key: cord-0889097-9j2ofgit authors: David, J. F.; Iyaniwura, S. A.; Yuan, P.; Tan, Y.; Kong, J. D.; Zhu, H. title: Modeling the potential impact of indirect transmission on COVID-19 epidemic date: 2021-02-01 journal: nan DOI: 10.1101/2021.01.28.20181040 sha: 8b1b20809e7800c5eab08975b4e939b1a3c1d298 doc_id: 889097 cord_uid: 9j2ofgit The spread of SARS-CoV-2 through direct transmission (person-to-person) has been the focus of most studies on the dynamics of COVID-19. The efficacy of social distancing and mask usage at reducing the risk of direct transmission of COVID-19 has been studied by many researchers. Little or no attention is given to indirect transmission of the virus through shared items, commonly touch surfaces and door handles. The impact of the persistence of SARS-CoV-2 on hard surfaces and in the environment, on the dynamics of COVID-19 remain largely unknown. Also, the current increase in the number of cases despite the strict non-pharmaceutical interventions suggests a need to study the indirect transmission of COVID-19 while incorporating testing of infected individuals as a preventive measure. Assessing the impact of indirect transmission of the virus may improve our understanding of the overall dynamics of COVID-19. We developed a novel deterministic susceptible-exposedinfected- removed-virus-death compartmental model to study the impact of indirect transmission pathway on the spread of COVID-19, the sources of infection, and prevention/control. We fitted the model to the cumulative number of confirmed cases at episode date in Toronto, Canada using a Markov Chain Monte Carlo optimization algorithm. We studied the effect of indirect transmission on the epidemic peak, peak time, epidemic final size and the effective reproduction number, based on different initial conditions and at different stages. Our findings revealed an increase in cases with indirect transmission. Our work highlights the importance of implementing additional preventive and control measures involving cleaning of surfaces, fumigation, and disinfection to lower the spread of COVID-19, especially in public areas like the grocery stores, malls and so on. We conclude that indirect transmission of SARS-CoV- 2 has a significant effect on the dynamics of COVID-19, and there is need to consider this transmission route for effective mitigation, prevention and control of COVID-19 epidemic. other existing model since we incorporated testing of both asymptomatic and 56 symptomatic individuals. In addition, our model is the first to use multiple transmission 57 routes to estimate the impact of indirect transmission on the peak, peak time, the 58 effective reproduction number and the epidemic final size. We focus our analysis on [24] . Similarly, on January 18, 2021, the city of 71 Toronto reported 583 newly confirmed cases, with 5 new deaths, resulting into 75,273 72 cumulative confirmed cases with 2,211 total COVID-19-related deaths, and 67,219 73 recovered cases [25] . In addition to cases transmitted through close contacts, several 74 evidences point to indirect transmission of COVID-19 in loblaw stores [20] and 75 Sobeys [21] , we present a SEIRVD model to study the effect of indirect transmission, number of the combined model is calculated using the next generational matrix 85 approach [26, 27] , and expressed as the sum of the effective reproduction numbers of 86 the direct transmission and that of indirect transmission pathways. Similarly, the final 87 size relation is estimated following the approaches in [28] [29] [30] . In addition, the The model diagram presented in Figure 1 is described by the system of non-linear which is the probability of the disease transmission from a contact between individuals 116 in S and the virus in the environment or contaminated surfaces V , and the number of 117 contacts per day per length. The parameter p 1 represents the proportion of susceptible individuals protected from 119 direct transmission as a result of effective mask usage, while p 2 is the proportion of 120 susceptible individuals protected from indirect transmission (i.e. through environmental 121 protection, such as sanitation, cleaning of surfaces and door handles, environmental 122 disinfection, fumigation and so on). Exposed individuals become infectious at a rate δ, 123 where a proportion r of these individuals are symptomatic, and the remaining (1 − r) 124 are asymptomatic. Asymptomatic individuals are tested at the rate γ A , where a 125 fraction α A become hospitalized, and the remaining 1 − α A are isolated. We believe 126 that asymptomatic individuals show mild or no symptoms, but a small proportion of 127 those tested who are more vulnerable could be hospitalized as a precautionary measure. 