key: cord-0705211-hwat5zz0 authors: Sichone, J.; Sinkala, M.; Kikonko, M.; Munsaka, S.; Simuunza, M. title: Assessing required SARS-CoV-2 blanket testing rates for possible control of the outbreak in the epicentre Lusaka province of Zambia with consideration for asymptomatic individuals: a simple mathematical modelling study. date: 2020-07-14 journal: nan DOI: 10.1101/2020.07.12.20152124 sha: 3716b8b32662774d8024641ed9b53a64d976381a doc_id: 705211 cord_uid: hwat5zz0 Abstract. Introduction: The novel Coronavirus disease (COVID-19), caused by the severe acute respiratory syndrome coronavirus - 2 (SARS-CoV-2), in Africa is characterised by a more substantial proportion of asymptomatic (or mildly symptomatic) individuals thought to be playing a role in the spread of the infection. The exact proportion and degree of infectiousness of asymptomatic individuals remains unclear. Studies however indicate that their management is crucial for control of SARS-CoV-2 transmission. Methodology: We developed a simplified deterministic susceptible-exposed-infectious-removed (SEIR) mathematical model to assess the effect of active isolation of SARS-CoV-2 infected but asymptomatic individuals through blanket testing for control of the outbreak in Lusaka Province of Zambia. Here we modelled two scenarios; (1) assuming asymptomatic individuals comprised 70% of all COVID-19 cases and (2) asymptomatic individuals comprised only 50% of the cases. For contrast, the model was assessed first under the assumption that asymptomatic individuals are equally as infectious as symptomatic individuals and then secondly, and more likely, assuming asymptomatic individuals are only half as infectious as symptomatic individuals. Results: For the model assuming 70% asymptomatic cases, a minimum sustained blanket testing rate of [≥] 7911 tests/100000 population was sufficient to control the outbreak if asymptomatic individuals are only half as infectious while if equal infectiousness was assumed then a testing rate of [≥] 10028 tests/ 100000 population would be required. For 50% asymptomatic, minimum blanket testing rates of [≥] 4540 tests/ 100000 population was sufficient to control the outbreak at both assumed levels of infectiousness for asymptomatic individuals relative to symptomatic individuals. Discussion and conclusion: Our model predicts that the current testing rates of {approx} 150/100,000 population are inadequate to control transmission of SARS-Cov-2 in Lusaka. Active isolation of COVID-19 cases including asymptomatic individuals through blanket testing can be used as a possible measure for control of the SARS-Cov-2 transmission in Lusaka, Zambia. Key words: SARS-Cov-2, asymptomatic transmission, deterministic model, blanket testing 2 Abstract. Introduction: The novel Coronavirus disease , caused by the severe acute respiratory syndrome coronavirus -2 (SARS-CoV-2), in Africa is characterised by a more substantial proportion of asymptomatic (or mildly symptomatic) individuals thought to be playing a role in the spread of the infection. The exact proportion and degree of infectiousness of asymptomatic individuals remains unclear. Studies however indicate that their management is crucial for control of SARS-CoV-2 transmission. We developed a simplified deterministic susceptible-exposed-infectious-removed (SEIR) mathematical model to assess the effect of active isolation of SARS-CoV-2 infected but asymptomatic individuals through blanket testing for control of the outbreak in Lusaka Province of Zambia. Here we modelled two scenarios; (1) assuming asymptomatic individuals comprised 70% of all COVID-19 cases and (2) asymptomatic individuals comprised only 50% of the cases. For contrast, the model was assessed first under the assumption that asymptomatic individuals are equally as infectious as symptomatic individuals and then secondly, and more likely, assuming asymptomatic individuals are only half as infectious as symptomatic individuals. Results: For the model assuming 70% asymptomatic cases, a minimum sustained blanket testing rate of ≥ 7911 tests/100000 population was sufficient to control the outbreak if asymptomatic individuals are only half as infectious while if equal infectiousness was assumed then a testing rate of ≥ 10028 tests/ 100000 population would be required. For 50% asymptomatic, minimum blanket testing rates of ≥ 4540 tests/ 100000 population was sufficient to control the outbreak at both assumed levels of infectiousness for asymptomatic individuals relative to symptomatic individuals. . CC-BY 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 14, 2020. . https://doi.org/10.1101/2020.07.12.20152124 doi: medRxiv preprint (SARS-CoV-2), has killed over 327,700 and infected over 4.9 million people globally by 21 st CC-BY 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 14, 2020. . https://doi.org/10.1101/2020.07.12.20152124 doi: medRxiv preprint 4 applied a simple mathematical modelling approach to explore the effect of increased blanket testing rates as a possible measure to capture and isolate asymptomatic individuals and control the COVID-19 outbreak in Lusaka Province of Zambia which is the epicenter of the outbreak in Zambia since the first recorded case in the