key: cord-0257837-dwrusno8 authors: Nashebi, R.; Sari, M.; Kotil, S. title: Using a real-world network to model the tradeoff between stay-at-home restriction, vaccination, social distancing and working hours on COVID-19 dynamics. date: 2022-04-16 journal: nan DOI: 10.1101/2022.04.15.22273449 sha: 7b7c4454ffc12e6a2f2af14a9a33d47dde7c9e45 doc_id: 257837 cord_uid: dwrusno8 Background. Human behavior, economic activity, vaccination, and social distancing are inseparably entangled in epidemic management. This study aims to investigate the effects of various parameters such as stay-at-home restrictions, work hours, vaccination and social distance on the containment of pandemics such as COVID-19. Methods. To achieve this, we developed an agent-based model based on a time-dynamic graph with stochastic transmission events. The graph is constructed from a real-world social network. The graph's edges have been categorized into three categories: home, workplaces, and social environment. The conditions needed to mitigate the spread of wild-type (WT) COVID-19 and the delta variant have been analyzed. Our purposeful agent-based model has carefully executed tens of thousands of individual-based simulations. We propose simple relationships for the trade-offs between effective reproduction number (Re), transmission rate, work hours, vaccination, and stay at home restrictions. Results. For the WT, it has been found that a 13% increase in vaccination impacts the reproduction number, like the magnitude of decreasing nine hours of work to four and a single day of stay-at-home order. For the delta, 16% vaccination has the same effect. Also, since we can keep track of household and non-household infections, we observed that the change in household transmission rate does not significantly alter the Re. Household infections are not limited by transmission rate due to the high frequency of connections. For COVID-19's specifications, the Re depends on the non-household transmissions rate. Conclusions. Vaccination and transmission reduction are almost interchangeable. Without vaccination or teaching people how to lower their transmission probability significantly, changing work hours or weekend restrictions will only make people more frustrated Human behavior in households, workplaces, social environment during weekends and weekdays 49 have a vital role in the dissemination of infectious diseases such as middle east respiratory (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.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 April 16, 2022. ; https://doi.org/10.1101/2022.04.15.22273449 doi: medRxiv preprint Agent-based modelling is a computational approach to modelling complex systems with 82 autonomous agent interactions [38, 39] . Consequently, agent-based models are essential tools for 83 understanding the impact of human behavior in transmitting infectious diseases in different 84 environments such as households, workplaces, and social environments. Aleta et al. [40] used an 85 agent-based model with three layers: school, workplace, and household. They used their model to 86 investigate the influence of the closure of schools and stay-at-home restrictions. Another study by 87 Hoertel et al. The basic reproduction number (Ro) indicates infectious diseases' contagiousness or 95 transmissibility when the population is only susceptible [44] . At the same time, the effective 96 reproduction number (Re) estimates an epidemic's growth rate, which is influenced by the 97 containment strategies, herd immunity and any other factor [44] . Thus, estimates of COVID-19 98 are not exclusively determined by the pathogen, and variability depends on local socio-behavioral 77, 78] , and multiscale models [82, 83] to simulate the trade-off between 107 pharmaceutical (vaccination) and non-pharmaceutical (social distancing, stay-at-home restriction, 108 decrease in working hours) intervention in the containment of COVID-19 pandemic. This study 109 presents an agent-based model based on a time-dynamic network with stochastic transmission 110 events to analyze the interplay between pharmaceutical and non-pharmaceutical interventions. 111 We made thousands of carefully executed individual level simulations of multiscale modelling on 112 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. coordinates that the volunteers' mobile phones could provide. [37, 43] . 139 We want to categorize this network into households, workplaces, and social environments. In 140 other words, we classify each edge and contact into three categories. We choose contacts with an 141 average pairwise distance of 20m or less, making 3245 unique contacts. Our primary analysis 142 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. Fig. S2 ). After investigation, we developed procedures (see 146 supplementary information Table S1 ) to categorize the network edges and contacts in the 147 household, workplace, and social environment. There are 1350 unique contacts, which occurred 148 between 1m and 5m. We use the visualization method to classify 123, 514, and 713 of them as 149 household, workplace, and social environment contacts, respectively. 