128 Hence our justification for assuming that a fraction α A of this population could be 129 hospitalized. Similarly, symptomatic individuals are tested at the rate γ S , where a 130 fraction α S become hospitalized, and the remaining 1 − α S are isolated. Asymptomatic, 131 symptomatic, hospitalized and isolated individuals recover from the disease at rates ρ A , 132 ρ S , ρ H and ρ W , respectively. In addition, symptomatic, hospitalized and isolated 133 individuals die at rates µ S , µ H , and µ W , respectively, ignoring deaths of asymptomatic 134 individuals since there are no available data. Table ( 1) is given as susceptible individuals that will be infected is reduced by p 1 (proportion protected from 157 direct transmission) and p 2 (proportion protected from indirect transmission), and the 158 reproduction number computed is called the effective reproduction number R e . Using 159 the next generation matrix approach [26, 27] as in [28] [29] [30] , we have the effective 160 reproduction number given as Note that N (0) = N since the total population is constant at all time. R e can also 162 be written as and The expression for R e in equation (2) denotes the secondary infections contributed by 165 direct transmission R D and indirect transmission R I . The final size relation 167 The final epidemic size can be derived from the solution of the final size relation. This 168 relation gives an estimate of the total number of infections and the epidemic size for the 169 period of the epidemic using the parameters in the model [28, 31, 32] . Therefore, in order 170 to estimate the total number of cases and deaths, we use the approach in [28] [29] [30] to 171 derive the final size relation as Equation (5) implies S ∞ > 0. 2. If the outbreak begins through direct contact and no infected individuals January 26, 2021 7/26 . 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 February 1, 2021. ; 3. If the outbreak begins through direct and indirect contact and no infected 210 individuals (I A = I S = I H = I W = 0), the final size relation takes the form Modeling scenarios 212 For model fitting, the initial values are set to the scenario in the data obtained from [33] 213 (see scenario 1 on Table 6 ). Table 3 ), while others are estimated from the MCMC parameter estimation (see 243 . 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 February 1, 2021. ; Table 2 . 259 January 26, 2021 9/26 . 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 February 1, 2021. ; Tables 2 and 3 . The results of the parameter estimation as in Table 2 indicate that most reported 260 cases in Toronto from March to August are reportedly through direct transmission since 261 the estimated shedding rate for symptomatic individuals is very low with ω 2 = 0.025193 262 (see Table 2 ). This shows that based on our model outcome from March 1 to August 31, 263 January 26, 2021 10/26 . 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 February 1, 2021. ; https://doi.org/10.1101/2021.01.28.20181040 doi: medRxiv preprint indirect transmission seem to have little effect on the number of confirmed cases in 264 Toronto. Therefore, we explore scenarios for when ω 2 will actually impact the epidemic 265 (i.e. when ω 2 ≥ 0.5) and show the potential effect of indirect transmission. Hence, in 266 the following subsection, we explore different situations in our numerical simulations 267 when ω 2 = 0.5 or varied. The reproduction number for stages I, II and III using Toronto 269 related scenario 270 In this section, we show the impact of the parameters estimated at different stages of 271 the epidemic on the reproduction number for Toronto scenario. Table 4 and 5 show 272 estimates of the reproduction number using three different stages for Toronto scenario. 273 In Table 4 the estimated parameter for the symptomatic shedding rate (ω 2 = 0.025193) 274 is used, while ω 2 = 0.5 is used in Table 5 for illustrative purpose. Other parameters 275 used are as given in Tables 2 and 3 . Here, we compare Tables 4 and 5 for when ω 2 = 0.025193 and ω 2 = 0.5, respectively. 277 We see from these tables that the impact of indirect transmission is lower in Toronto 278 due to lower amount of viruses being shed by symptomatic individuals (ω 2 = 0.025193). 279 Using Table 5 for illustration, we have that the reproduction number changing and 280 increasing when more viruses are being shed. For both tables, even though the 281 contribution of R D to the total R e seems higher than R I , the value of R e is still able 282 to increase with increase in ω 2 . The full description of how changes in ω 2 affects the 283 reproduction number R e is shown in Figure 5 . For both direct and indirect transmission, the reproduction numbers are highest in 285 stage I and lowest in stage III, which means that infection is highest in stage I. We can 286 interpret biologically that if interventions and control measures in stage I are kept the 287 same throughout the outbreak, the epidemic peak will be quickly reached within a 288 shorter peak time and with a higher reproduction number compared to other stages. Table 6 shows three different scenarios with initial conditions, and different estimates of 292 the number of symptomatic individuals. Table 6 are presented in Fig 3 and Table 6 and 305 Fig 4a) . The final size for this scenario is given as 207250. Table 6 . The parameters used are given in Tables 2 and 3 except for ω 2 = 0.5. For the scenario with V 0 = 5 and no infected