key: cord-0749435-idne644s authors: Stanojevic, S. G.; Ponjavic, M.; Stanojevic, S.; Stevanovic, A.; Radojicic, S. title: Simulation and prediction of further spread of COVID-19 in The Republic of Serbia by SEIRDS model of disease transmission date: 2020-10-23 journal: nan DOI: 10.1101/2020.10.21.20216986 sha: c789d20702d2250346cb20d3ef1a991b52bcd7a0 doc_id: 749435 cord_uid: idne644s As a response to the pandemic caused by SARSCov-2 virus, on 15 March, 2020, the Republic of Serbia introduced comprehensive anti-epidemic measures to curb COVID 19. After a slowdown in the epidemic, on 6 May, 2020, the regulatory authorities decided to relax the implemented measures. However, the epidemiological situation soon worsened again. As of 15 October, 2020, a total of 35,454 cases of SARSCov-2 infection have been reported in Serbia, including 770 deaths caused by COVID19. In order to better understand the epidemic dynamics and predict possible outcomes, we have developed a mathematical model SEIRDS (S-susceptible, E-exposed, I-infected, R-recovered, D-dead due to COVID19 infection, S-susceptible). When developing the model, we took into account the differences between different population strata, which can impact the disease dynamics and outcome. The model can be used to simulate various scenarios of the implemented intervention measures and calculate possible epidemic outcomes, including the necessary hospital capacities. Considering promising results regarding the development of a vaccine against COVID19, the model is enabled to simulate vaccination among different population strata. The findings from various simulation scenarios have shown that, with implementation of strict measures of contact reduction, it is possible to control COVID19 and reduce number of deaths. The findings also show that limiting effective contacts within the most susceptible population strata merits a special attention. However, the findings also show that the disease has a potential to remain in the population for a long time, likely with a seasonal pattern. If a vaccine, with efficacy equal or higher than 65%, becomes available it could help to significantly slow down or completely stop circulation of the virus in human population. The effects of vaccination depend primarily on: 1. Efficacy of available vaccine(s), 2. Prioritization of the population categories for vaccination, and 3. Overall vaccination coverage of the population, assuming that the vaccine(s) develop solid immunity in vaccinated individuals. With expected basic reproduction number of Ro=2.46 and vaccine efficacy of 68%, an 87%- coverage would be sufficient to stop the virus circulation. On 11 March, 2020, the World Health Organization characterised the disease caused by the novel SARS period, severity of clinical signs, and mortality rate caused by COVID19. Unlike the classic SIR model, SEIRDS (S-susceptible, E-exposed, I-infected, R-recovered, D-dead due to COVID19 infection, S- This section presents the research methodology and the proposed model, which was used to predict the 101 further dynamics of the epidemic in Serbia. We also presented the data that were used to model the individuals in the population It. It depends on the number of infectious individuals (It) and how frequently they make contacts with other persons. In a situation of homogenous mixing among the population, the 114 force of infection λ can be express ae follows: 115 116 The change of rates in every compartment per unit time in SEIRDS model is presented in the following 117 series of differential equations: 118 Rt+1=rIt -(m+ω)Rt (5) Dt+1= δIt (6) where ƒ is rate of onset of infections expressed as the reciprocal of the latent infection period, r is the rate 124 at which infectious individuals are recovered, δ is the rate at which infectious individuals die from COVID 125 19 infection and ω is rate of waning of immunity. The total population at any particular interval of time t is: 126 Nt = St+ Et+ It+ Rt+ Dt+bNt-1-mSt-1 (7) where parameters b and m are per capita daily birth and death rates unrelated to COVID19. various levels of contact reduction, ranging from 25% to 75%, taking into account the realistic possibilities of maintaining a minimum work process, functioning of the society and feasibility of such measures. Given that intervention measures, applied in response to the emergence of COVID19, are not the 143 same for all population strata, homogeneous mixing can be expected only within same population stratum. The rate of effective contacts , after the application of intervention measures, is no longer identical at the Now our model will be expressed as follows: In this model susceptible, exposed, infectious, recovered, deaths and total population are: 163 164 166 167 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted October 23, 2020. 176 and the critical vaccination coverage required to achieved herd immunity can be obtained by multiplying 178 herd immunity threshold with reciprocal value of vaccine efficacy, ve: Most people infected with SARS-CoV-2 develop an immune response followed by the development 181 of specific antibodies between 10 and 21 days after getting infected [12] . Specific IgM and IgG antibodies against SARS-CoV-2 develop 6 to 15 days after the onset of the disease [13] [14] [15] [16] [17] . According to some studies, the presence of antibodies has been confirmed in less than 40% of the patients within 1 week after the onset of the disease, whereas percentage reaches 100% of subjects 15 days after the onset of disease [18] . Although duration of the immune response against CVOVID 19 is still unknown, comparing with other coronaviruses, immunity wane within 12 to 52 weeks after the first symptoms appear [19] , while in the case 187 of SARS-CoV-1 infection, the presence of IgG antibodies was confirmed in 90% and 50% of infected 188 patients, respectively, over two and three years, respectively [29] . Based on these findings, we assumed The compartment S(t) is slightly modified as follow: 206 The other of compartments of SERIDS model remain unchanged. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. is used as a source of the data: on the percentage of hospitalised patients and those whose therapy requires 235 intensive care, used for prediction of required hospital capacities, as shown in Table 1 [8]. Parameters such as δ and r are related to the infectious fatality rate (IFR) for COVID 19 and 237 average times taken from infection to death (TD) or recovery (TR). These parameters were calculated using 238 the following formulas: The IFRs, shown in Table 3 , were taken from literature and compared with local IFR value which was 242 calculated based on officially registered deaths published by the health system of the Republic of Serbia [2]. The Calculation of local IFR is presented in section 2.4. Population data, (e.g. total population, age 244 structure, and stratification) are presented in Tables 1 and 2. A summary of all model parameters is given 245 in Table 3 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted October 23, 2020. ; https://doi.org/10.1101/2020. 10 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted October 23, 2020. proportion susceptible >1/Ro and the proportion of population that is recovered (immune) is below the herd 362 immunity threshold. Fig. 2 panels a) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted October 23, 2020. ; https://doi.org/10.1101/2020.10.21.20216986 doi: medRxiv preprint days after the epidemic onset and it was 25,754 infected in one day. In the first year of the epidemic changed significantly. The initial infection doubling time was 9 days, the epidemic wave peak was reached after 164 days and it yield 65,327 infected people in one day. In the first year of the epidemic 5,021,561 394 people would get infected and 4,923 would die. Table 6 Table 6 and in Fig. 3 and Fig. 4) . Openings of pre-school and elementary school's facilities leads to a visible 405 jump in the number of infected and hospitalized in all strata. This finding clearly shows that children, although least susceptible to developing more severe clinical pictures, are important when transmitting 407 SARSCov-2 (Scenario 3 in Table 6 and Fig. 3) . Opening of the high schools and colleges also leads to a 408 visible increase in the number of newly infected and hospitalized patients, including an increase in the 409 number of deaths (Scenario 5 in Table 6 358 (3,120) beds in intensive care units (Fig. 4) . . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted October 23, 2020. ; https://doi.org/10.1101/2020. 10 is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted October 23, 2020. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted October 23, 2020. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted October 23, 2020. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted October 23, 2020. less intense than the measures applied at the beginning of the epidemic (Scenario 4), it is necessary to provide 3,508 beds in COVID hospitals and 2,617 beds in intensive care units in the entire country. The model also shows that the needs for hospital capacities decline with the ending of the first epidemic wave, since daily incidence decreases and during the second and third waves it never reaches the initial peaks, 471 but these needs still remain substantial. For example, in the case of Scenario 1, at the top of the second epidemic wave, it is necessary to provide 3,643 beds in COVID hospitals and 2,575 in intensive care units, which makes 30% and 25% of the required capacities of the first wave of the epidemic. Based on the cyclical patterns of the epidemic waves and duration of simulated epidemics, the 475 model demonstrated that the disease has a potential to linger in population and that it will most probably 476 have a seasonal pattern. Therefore, potential vaccines can have an enormous potential and significance 477 for COVID19 control. Depending on the efficacy of future vaccines, the disease can be stopped and curbed 478 almost solely by implementing the measure of vaccination. However, the necessary conditions for these . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted October 23, 2020. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted October 23, 2020. ; https://doi.org/10.1101/2020. 10 World Health Organization (WHO), Coronavirus disease (COVID-19) outbreak situation Extended SIR prediction of 503 the epidemics trend of COVID-19 in Italy and compared with Hunan Early dynamics of 506 transmission and control of COVID-19: a mathematical modelling study. The Lancet infectious diseases A contribution to the mathematical theory of epidemics. 2742 Impact of non-pharmaceutical interventions 516 (NPIs) to reduce COVID-19 mortality and healthcare demand Characteristics of and important lessons from the coronavirus disease 2019 (COVID-19) outbreak in China: Summary of a Report of 72 314 Cases from the Chinese Center for Disease 521 Control and Prevention White with an introduction by Paul E.M. Fine. An Introduction to Infectious ELISAs for detecting antibodies against SARS-CoV-2. medRxiv Antibody responses to SARS-CoV-2 in COVID-534 19 patients: the perspective application of serological tests in clinical practice. medRxiv. of novel coronavirus disease 2019 SARS-CoV-2 specific 539 antibody responses in COVID-19 patients Antibody responses to SARS-CoV-2 in patients 541 of novel coronavirus disease 2019. medRxiv The dynamics of humoral immune responses following SARS-CoV-2 infection 543 and the potential for reinfection. The Journal of general virology Mathematical 545 and Statistical Estimation Approaches in Epidemiology Blackwell Science Ltd, a Blackwell 548 Publishing company Assessment of the SARS-CoV-2 basic reproduction number, R0, 550 based on the early phase of COVID-19 outbreak in Italy World Developments Indicators ds=d5bncppjof8f9_&met_y=sp_dyn_le00_in&idim=country:S 553 RB:HRV:BIH&hl=en&dl=en#!ctype=l&strail=false&bcs=d&nselm=h&met_y=sp_dyn_le00_in&scale_y=lin& 554 ind_y=false&rdim=world&idim=country:SRB&ifdim=world&hl=en_US&dl=en&ind=false Infection fatality risk for SARS-CoV-2: a nationwide seroepidemiological 559 study in the noninstitutionalized population of Spain. medRxiv Simulating the spread of COVID CDC Centre for Evidence-Based Medicine develops, promotes and disseminates better 576 evidence for healthcare. Estimating the infection fatality ratio in England Did COVID-19 infections decline before UK lockdown? Centre for Evidence-Based Medicine develops, promotes and disseminates better 581 evidence for healthcare. COVID-19: What proportion are asymptomatic? Infection fatality risk for SARS-CoV-2: a nationwide seroepidemiological