150 We established an automated classification algorithm to classify the remaining 1895 unique 151 encounters, which occurred between 6m and 20m distances. We develop the algorithm using 163 We have developed a discrete-time stochastic agent-based model, parameterized to simulate 164 distinct types of COVID-19 outbreaks across the Haslemere data set. An agent in our simulation 165 can be in the following states: E(t) (exposed), PS(t) (pre-symptomatic, documented), 166 A(t) (asymptomatic, undocumented), S(t) (symptomatic, documented), H(t) (hospitalized) 167 and R(t) (recovered) (Fig. 1C ). In our model, symptomatic individuals are symptomatic 168 concerning medical records; those who do not report symptoms are considered undocumented 169 (asymptomatic). The agent-based model starts with an exposed individual. Initially, the 170 jth individual is exposed to the virus, and he/she cannot infect others during his/her latent period 171 for d1=2.7 days (see supplementary information Table S2 ). After the latency period finishes, 172 the jth individual ends up in one of the two branches: pre-symptomatic with a ratio of s or 173 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 April 16, 2022. ; https://doi.org/10.1101/2022.04.15.22273449 doi: medRxiv preprint asymptomatic with (1s). When the period of delay from the onset finishes, we generate a 174 random number ε, and there are two probabilities for the j th individual to proceed; the first one, 175 if ε<1-s, he/she proceeds to the asymptomatic stage. The infectious period of the asymptomatic 176 stage is d3=5.4 days (see supplementary information in Table S2 ). Through the infectious period Table S2 . Constructing contact matrices and simulation with real-world social network data 194 We construct classification matrices for households, Hi,j, workplaces, Wi,j, and social There are three days in the Haslemere data: Thursday, Friday, and Saturday. Our simulations take 200 14 days, so we construct the more prolonged contact network using real data. The Weekday 201 contacts are taken from Thursday to Friday. We repeat each day sequentially and in whole. We Haslemere data. We start the simulation with two exposed individuals. The first 14 days are 204 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 April 16, 2022. ; https://doi.org/10.1101/2022.04.15.22273449 doi: medRxiv preprint designed as a warmup run. After 14 days, we randomly chose two individuals whose states are 205 exposed, presymptomatic, asymptomatic, or symptomatic. 206 We start with a more realistic initial sample of states by this method. Then, we restart the 207 simulation for another fourteen. We calculate the effective reproduction number (Re), infection 208 occurrence ratio, and secondary attack rate (SAR) of households from the second set of 14-day 209 simulations. We run five hundred trial simulations for each scenario. The default parameter 210 values for the simulations were present in Table S2 . By starting with only two infected 211 individuals, we aimed that the total cases at the end of 14 days do not exceed 10% of the total 217 We specify the probability that a susceptible agent i th becomes infected by a j th infectious agent in 218 a 5-minute interval is given as a function of distance in equation (1) for household and in counting the descendants of a discovered agent after the simulation is finished, then averaged for 231 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. We also compute the absolute error between the estimated and the exact household SAR model 257 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. Changing number of work hours during weekdays 261 We alter work hours during weekdays by changing the work edges of the network. According to 262 our classification methodology of the network, individuals work for 9 hours from 09:00 AM up 263 to 06:00 PM during weekdays. To decrease work hours from 9 hours to 9 -i (1≤ I ≤ 9) hours 264 during weekdays, we identify a home, work, and social environment edges between 06:00 PM Simulating stay-at-home restrictions 274 We have four stay-at-home restrictions scenarios: restrictions on Sunday, restrictions on Sunday 275 and Saturday, restrictions on Sunday, Saturday and Friday and restrictions on Sunday, Saturday, 276 Friday, and Thursday. After we form the 14 days of the contact network, we replace all non-277 household (workplace and social environment) contacts that occurred in a 5-minute time step 278 with a household contact that also occurred in that 5-minute interval. The