries were first provided by Dalenius [1]. Khan et. al. [2] studied the optimum strata width as a Mathematical Programming Problem that was solved using the dynamic programming technique. Khan et. al. [3] studied the problem of optimum stratifica- tion and formulated as a MPP assuming exponential frequency distribution of the main study variable. The stratum boundaries are optimum in the sense that they minimize the sampling PLOS ONE PLOS ONE | https://doi.org/10.1371/journal.pone.0271220 July 28, 2022 1/9 a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 OPEN ACCESS Citation: Abo_El.Hassan FS, Hamed R, Ismail EA, Ezzat SM (2022) Optimum stratum boundaries and sample sizes for Covid-19 data in Egypt. PLoS ONE 17(7): e0271220. https://doi.org/10.1371/journal. pone.0271220 Editor: Dylan A Mordaunt, Flinders University, AUSTRALIA Received: October 23, 2021 Accepted: June 24, 2022 Published: July 28, 2022 Copyright: © 2022 Abo_El.Hassan et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All data files are available from the WHO database (1- https:// github.com/owid/covid-19-data/tree/master/public/ data/#%EF%B8%8F-download-our-complete- covid-19-dataset–csv–xlsx–json). Funding: The authors received no specific funding for this work. Competing interests: The authors have declared that no competing interests exist.