individuals at the beginning (Scenario 307 2 in Table 6 respectively. In addition, the final size for this scenario is estimated as 15143, which is 313 lower than the final size in scenario 1. Table 6 . The parameters used are given in Tables 2 and 3 except for ω 2 = 0.5. The cumulative number of cases and prevalence of symptomatic individuals for the 315 scenario with a few infected individuals at the beginning of the epidemic and V 0 = 5 316 (Scenario 3 in Table 6 ) are shown in Figs 3c and 4c, respectively. This scenario is used 317 to model an instance where the epidemic starts with both transmission routes. Here, 318 there are about 60685 symptomatic individuals at the epidemic peak, which occurs at 319 day 83. For the case with only direct transmission, the epidemic peaked at day 84 with 320 38807 symptomatic individuals. The final size for this scenario is estimated as 219850, 321 which is the highest of all scenarios. 322 We observe from the results presented in this section that no matter where and how 323 the outbreak is starting, the case of direct and indirect transmission lead to more 324 infections (almost doubling) than that of only direct transmission. This is due to the 325 impact of indirect transmission which are not accounted for in the case with only direct 326 transmission. In addition, we notice that scenario 2 has the lowest peak size and the 327 same peak time. This is because there are no infected individuals in the population to 328 shed viruses at the beginning of the epidemic. Note that no matter where the epidemic 329 is starting (direct or indirect route for different scenarios), the disease is still able to 330 spread but with different peak. But all scenarios in Table 6 show that the epidemic is 331 much worse for scenario 3, i.e. the situation where the outbreak begins through direct 332 and indirect transmission routes. In addition, we observe from our model outcome that 333 the epidemic will reach its peak a day earlier (day 83) for direct and indirect 334 transmission if we have some infected individuals at the beginning of the outbreak as in 335 Scenarios 1 and 3. There seems to be no significant difference in the peak times of Here, we present contour plots of the final epidemic size and the effective reproduction 340 number with respect to ω 1 and ω 2 . The left panel of Fig 5 shows the final epidemic size 341 of our model plotted with respect to the shedding rates ω 1 and ω 2 (Figs 5a, 5c and 5e in 342 column 1). These figures are for parameters, interventions and control measures in 343 stages I, II, and III, respectively as given in Table 2 . We observe from these plots that 344 the shedding rate of asymptomatic individuals (ω 1 ) has no obvious effect on the final 345 epidemic size for the three stages. On the other hand, as one may expect, an increase in 346 the shedding rate of symptomatic individuals (ω 2 ) increases the final epidemic size for 347 all stages, especially for stage II since the data accounts for symptomatic individuals. The epidemic size is largest in stage I, reduced in stage II, and smallest in stage III. These results are shown in the first column of Figure 5 . 15 15 15 15 15 15 16 16 16 16 16 16 17 17 17 17 17 17 18 18 18 18 18 18 19 19 19 19 19 19 20 20 20 20 20 20 21 21 21 21 21 21 22 22 22 22 22 22 23 23 23 23 23 I, II, and III from Table 2 , for the Toronto related scenario. Column 1 which consists of Figs 5a, 5c, and 5e are showing the effect of varying the shedding rates ω 1 and ω 2 on the final epidemic sizes for stages I, II, and III respectively, while column 2 which consist of Figs 5b, 5d, and 5f are showing the effect of varying the shedding rates ω 1 and ω 2 on the reproduction number R e stages I, II, and III respectively. Other parameters are as given in Tables 2 and 3 . Rows 1, 2 and 3 are for stages I, II and III, respectively. The right panel of Fig 5 shows the contour plots of the reproduction number R e 351 with respect to the shedding rates ω 1 and ω 2 (Figs 5b, 5d , and 5f in column 2) for 352 stages I, II, and III described in Table 2 . For all stages, we observe from these plots that 353 the reproduction number increases as ω 2 increases, and an increase in ω 1 has no obvious 354 effect, which is similar to the trend shown from the contour plots of the final epidemic 355 sizes (column 1). This shows the impact of shedding of viruses in increasing cases since 356 an increase in the value of ω 2 means that more viruses are shed by symptomatic including lockdown, social distancing, mask usage were kept as in stage III, in addition 369 to the effort to decrease indirect transmission by reducing the shedding rates, the 370 disease will quickly die out (as seen from the reproduction number in stage III with low 371 ω 1 and ω 2 ) and an increase in the final epidemic size will not be significant. In this section, we explore the effect of varying the indirect transmission rate β I and the 377 proportion of individuals protected from indirect transmission p 2 , on the final epidemic 378 size for stages I, II and III. In Fig 6, we present contour plots of