infection probability is parameterized by two parameters, β and α. The α indicates the 282 probability of decay with the distance of contacts, whereas β is the maximum transmission 283 probability (at a distance of 0). We have obtained these parameters by sampling many 284 simulations that fit the COVID-19's RO and secondary attack rate. We use two β parameters, βh, 285 and βo, to distinguish between the infectiousness in households and outside. In our simulations, 286 we reduce the infectious probability to simulate a population where people reduce the probability 287 of infection by personal social distancing measures. The parameter β could be the total virus 288 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The agents that are vaccinated are chosen randomly. The vaccinated agents have reduced β value. 308 We have assumed a 93% and 88% reduction in infectiousness for the wild type and delta variants, 309 respectively [48] . So, β for the vaccinated, wild type and delta variant is 0.012 and 0.067, 310 respectively, whilst α is unchanged. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. After constructing the network and the tools for alteration, we first investigated how three 334 environments contribute to disseminating the disease on an unaltered network. In that analysis, 335 we also vary the social distancing parameter. Secondly, we investigate the effect of stay-at-home 336 orders on weekends. Thirdly, we investigate all parameters together: change of work hours, 337 vaccination, stay-at-home orders, and social distancing. To simulate this phenomenon, we reduce the total transmission rate by decreasing the non-345 household transmission (βo) while fixing the household transmission rate βh. Squares with a line 346 in Fig. 2a show Re's dependence on varying βo when βh is constant. Additionally, triangles with a 347 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 April 16, 2022. ; https://doi.org/10.1101/2022.04.15.22273449 doi: medRxiv preprint line show the dependence of Re on varying βo when βh is also changing, βo = βh. The latter 348 simulations are made to assess the effect of making the distinction between βo and βh. 349 Interestingly, until Re<1, Re does not depend on the decrease of βh. Only after Ro<1 further 350 decreasing in βh decreases Re more than when βh is kept at its maximum. The household, workplace, and social environment infection occurrence ratio has been counted 352 for Re (for real networks). Overall, the household infections are dominant when Re<1 and most of 353 the infections occur in the social environment when Re<2.5. 354 We capture the only difference between Fig. 2b (βh kept constant) and Fig. 2c Re's decreasing is much faster than the real networks (Fig. 2a) . Thus, decreasing Re in real 369 networks is harder and retains infection chains. Overall, we speculate that the household transmission reaches its capacity at low βh due to (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. reported from the Al-Jawf Region, Saudi Arabia, including seven cases, six of which were 379 household contacts [81] . According to our results (Fig. 2a) The discrepancy is that the unique pairs for H connections are scarce, but their frequency is 408 significantly higher. 409 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. Fig. 4b, and Fig. 4c . As detailed in the methods, the household edges replace the social 423 environment edges to implement the weekend restrictions. 424 We have found that stay-at-home restrictions during the weekends cause a decrease in Re. Figure 425 5a shows that Ro drops from 2.95 to 2.71 for restrictions on Saturdays and to 2.56 when 426 restrictions are on Saturdays and Sundays. Fig. 5b, Fig. 5c, Fig. 5d show the ratio of infection 427 occurrence ratio for increasing Re when implementing stay-at-home restrictions during weekends. When stay-at-home restrictions increase, the social environment's infection decreases, and work 429 infections increase. The subsequent alteration to the network is on working hours. We alter working hours by 437 changing working edges. For example, if the working hours decreased from nine to eight hours, 438 the work edges between 5 pm to 6 pm are converted to a sample from the edges between 6 pm to 439 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 April 16, 2022. ; https://doi.org/10.1101/2022.04.15.22273449 doi: medRxiv preprint 11 pm, as detailed in the methods. The edge frequencies of the altered networks are given in 440 supplementary information Fig. 6a, Fig. 6b, Fig. 6c, Fig. 6d, and Fig. 6e . Plotting for all simulations is hindered due to the multidimensionality of the results. Deducing a 451 closed-form solution is also almost impossible. Instead, we wanted to approximate the solutions 452 by fitting a multidimensional linear surface (Taylor expansion). The