key: cord-0855925-c5rjz9r9 authors: Stevenson, F. D.; Mellado, B.; Choma, J.; Lieberman, B.; Correa, F.; Dahbi, S.-E.; Hayashi, K.; Monnakgotla, K.; Naude, J.; Ruan, X.; Maslo, C. title: Risk Adjusted Non-Pharmaceutical Interventions for the Management of COVID-19 in South Africa date: 2020-07-17 journal: nan DOI: 10.1101/2020.07.15.20149559 sha: 30215c343fab6c217b3d1952245a3193bddbdb9b doc_id: 855925 cord_uid: c5rjz9r9 A global analysis of the impact of non-pharmaceutical interventions (NPIs) on the dynamics of the spread of the COVID-19 indicates that these can be classified using the stringency index proposed by the Oxford COVID-19 Government Response Tracker(OxCGRT) team. The world average for the coefficient that linearises the level of transmission with respect to the OxCGRT stringency index is s= 0.01{+/-}0.0017 (95%C.I.). The corresponding South African coefficient is s= 0.0078{+/-}0.00036 (95%C.I.), compatible with the world average. Here, we implement the stringency index for the recently announced 5-tier regulatory alert system. Predictions are made for the spread of the virus for each alert level. Assuming constant rates of recovery and mortality, it is essential to increase s. For the system to remain sub-critical, the rate with which s increases should outpace that of the decrease of the stringency index. Monitoring of s becomes essential to controlling the post-lockdown phase. Data from the Gauteng province obtained in May 2020 has been used to re-calibrate the model, where s was found increase by 20% with respect to the period before lockdown. Predictions for the province are made in this light. for making informed decisions with regards to the restrictions necessary at any given ics. This is crucial because there has been research that suggests that people who 30 are asymptomatic make up a large portion of the total people infected. 3 A detailed 31 explanation on the country specific SIRD models and a global overview of the ef-32 fectiveness of the various NPIs that have been implemented around the world can 33 be seen in the parent paper 2 . The mathematical model's parameters were fit to the The OxCGRT has developed a valuable database for comparing countries re-48 sponse strategies. 4 5 The database contains the following levels of control (coded 49 using ordinal numbers) and timing for 139 countries: 50 OxCGRT Indicator Intervention Response S1: School closure S2: Workplace closure S3: Cancel public events S4: Close public transport S5: Public information campaign S6: Domestic travel bans S7: International travel bans Also included in this data set is a Stringency Index 6 , p, in our notation, which 51 provides a single number that captures the overall level of intervention implied by 52 combinations of the ordinal numbers S1-S7. The Oxford stringency index is calcu-53 lated using a weighted average of the above seven non-pharmaceutical interventions 6 . For each policy response measure S1-S7, OxCGRT use the ordinal value (and add 55 one if the policy is general rather than targeted). This creates a score between 0 and 56 2 and for S5, and 0 and 3 for the other six responses 5 . The OxCGRT stringency index is given by: 59 p = 1 7 Levels 66 It is necessary for the South African Alert Levels (L1-L5) to be characterised in 67 terms of the Oxford indicators (NPIs) S1-S7 so that predictions can be made using 68 the aforementioned model. 69 The calculation of a stringency index for South Africa will be similarly based of implementation for each NPI (S1-S7) that is appropriate for the specific South 75 African Alert Levels. 76 The chosen cardinality of the interventions in a South African Context can be 77 seen in Table 2 . 78 Intervention Cardinality S1: N 1 = 4 S2: N 2 = 4 S3: N 3 = 1 S4: N 4 = 4 S5: N 5 = 1 S6: N 6 = 4 S7: N 7 = 2 The following assumptions are made for S1, S3 and S5 control interventions 7 : • The "School Closure" S1 intervention will be a function of both the alert level 88 and the stage of school reopening. • The "Cancel Public Events" S3 intervention measure will be implemented for 90 all of the South African Alert Levels. This assumption is made based on 91 the following statement from the South African Government: "The following 92 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. (which was not certified by peer review) The copyright holder for this preprint this version posted July 17, 2020. . https://doi.org/10.1101/2020.07.15.20149559 doi: medRxiv preprint restrictions will remain in place after the national lock-down, and regardless of the level of alert at any given time: Sit-in restaurants and hotels; Bars and 94 shebeens; Conference and convention centres; Entertainment venues, including 95 cinemas, theatres, and concerts; Sporting events; Religious, cultural and social 96 gatherings. No gatherings of more than 10 people outside of a workplace will 97 be permitted." • The "Public Information Campaign" S5 intervention measure will be imple- The results reported in Table 3 The rationale for the scoring of the indicators S2, S4, S6 and S7 can be found 110 in Appendix A. Explanation of the effects of the S1 indicator on the stringency 111 index can be found in Appendix B. It should be noted that the S1 indicator is time 5 . 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 July 17, 2020. . The achieved stringency index boundaries for the South African alert system 126 compare favourably with those of countries around the world. Level Achievable SA Index Countries 6 . 