country on 18 th March 2020. [44] . Recent studies have modelled the spread and expected burden of the COVID-19 outbreak in Africa and Zambia and explored the effects of various control measures such as applying different levels of physical distancing and shielding in the population [42, 43, 51, 72] . Although this provides vital information to guide policy for Zambia, some interventions may not be easy to monitor in practice. Additionally, while such interventions have already been instituted, cases continue to rise in Zambia and other African countries [20, 43, 44, 50] . Assessment of more COVID-19 control options through mathematical modelling based on the known epidemiology of the disease would therefore serve to supplement current information on the possible management of the outbreak in Zambia. Lusaka is a busy corporate and commercial hub of Zambia and an outlet to the rest of the world with the busy Kenneth Kaunda International Airport. It is therefore no surprise that the first . CC-BY 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 14, 2020. The spread of SARS-Cov-2 in Lusaka province was modelled through a simplified deterministic susceptible-exposed-infectious-removed (SEIR) compartmental mathematical model as shown in CC-BY 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 14, 2020. . https://doi.org/10.1101/2020.07.12.20152124 doi: medRxiv preprint 6 relationship to a compartment. Infectious individuals are split into symptomatic and asymptomatic individuals. The model both directly and indirectly incorporated the current mitigation measures in place to attempt to predict the trajectory of the outbreak in Lusaka accurately. We started by denoting the infection states as total number of susceptible S(t), exposed E(t), infectious I(t), removed R(t) and dead persons D(t) at any given time (t) in the population of size N. For our analysis, the total population size was assumed to be constant and demographics of natural birth and deaths rates were considered negligible [17, 70] . Table 1 Once they have become infectious, they may belong to either one of two classes of infectious individuals; symptomatic infectious ( ), or asymptomatic infectious ( ) determined by the fraction for symptomatic persons ɛ. Based on current interventions in Lusaka, the symptomatic . CC-BY 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 14, 2020. 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 14, 2020. are taken to be generally unnoticed in the community but also recover at a rate in which time they can infect susceptible individuals before they become removed as ( ) and no longer infectious. Note that some asymptomatic individuals develop symptoms much later in their infection but this does not substantially affect our model because at that time they would still be removed ( ) if they become diagnosed and quarantined through targeted testing. In this study, we assumed that the current mostly targeted testing for COVID-19 in Lusaka province is restrictive and probably missing some asymptomatic individuals [53] . Therefore, a parameter ( ) was introduced in the model which describes blanket testing applied as tests per 100000 populations used to identify and isolate all infectious individuals in the community (symptomatic and asymptomatic) through sustained random mass testing. The total removed individuals for the model ( ) are given as ( ) + ( ) while the total confirmed cases are given as of which a fraction (Case fatality rate -CFR) are recorded dead ( ). . CC-BY 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 14, 2020. . https://doi.org/10.1101/2020.07.12.20152124 doi: medRxiv preprint Model optimisation and simulation was done using Vensim PLE systems dynamics modelling software for Windows (version-7) [48] . This was done for two scenarios of 70% and a modest 50% assumed proportion of asymptomatic infectious individuals in the population. Data from the first three months of the outbreak in Lusaka as given in the Zambia COVID-19 situation reports No. 1-64 [44] was used to configure the model and optimise parameters. However, due to presence of imported cases in the early days and the considerable variations in recorded cases between some days (probably influenced by variations in availability of testing kits), only data from 10 th April 2020 to 16 th May 2020 was used. This is because this period had more consistent data and by then 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 14, 2020. . https://doi.org/10.1101/2020.07.12.20152124 doi: medRxiv preprint (as a key indicator of control of the outbreak), several iterations of this simulation were then performed using increasingly higher values for . No ethical issues were encountered as no human or animal subjects were used in this study and cases were anonymous. The model had significant fit to outbreak data under all the assessed conditions and therefore could be used for the general purpose of analysing the outbreak under all these general scenarios. Figure 2 shows results of model optimisation and fit to outbreak data for both the 70% and 50% asymptomatic scenarios assuming equal infectiousness for asymptomatic and symptomatic individuals (denoted as A1 and A2). . CC-BY 