linear surfaces yielded a poor fit. A nonlinear dependence is clearly observed when the data (which was not certified by peer review) 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 April 16, 2022. ; https://doi.org/10.1101/2022.04.15.22273449 doi: medRxiv preprint specifically, for the WT, one day of the weekend restriction equals more than 4 hours of work per 465 weekday. In comparison, one day of restriction is equal to 13.3% vaccination. For the delta 466 variant, the effect of the decrease in working hours and weekend restrictions act the same, while 467 one day of restriction is equal to 20% per cent of vaccination. However, the relative effect of 468 vaccination is 20% less effective than the WT. It is important to note that the validity of functions is limited to the simulated ranges of The parameters that we have simulated, DW and SH, vary marginally. For example, DW 481 (Decrease in Work hours) only changes from 0 to 4 hours. In terms of working hours, the DW 482 varies from 9 hours to 5 hours of work. In the simulated range, Re is not significantly affected. Perhaps simulating for the remaining hours, from 9 to 0 hours of work, would show the non-484 linearity that we have suspected. However, the point we want to make is that a marginal decrease 485 in working hours (several hours) leads to a minimal decrease in Re. The working hours must be 486 decreased substantially to decrease Re significantly. However, its burden on economic activity 487 would be profound. The range for SH (stay-at-home restrictions) has been simulated from 0 to 4 days. The (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. complicated simulations on the real network. This network is also inherently heterogeneous. Understanding the numerical solutions is troublesome when there are many parameters. We have 503 guessed a simple mathematical expression for the whole simulation to circumvent that problem. First of all, the restrictions can be added to each other. All measures are worth considering. However, any measure that is not taken to almost completion does not significantly affect the 509 outbreak. This means that at least one measure must be performed to its maximum level. Mixing [33]. Since there are only three days of data, we reuse the data five times. We tried to decrease 519 the effect of this by only performing brief simulations. Simulations last for 14 days, and we only 520 allow for a maximum of around twenty infections per simulation. We recommend for social 521 network data miners increase their sample size during data collecting from a population. It is 522 important to note that our results depend heavily on the real-world network. We claim that our 523 results are correct on our real-world network. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. Consequently, the interplay between pharmaceutical and non-pharmaceutical intervention in the 535 containment of COVID-19 has been investigated. The computed results showed that the restrictions could be added to each other. All measures are 537 worth considering. Vaccination and transmission reduction are almost interchangeable. Our 538 simulations have been shown that without vaccination or teaching people how to lower their 539 transmission probability significantly, changing work hours or weekend restrictions will only 540 make people more frustrated. This study reassures us to investigate the influence of human behavior, economic activity, 542 vaccination, and social distancing by using a more realistic network. The real network that has 543 been used in this study does not include children under thirteen. We also recommend for social 544 network data miners increase their sample size during data collecting from a population. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. york-state-pause-executive-order (2020) 584 All rights reserved. No reuse allowed without permission. 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The copyright holder for this preprint this version posted Risk 645 assessment at work and prevention strategies on COVID-19 in Italy Scientific consensus on the COVID-19 pandemic: we 649 need to act now 652 Supplemental Information for: Sparking "The BBC Four Pandemic": Leveraging citizen 653 science and mobile phones to model the spread of disease Tutorial on agent-based modelling and simulation Agent-Based Modeling in 657 Public Health: Current Applications and Future Directions Modeling the Impact of Social Distancing Contact Tracing and Household Quarantine on Second-Wave Scenarios of the COVID-663 19 Epidemic A Stochastic Agent-Based Model of the SARS-CoV-2 Simulating Phase 668 Transitions and Control Measures for Network Epidemics Caused by Infections with Sparking 'The BBC 671 Four Pandemic': leveraging citizen science and mobile phones to model the spread of 672 disease No reuse allowed without permission. 