key: cord-0757887-vo24dlg8 authors: Sedaghat, a.; Oloomi, S. A. A.; Malayer, M. A.; MOSAVI, A. title: Trends of COVID-19(Coronavirus Disease)in GCC Countries using SEIR-PAD Dynamic Model date: 2020-12-11 journal: nan DOI: 10.1101/2020.11.29.20240515 sha: 93ddd9a695d264d5221b2d6667151b3ae8a2e772 doc_id: 757887 cord_uid: vo24dlg8 Extension of SIR type models has been reported in a number of publications in the mathematics community. But little is done on validation of these models to fit adequately with multiple clinical data of an infectious disease. In this paper, we introduce the SEIR-PAD model to assess susceptible, exposed, infected, recovered, super-spreader, asymptomatic infected, and deceased populations. SEIR-PAD model consists of 7-set of ordinary differential equations with 8 unknown coefficients which are solved numerically in MATLAB using an optimization algorithm. Four sets of COVID-19 clinical data consist of cumulative populations of infected, deceased, recovered, and susceptible are used from the start of the outbreak until 23rd June 2020 to fit with SEIR-PAD model results. Results for trends of COVID-19 in GCC countries indicate that the disease may be terminated after 200 to 300 days from the start of the outbreak depends on current measures and policies. SEIR-PAD model provides a robust and strong tool to predict trends of COVID-19 for better management and/or foreseeing effects of certain enforcing laws by governments, health organizations, or policymakers. The coronavirus was first observed in chickens in 1930 and no traces were observed in humans until 1960. Seven type of coronaviruses to date were recognised which affected humans. Four types of the coronaviruses were not fatal. This include the coronavirus type 229E and OC43 . CC-BY 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted December 11, 2020. ; https://doi.org/10.1101/2020.11.29.20240515 doi: medRxiv preprint which caused common cold least severe disease; the coronavirus NL63 which caused suffering for babies from bronchiolitis in the Netherlands in 2004; and the coronavirus HKU1 which affected elderlies with pneumonia in Hong-Kong in 2005 [1] . In 2002, the fatal coronavirus with severe acute respiratory syndrome (Sars) named SARS-CoV was first observed in humans which is very similar to the current COVID-19. This virus affected elderly people with symptoms included fever, sore throat, cough, and muscle pain from 2002 until 2014. A deadlier coronavirus appeared after nearly a decade in Saudi Arabia known as Middle East respiratory syndrome coronavirus (MERS-CoV) in 2012 [2] . The MERS-CoV had largest impact in Saudi Arabia and reappeared in 2015 in South Korea and in 2018 in Saudi Arabia and United Arab Emirates which caused more than 35% mortality rate among infected people with fever, cough, and shortness of breath [3, 4] . Alasmawi et al. Ndaïrou et al. [7] applied similar SEIR type model for studying outbreak of COVID-19 in Wuhan, China with addition of fatality population in the model. Two set of clinical data including confirmed daily cases and daily death were used. Recently, Xue et al. [8] used similar SEIR type model for COVID-19 in Wuhan (China), Toronto (Canada), and the Italy. They found model coefficients using the optimization algorithm (MCMC) yet they validated their model against only two set of clinical data. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted December 11, 2020. ; https://doi.org/10.1101/2020.11.29.20240515 doi: medRxiv preprint In the above literature, it is ambiguous why 5 to 8 set of ordinary differential equations (ODE) should be used to study only one-parameter or one or two set of clinical data. With recent COVID-19 development, we can easily use 4 set of clinical data for validation of any SEIR type models. In this paper, we have developed SEIR-PAD model compose of 7 populations influenced by COVID-19 outbreak. The aim is to computationally predict trends of COVID-19 in GCC countries. SEIR-PAD model ODE equations are solved using an optimization technique (fminsearch) in MATLAB to find best model coefficients utilizing available clinical data in GCC countries. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted December 11, 2020. ; https://doi.org/10.1101/2020.11.29.20240515 doi: medRxiv preprint SEIR-PAD model has 8 unknown transmission coefficients x=[x1 x2 …x8] that can be obtained by an optimization algorithm in MATLAB by fitting available clinical data. The rest of transmission coefficients simply linearly relate flow in and flow out of populations as follows: The total population N is constant and is defined by: . CC-BY 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted December 11, 2020. ; https://doi.org/10.1101/2020.11.29.20240515 doi: medRxiv preprint MATLAB ode45 solver [11] is used together with the optimization tool (fminsearch) [12] to find best fitted solutions to the available COVID-19 clinical data using the following convergence criterion: Equation (10) is used for minimizing the root-mean-square ratio (rms ) of the four populations. Fminsearch in MATLAB returns the transmission rate coefficients that minimize the summation in Equation (10). Root-mean-square ratio (rms ) uses the coefficient of determination which is broadly used for comparing prediction variables with actual clinical data. The coefficient of determination (R 2 ) compares a predicted value ( ) against clinical data ( ) to provide rms as follows [13] : In equation (11), z represents a population and ̅ is an average value of the same population. Better prediction yields R 2 value close to one whilst rms merges to zero. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted December 11, 2020. Total expected deceased cases are 567 (see Fig. 2b ) cases by expected end of the pandemic after 220 days from start of outbreak; i.e. 1 st October 2020. This is based on present policies and preventive measure set for the country. As shown in Fig. 2c , expected total recovered cases by the end of pandemic is predicted 56,100 cases. Total susceptible population will be 723,250 by the end of pandemic (see Fig. 2d ). is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted December 11, 2020. ; https://doi.org/10.1101/2020.11.29.20240515 doi: medRxiv preprint June 2020 with 5,535 active cases (see Fig. 3a ). Total expected deceased cases are 73 (see Fig. 3b ) cases by expected end of the pandemic after 200 days from start of outbreak; i.e. 11 th September 2020. This is based on present preventive measures set by the Bahrain government. As shown in Fig. 3c , expected total recovered cases by the end of pandemic is predicted 29,200 cases. Total susceptible population will be 751,540 by the end of pandemic (see Fig. 3d ). . CC-BY 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted December 11, 2020. ; https://doi.org/10.1101/2020.11.29.20240515 doi: medRxiv preprint This is based on present preventive measures set by the Oman government. As shown in Fig. 4c , expected total recovered cases by the end of pandemic is predicted 69,260 cases. Total susceptible population will be 716,390 by the end of pandemic (see Fig. 4d ). . CC-BY 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted December 11, 2020. ; https://doi.org/10.1101/2020.11.29.20240515 doi: medRxiv preprint with 33,896 active cases (see Fig. 5a ). Total expected deceased cases are 152 (see Fig. 5b) cases by expected end of the pandemic after 184 days from start of outbreak; i.e. 1 st September 2020. This is based on present preventive measures set by the Qatar government. As shown in Fig. 5c , expected total recovered cases by the end of pandemic is predicted 75,700 cases. Total susceptible population will be 1,212,500 by the end of pandemic (see Fig. 5d ). . CC-BY 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted December 11, 2020. ; https://doi.org/10.1101/2020.11.29.20240515 doi: medRxiv preprint is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted December 11, 2020. ; https://doi.org/10.1101/2020.11.29.20240515 doi: medRxiv preprint Fig. 6c , expected total recovered cases by the end of pandemic is predicted 137,480 cases. Total susceptible population will be 1,338,400 by the end of pandemic (see Fig. 6d ). is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted December 11, 2020. ; https://doi.org/10.1101/2020.11.29.20240515 doi: medRxiv preprint Fig. 7c , expected total recovered cases by the end of pandemic is predicted 40,580 cases. Total susceptible population will be 51,950 by the end of pandemic (see Fig. 7d ). An eight parameter SEIR-PAD model is developed to study the COVID-19 pandemic. The SEIR-PAD is successfully implemented for four populations with available clinical data in MATLAB and best fitted model parameters are obtained using the optimization algorithm discussed here. The SEIR-PAD model is validated for predicting trends of COVID-19 in GCC countries. It is concluded that: . CC-BY 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted December 11, 2020. ; https://doi.org/10.1101/2020.11.29.20240515 doi: medRxiv preprint • Peak day of infection is predicted on 13 th with 5,766 active cases, and the total expected deceased cases of 73 by expected end of the pandemic on 11 th 357 active cases, and the total expected deceased cases of 760 by expected end of the pandemic on 21 st • Peak day of infection is predicted on 30 th May 2020 with 30,134 active cases, and the total expected deceased cases of 152 by expected end of the pandemic on 1 st with 39,158 active cases, and the total expected deceased cases of 1544 by expected end of the pandemic on 26 th with 15,867 active cases, and the total expected deceased cases of 581 by expected end of the pandemic on 22 nd A Brief History of Human Coronaviruses Treatment strategies for Middle East respiratory syndrome coronavirus Modeling of a super-spreading event of the MERScorona virus during the Hajj season using simulation of the existing data The characteristics of middle eastern respiratory syndrome coronavirus transmission dynamics in South Korea Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan A data-driven network model for the emerging COVID-19 epidemics in Wuhan A Contribution to the Mathematical Theory of Epidemics Probability and Statistics for Engineering and the Sciences Principal component analysis to study the relations between the spread rates of COVID-19 in high risks countries