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 July 17, 2020. . The predictions performed here conform to the prescription detailed in the par-129 ent paper 2 , where two steps are followed. Firstly, the parameters of the model are 130 extracted before and during the lockdown using South African data provided by the 131 NICD and the Department of Health. These parameters constitute the initial condi-132 tions for the forward temporal evolution of a SIRD model. Secondly, a SIRD model 133 is used by reasoning that the daily recovery rate and daily mortality parameter, γ 0 134 and d 0 , respectively, remain constant and the transmission rate follows the functional 135 form: where t = 0 corresponds to the end of the initial lockdown period and the removal 137 of some interventions, such that p < p max . The implementation of new less restrictive measures will yield ∆p = p − p max < 139 0, where β(t, p) > β f . Here, β f is the asymptotic value of the transmission rate 140 achieved during lockdown with p max , which in South Africa is considered to be equal 141 to 100. The parameters β 0 , α s are obtained from the data reported before and 142 after the lockdown was enacted. Table 5 Wuhan data and multi-dimensional data from the Gauteng City-Region Observatory. Documenting the details of this study goes beyond the scope of this paper. The 153 estimate used here is consistent with the current mortality rate for SA, which seems 154 to have stabilised at 2% for the moment. 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 July 17, 2020. 2% and 3%. Here a more conservative approach is adopted. The country-to-country 173 variation, which is of order of 10% (68% C.I.), is considered to be a more realistic 174 estimate of the potential deviation from the linear behavior assumed 2 in Eq. (4). The parameters obtained for South Africa, shown in Table 5 , are initially applied 186 to the Gauteng Province data to produce estimate predictions for Levels 4 and 5. These predictions are compared to Gauteng's May data in Figure 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 July 17, 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 July 17, 2020. where t ranges from March 15 th to May 26 th 2020. The β equation for re-206 calibration becomes of the form: The value of α 4 is then determined through a regression fit on Gauteng's May 208 data. The re-calibration parameters are shown in Table 6 . It is important to note 209 that the efficiency of the NPIs, or the adherence to social distancing, has increased 210 by 20%. Figure 5 shows the alert Level 4 modelling for Gauteng versus data with the 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 July 17, 2020. . https://doi.org/10.1101/2020.07.15.20149559 doi: medRxiv preprint γ gp α 4 0.035 0.0089 It can be reasoned that γ c and d c should display a weak time dependence in that 228 11 . 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 July 17, 2020. . they primarily depend on medical advances, rather than on NPIs. In this setup the condition for the system to remain sub-critical can be expressed as follows: where the temporal partial derivatives are evaluated at the point of criticality defined 231 by v c (t). Given constant γ and d, it is essential to increase α s . For the system to remain 3 that took place in the province in June 2020. In the South African case, and given the still relatively low value of α s , it seems 240 evident that it will be difficult to pass from Level 3 to Level 2 in the short to mid 241 term without a significant increase of the efficiency of the NPIs. The data that will 242 be collected in July will be critical to understand the evolution of α s and its potential 243 enhancement due to adherence to social distancing measures in a system where the 244 stringency index moves relatively slowly. Given the emergence of "hot-spots" dynamics in South Africa, it is essential to will not be seen immediately and we have quantified this fact within our model. 12 . 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 July 17, 2020. . There are essentially two options for control given the current NPI framework: 13 . 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 July 17, 2020. . Tables A.7-A.11 outline the rational for the scoring of the S2, S4, S6 and S7 indica-289 tors in terms of the South African alert levels. OxCGRT Value Rationale Indicator S2: 0 All businesses are allowed to operate. S4: 0 All public transport is operational with strict hygiene requirements. S6: 0. Inter-provincial travel is allowed. S7: 0.5 There is an international travel restriction. Stringency Level 36 + (100 * S1/7) There is an international travel ban. Stringency Level 50 + (100 * S1/7) 14 . 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 July 17, 2020. There is an international travel ban. Stringency Level 61 + (100 * S1/7) There is an international travel ban. Stringency Level 75 + (100 * S1/7) . 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 July 17, 2020. 1 All non-essential services are closed. S4: 1 All non-essential public movement is banned. Only essential workers may use limited public transport. S6: 1 Inter-provincial travel not allowed S7: 1 There is an international travel ban. Stringency Level 86 + (100 * S1/7) The government announced that the staged reopening of schools will not coin- 16 . 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 July 17, 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 July 17, 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 July 17, 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 July 17, 2020. 20 . 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 July 17, 2020. . President cyril ramaphosa: South africa's response to 342 coronavirus covid-19 pandemic -south african government Appendix C. Additional Graphs