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The copyright holder for this preprint this version posted Complexity of the Basic Reproduction Number (R0) Population density and basic reproductive 677 number of COVID-19 across United States counties Infectious Diseases of Humans, Dynamics and Control: OUP 679 Oxford Delta Variant: What We Know 681 About the Science Effectiveness of Covid-19 Vaccines against the B.1.617.2 (Delta) Variant Estimating the time interval between transmission generations and the 687 presymptomatic period by contact tracing surveillance data from 31 provinces in the 688 mainland of China Hospitalisation and Recovery or Death: Statistical Analysis of Belgian COVID-19 Impact of vaccine supplies and 695 delays on optimal control of the COVID-19 pandemic: mapping interventions for the A primer 699 on using mathematics to understand COVID-19 dynamics: Modeling, analysis and 700 simulations Will an imperfect vaccine 703 curtail the COVID-19 pandemic in the 706 Vaccination and non-pharmaceutical interventions for COVID-19: a mathematical 707 modelling study Optimality in COVID-19 vaccination strategies determined by 711 heterogeneity in human-human interaction networks Oxford Coronavirus 715 Government Response Tracker, Our World in Data Timing of State and Territorial COVID-19 Stay-at-Home Orders and Changes in Population Movement -United States Public Attitudes, Behaviors, and Beliefs 728 Related to COVID-19, Stay-at-Home Orders, Nonessential Business Closures, and Public 729 Health Guidance -United States No reuse allowed without permission. 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The copyright holder for this preprint this version posted Optimal allocation of limited vaccine to control 733 an infectious disease: Simple analytical conditions COVID-19) Cases Mathematical model of COVID-19 with 739 comorbidity and controlling using non-pharmaceutical interventions and vaccination Modeling 742 of Vaccination and Contact Tracing as Tools to Control the COVID Kong Jude and Raad Angie 745 2021Integrated vaccination and non-pharmaceutical interventions based strategies in as a case study: a mathematical modelling studyJ The Joint Impact of COVID-19 Vaccination and 749 Non-Pharmaceutical Interventions on Infections, Hospitalizations, and Mortality: An 750 Agent-Based Simulation A multi-scale agent-based 753 model of infectious disease transmission to assess the impact of vaccination and non 754 pharmaceutical interventions: The COVID-19 case Non-pharmaceutical interventions, 761 vaccination, and the SARS-CoV-2 delta variant in England: a mathematical modelling 762 All rights reserved. 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The copyright holder for this preprint this version posted Assessing the efficacy of interventions to control 765 indoor SARS-Cov-2 transmission: An agent-based modeling approach Using data-driven agent-based models for forecasting 769 emerging infectious diseases Modeling of 771 Vaccination and Contact Tracing as Tools to Control the COVID Assessing the efficacy of interventions to control 774 indoor SARS-Cov-2 transmission: An agent-based modeling approach 777 Vaccination and non-pharmaceutical interventions for COVID-19: a mathematical 778 modelling study Mathematical model of COVID-19 with 781 comorbidity and controlling using non-pharmaceutical interventions and 782 vaccination Kong Jude and Raad Angie 785 2021Integrated vaccination and non-pharmaceutical interventions based strategies 786 in Ontario, Canada, as a case study: a mathematical modelling studyJ The Joint Impact of COVID-19 Vaccination and Non-789 Pharmaceutical Interventions on Infections, Hospitalizations, and Mortality: An 790 Agent-Based Simulation No reuse allowed without permission. 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The copyright holder for this preprint this version posted Non-pharmaceutical interventions, vaccination, and the 794 SARS-CoV-2 delta variant in England: a mathematical modelling study, The Lancet Issue 10313 Fontanet Interhuman transmissibility of Middle East 798 respiratory syndrome coronavirus: estimation of pandemic risk Lancet Lipsitch Nuanced risk assessment for emerging 801 infectious diseases Lancet Middle East respiratory syndrome coronavirus: quantification of the extent of the 804 epidemic, surveillance biases, and transmissibility WHO MERS Global Summary and Assessment of Risk, WHO/MERS/RA/August18 A multi-scale agent-based 809 model of infectious disease transmission to assess the impact of vaccination and non 810 pharmaceutical interventions: The COVID-19 case Emergent effects of contact tracing robustly stabilize outbreaks Contagion! the bbc four pandemic-the 816 model behind the documentary All rights reserved. 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