the final epidemic size 379 with respect to the parameters β I and p 2 . Figs 6a, 6b, and 6c are for stages I, II and III, 380 respectively as given in Table 2 . Table 2 . Figs 6a, 6b, and 6c are for varying the indirect transmission rate β I and the proportion of individuals protected from indirect transmission p 2 , with ω 2 = 0.5 in stages I, II, and III, respectively. Other parameters are as given in Tables 2 and 3 . For all stages, we observe from these plots that the final epidemic size decreases as 382 p 2 increases, and increases as β 1 increases. This shows the role of environmental 383 protection in averting cases since an increase in the values of p 2 means that more people 384 are protected from contracting infections through indirect transmission, thereby 385 lowering the epidemic size as observed from the contour plots. On the other hand, an 386 increase in the values of β I implies that infections are transmitted through indirect 387 route at a higher rate, leading to a larger outbreak. In addition, we observe that stage 388 III (Fig 6c) has lowest final epidemic sizes, followed by stage II, while stage I has 389 highest final sizes. This means that if parameters and measures in stage III are 390 implemented during an outbreak, the disease is still able to spread but with a lower 391 final size when compared to other stages. We can biologically interpret that different 392 control measures, especially measures related to indirect transmission (like β I and p 2 ) 393 need to be implemented in order to curtail or eliminate the epidemic. Tables 2 and 3 . Figs 7a, 7b and 7c are for stages I, II, and III respectively. We also notice in stage II (Fig 7b) that the prevalence of symptomatic individuals at 412 the peak increases slightly as ω 1 increases for both DI and D with a lower number of 413 symptomatic individuals at the peak, and with a longer peak time when compared to 414 stage I. When parameters and measures in stage II are kept, the epidemic is delayed 415 compared to stage I. In contrast to stages I and II, stage III (Fig 7c) shows that the 416 prevalence of infected individuals decreases with time and the disease dies out. Also, we 417 see no significant different in I S for doth DI and D when ω 1 is varied. This biologically 418 means that the shedding of the virus by asymptomatic individuals has a slight impact 419 on the transmission of infection for all stages, and many models ignoring transmission 420 resulting from the viruses being shed may not account for this slight impact. Here we vary the shedding rate of symptomatic individuals ω 2 . Fig. 8 shows the 424 prevalence of symptomatic individuals over time for stages I, II, and III in Table 2 increases. As ω 2 increases, epidemic occurs faster, and quickly reaches it peak with an 431 increasing number of infected individuals at the peak, and a decreasing peak time. In 432 contrast, for stage I (Fig 8a) and D (Dashed curves), we observe that the prevalence of 433 symptomatic individuals decreases slightly with an increase in ω 2 . As ω 2 increases, both 434 the number of symptomatic individuals at the peak and the peak time decrease. In 435 order words, if parameters in stage I are implemented and more viruses are being shed 436 by symptomatic individuals, we have more infections for DI and less infections for D. In 437 addition, the difference in the peak of DI and D becomes wider as ω 2 increases, showing 438 how ω 2 affects DI more compared to D. Stage I also buttresses our points and 439 arguments from 7a that the peak in DI is higher than that of D regardless of the value 440 of ω 2 , with DI accounting for the contribution of indirect transmission. Despite the In stage II (Fig 8b) and DI (solid curves), we observe that an increase in ω 2 444 significantly increases the number of symptomatic individuals at the peak and with a 445 decreasing peak time. Simply put, when ω 2 increases, the infected individuals at the 446 peak increases, the peak time decreases, meaning more infections which cause the 447 epidemic to reach its peak at a shorter time. Similar trend is shown in stage II (Fig 8b) 448 and D (dashed curves), except that an increase in ω 2 slightly increases the number of 449 symptomatic individuals at the peak. In addition, epidemic is delayed in stage II 450 compared to stage I, and the effect of ω 2 in stage II is significantly higher than that of 451 stage I. Similar to our results in Fig 7c , ω 2 = 1.0 accounted for more infections for DI, 452 but the disease in this stage dies out within a shorter period of time. In For all values of 453 ω 2 , and for DI and D in stage II, the epidemic started at about 100 days or latter, and 454 ended at different time. But an increase in ω 2 decreases the epidemic ending time (i.e., 455 the lowest ω 2 has the longest ending time). If ω 2 is kept lower (for example, ω 2 ≤ 0.1), 456 the epidemic will occur late, but with a very low peak. 