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 14, 2020. . https://doi.org/10.1101/2020.07.12.20152124 doi: medRxiv preprint . CC-BY 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 14, 2020. . https://doi.org/10.1101/2020.07.12.20152124 doi: medRxiv preprint detected. However, this more substantial proportion of asymptomatic individuals (70%) is 8 associated with higher expected peak values of both total active infectious individuals and total 9 quarantined individuals. It is also observed that the outbreak is expected to peak much earlier for 10 all variables in Table 2 for the 70% asymptomatic individual's scenario compared to only 50% 11 asymptomatic. Note that the model predictions for the Lusaka COVID-19 outbreak given in Table 12 2 are however subject to the effectiveness of the containment policies in Lusaka province over 13 time. Figures 4 -7 and Table 3 give the results of the effect of increasing blanket testing rates (θ) (Table 3) . However, 29 if the asymptomatic individuals only make up 50% of all cases and are only half as infectious 30 . CC-BY 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 14, 2020. 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 14, 2020. . https://doi.org/10.1101/2020.07.12.20152124 doi: medRxiv preprint . CC-BY 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 14, 2020. . https://doi.org/10.1101/2020.07.12.20152124 doi: medRxiv preprint Discussion. 57 In this study, we developed a simple deterministic model to forecast the spread of infection and 58 assess required blanket testing rates for the control of the novel SARS-Cov-2 outbreak in Lusaka 59 province, Zambia, with specific consideration for asymptomatic infectious individuals. In the early CC-BY 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 14, 2020. . https://doi.org/10.1101/2020.07.12.20152124 doi: medRxiv preprint 16 2021 (Table 2) . This lower projection is plausible given that it is an estimate for Lusaka province CC-BY 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 14, 2020. CC-BY 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 14, 2020. . https://doi.org/10.1101/2020.07.12.20152124 doi: medRxiv preprint asymptomatic infections may be even more pertinent than other regions of the world. This is 126 because Africa has been found to have a younger population and with lower personal . Further modelling studies using more refined models and more 146 outbreak data should, therefore, be conducted to study the COVID-19 outbreak in Lusaka. . CC-BY 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 14, 2020. SEIR: susceptible-exposed-infectious-removed compartmental mathematical model. CC-BY 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 14, 2020. . CC-BY 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 14, 2020. Available from: https://www.citypopulation.de/php/zambia-admin.php?adm1id=05. . CC-BY 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 14, 2020. CC-BY 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 14, 2020. . CC-BY 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 14, 2020. Modelling the COVID-19 epidemic and implementation of population-wide interventions 193 in Italy Estimating the reproductive number and the outbreak size of COVID-19 in 195 The effect of control strategies to reduce social mixing 198 on outcomes of the COVID-19 epidemic in Wuhan, China: a modelling study The first 2019 novel coronavirus case in Nepal Clinical characteristics of 138 hospitalized patients with 2019 novel coronavirus-205 infected pneumonia in Our World in data: Coronavirus Pandemic (COVID-19) -the data The epidemiology and pathogenesis of coronavirus disease 210 (COVID-19) outbreak Estimating the 306 generation interval for COVID-19 based on symptom onset data Quantifying SARS-CoV-2 transmission suggests epidemic control with digital 309 contact tracing Estimating the asymptomatic proportion 311 of coronavirus disease 2019 (COVID-19) cases on board the Diamond Princess cruise ship Presymptomatic SARS-CoV-2 infections and 316 transmission in a skilled nursing facility. NEJM Suppression of COVID-19 319 outbreak in the municipality of Asymptomatic transmission still an 'open question situation-reports 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 The potential effects of widespread community 326 transmission of SARS-CoV-2 infection in the World Health Organization African Region: 327 a predictive model Immunity, parasites, genetics and sex 329 hormones: contributors to mild inflammatory responses in COVID-19? The relatively young and rural population 332 may limit the spread and severity of Covid-19 in Africa: a modelling study The estimation of the basic reproduction number for infectious diseases 67) van den Driessche P. Reproduction numbers of infectious disease models Estimating the reproductive 339 numbers for the 2008-2009 cholera outbreaks in Zimbabwe Cholera in Haiti: reproductive numbers and 342 vaccination coverage estimates. Scientific reports An introduction to mathematical modeling of infectious diseases. Spriger Cholera transmission dynamic models for public health practitioners Themes Epidemiol. 2014 Dec 1;11(1):1. . CC-BY 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 14, 2020.