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 February 1, 2021. ; https://doi.org/10.1101/2021.01.28.20181040 doi: medRxiv preprint and II. When these measures are implemented, the difference between DI and D may 460 not be obvious. It is good to also note that varying ω 2 has a greater effect on the peak 461 size and peak time compared to varying ω 1 . This biologically means that the shedding 462 of the virus by symptomatic individuals has a huge impact on both direct and indirect 463 transmission (DI), especially when ω 2 ≥ 0.4. Models with no indirect transmission and 464 estimating the prevalence of symptomatic individuals, will account for the plots shown 465 with dashed curves (D) without accounting for the differences in the solid curves (DI) 466 and dashed curves (D). In other words, changes in ω 2 impact the dynamics, the peak 467 and the peak time more than changes in ω 1 . Effect of varying the symptomatic shedding rate ω 2 on the peak 469 size and peak time in stage II individual (ω 2 ) increases for both DI and D. Simply put, when ω 2 increases, the infected 476 individuals at the peak size increases, the peak time decreases, meaning more infections 477 which cause the epidemic to reach its peak at a shorter time. Although, the increase in 478 peak size with increase in shedding rate is higher and more obvious in DI (blue bar) showing how ω 2 affects DI more compared to D. Furthermore, we see from 9a that the 486 peak size in DI is higher than that of D regardless of the value of ω 2 , with DI 487 accounting for the contribution of indirect transmission. In Fig. 9b , for all values of ω 2 , 488 and for DI and D, the lowest ω 2 has the longest peak time). If ω 2 is kept lower (for 489 example, ω 2 ≤ 0.1), the epidemic will occur late and with a very low peak size. . 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 February 1, 2021. ; From these simulations, it is obvious that difference and changes in control measures 491 related to indirect transmission could cause changes in the peak size of the epidemic. In 492 fact, they also have significant effect on the time of the peak and the end of the epidemic. 493 This concludes the importance and effort needed to lower transmission occurring epidemic size. Our study shows that the shedding of viruses, especially by symptomatic 503 individuals has a huge effect on COVID-19 transmission, and efforts towards reducing 504 virus shedding will significantly reduce the epidemic. We show that the epidemic of 505 COVID-19 could be better curtailed when additional interventions relating to indirect 506 transmission are combined with the current control measures. We see that reducing the 507 shedding of SAR-CoV-2 to the minimum possible will reduce the peak, peak time, 508 effective reproduction number and the final epidemic size. Our results show larger epidemic peak and final sizes for the case of both direct and 510 indirect transmission (DI) compared to that of only direct transmission (D), irrespective 511 of the initial condition and the stage of the infection. The most successful strategy that 512 give the lowest peak and the highest peak time for symptomatic individuals is to reduce 513 the shedding rates of both asymptomatic and symptomatic individuals to lower than 514 0.01 and 0.1 (i.e. ω 1 < 0.01 and ω 2 < 0.1) respectively. In addition, we show that the 515 final epidemic size is highest when transmission rate (β I ) is high and the rate of . 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 February 1, 2021. ; https://doi.org/10.1101/2021.01.28.20181040 doi: medRxiv preprint for different opinion and behaviour, and the complexities that exist in behavioural 541 changes. Even though, these conditions are somewhat important factors in modeling the 542 transmission of COVID-19, modeling their effects would make the model more 543 complicated, which is beyond the scope of this study, and therefore considered as one of 544 the future works we intend to explore. Despite these limitations, our findings show that 545 reducing the transmission of the virus through indirect route would significantly 546 decrease the spread of the disease, especially when efforts are concentrated more on the 547 symptomatic individuals through further isolation and/or hospitalization. We believe 548 that models that do not consider indirect transmission of the virus may underestimate 549 the cases, and consequently the final epidemic size and the reproduction number. In 550 addition, models considering only direct transmission will overestimate the peak time 551 since the peak time is reduced when more viruses are shed. Efforts such as fumigation, 552 cleaning of surfaces, sanitation, towards reducing transmission from this route will help 553 at lowering the epidemic of COVID-19. In addition, Toronto and other related cities How will country-based mitigation measures influence the course of the COVID-19 epidemic? The Lancet The incubation period of coronavirus disease 2019 (COVID-19) from publicly reported confirmed cases: estimation and application The coronavirus pandemic and aerosols: Does COVID-19 transmit via expiratory particles? Indirect virus transmission in cluster of COVID-19 cases Di Napoli R. 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