A Human-Pathogen Model for COVID-19 Outbreak

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ISSN: 2474-3658 Ojiambo et al. J Infect Dis Epidemiol 2020, 6:184 DOI: 10.23937/2474-3658/1510184 Volume 6 | Issue 6 Journal of Open Access Infectious Diseases and Epidemiology

Research Article A Human-Pathogen Model for COVID-19 Outbreak: Flattening Epidemic Curve in Kenya Viona Ojiambo1*, Mark Kimathi2, Samuel Mwalili1,3, Duncan Kioi Gathungu1 and Rachel Mbogo3

1Jomo Kenyatta University of Agriculture and Technology, Kenya 2Machakos University, Kenya Check for 3Strathmore University, Kenya updates

*Corresponding authors: Viona Ojiambo, Jomo Kenyatta University of Agriculture and Technology, P.O. Box 62000- 00200, Nairobi, Kenya

es globally had exceeded sixteen million [3] with Africa Abstract recording approximately seven hundred thousand of This work introduces a deterministic model of COVID-19 those cases. The 1st case in Kenya was reported on the spread aimed at analyzing non-pharmaceutical interven- th tions in Kenya. The model accounts for symptomatic, as- 13 of March 2020 [4] and currently there are close to ymptomatic and environmental transmission. Using the twenty thousand confirmed cases [3]. SEIR (Susceptible-Exposed- Infected-Recovered) compartmental model with additional component of the pathogen, The three main types of infectiousness of COVID-19 the dynamics of COVID-19 outbreak is simulated while fo- are asymptomatic, pre-asymptomatic and symptomatic. cussing on the impact of different control measures in the The incubation period for COVID-19 in the pre-asymp- reduction of the basic reproduction number. The resulting tomatic infectious group, which is the time between ex- system of ordinary differential equations (ODEs) is solved using a combination of fourth and fifth-order Runge-Kutta posure to the virus (becoming infected) and symptom methods. Simulation results indicate that non-pharmaceuti- onset, is on average 5-6 days, however it can be up to cal measures such as school closure, social distancing and 14 days. During this period some infected persons can movement restriction emphatically flatten the epidemic peak be contagious. In a symptomatic COVID-19 case, the curve by reducing the basic reproduction number. disease manifests itself with signs and symptoms. As- Keywords ymptomatic transmission refers to transmission of the Basic reproduction number, COVID-19, Intervention, SARS- virus from a person, who does not develop symptoms CoV-2, SEIR-P, Simulation [5]. The basic reproductive number (R0), defined as the average number of secondary infections produced by a Introduction typical case of an infection in a population where every- Corona Virus Disease (COVID-19) is an infectious one is susceptible [6], is affected by the rate of contacts disease that is caused by Severe Acute Respiratory Syn- in the host population, the probability of infection being drome Coronavirus 2 (SARS-CoV-2). The first case was transmitted during contact and the duration of infec- R . reported in main-land China, City of Wuhan, Hubei on tiousness. The COVID-19 0 in Kenya ranges from 1 78 29th December 2019 [1]. Later on, the novel disease to 3.46 [7]. The outbreak is thought to spread through a spread to countries in contact with China resulting in population via direct contact with infectious individuals World Health Organization (WHO) declaring it as a Pub- [8] or cross transmission through pathogen contamina- lic Health Emergency of International Concern (PHEIC) tion in the environment. Specifically, the virus is primar- on 30 January 2020 World Health Organisation [2]. As of ily spread between people during close contact, often 27th July 2020 the number of reported confirmed cas- via small droplets produced by coughing, sneezing, or

Citation: Ojiambo V, Kimathi M, Mwalili S, Kioi D, Mbogo R (2020) A Human-Pathogen Model for COVID-19 Outbreak: Flattening Epidemic Curve in Kenya. J Infect Dis Epidemiol 6:184. doi. org/10.23937/2474-3658/1510184 Accepted: December 29, 2020: Published: December 31, 2020 Copyright: © 2020 Ojiambo V, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Ojiambo et al. J Infect Dis Epidemiol 2020, 6:184 • Page 1 of 8 • DOI: 10.23937/2474-3658/1510184 ISSN: 2474-3658 talking [5,6,9,10,11]. After breathing out these droplets sults shall inform health experts in their research of effi- usually fall to the ground or on to surfaces rather than cient and effective ways of flattening the curve. remain in the air over long distances [6,7,9]. People may also become infected by touching a contaminated Materials and Methods surface and then touching their eyes, nose, or mouth In this study a human-pathogen SEIR-P model for [9,10]. The virus can survive on surfaces for up to 72 COVID-19 outbreak is formulated. The model considers hours [11]. a short-time period thereby ignoring the demographics of births and natural death. The total human popula- This kind of transmission has had adverse social and economic impact because all segments of the popu- tion is subdivided into the susceptible human beings S t E t lation are significantly affected. The disease ispartic- ( ), the exposed human beings ( ), the asymptomatic infectious population I (t), the symptomatic infectious ularly detrimental to vulnerable social groups such as A population I (t), the critical infectious population I (t), older age-groups, persons with disabilities and people M C with other underlying diseases. If the pandemic is not the hospitalized population H(t) in ordinary wards and properly addressed through policy, the social crisis gen- U(t) in Intensive Care Unit (ICU), the fatalities D(t) and erated from COVID-19 could also increase inequality, the recovered population R(t). The pathogen vector in exclusion, discrimination and global unemployment in the environment is denoted by P(t). the medium and long term United Nations: Department The model in Figure 1 culminates to a ten dimension- of Economic and Social Affairs Inclusion [12]. Inorder al system of ordinary differential equations as follows; to achieve suitable control measures of COVID-19, a dS β SP ββSI(++ I I )() SU + H Susceptible-Exposed-Infected-Recovered (SEIR) mathe- =−−1 23AM C− , matical prediction model is required. Prediction trends dt N N N from the model are largely influenced by policy and so- dE β SP ββSI(++ I I )() SU + H cial responsibility of a given country [13]. These trends =++−1 23AM C ωE, enable us to understand how SARS-CoV-2 could spread dt N N N across a given population and inform control measures dI A =δω Ε−( τ + γ ),I that might mitigate future transmissions [11]. Nonphar- dt A A AA maceutical interventions based on sustained physical distancing have a strong potential to lower and flatten dIM =−−(1δA δω C )EI − τ MM , the epidemic peak in the absence of a vaccine [14]. Pre- dt mature and sudden lifting of such interventions could dI lead to an earlier secondary peak [15]. C =δωEI −+( τ γ ), (2.1) dt C C CC An epidemiological study was done on a human-pathogen model that incorporated individuals dH =τAAI + τ M I M + τ CC IU + φ −+( ξλHH + γ ), H with robust immunity in its compartments; the model dt examined human behavior during the disease outbreak, dU such as ignorance of social distancing so as to advise =ξHU −+( φλU ), health care workers (HCW) [16]. It was established that dt nonpharmaceutical interventions play a major role in dD flattening the epidemic peak. =λHUI ++ λλ, dt H U CC According to the WHO/China Joint Mission Report, 80% of laboratory-confirmed cases in China up to 20 dR =γγHHI + AA, February 2020 have had mild to moderate disease in- dt cluding both non-pneumonia and pneumonia cases; dP whilst 13.8% developed severe disease and 6.1% devel- =η12(IAM ++ I I C )( + ηµ UH +− )P P . oped to a critical stage requiring intensive care [9]. It dt is therefore paramount to come up with an epidemio- with the initial conditions: logical model that factors in hospitalization of the mild S(0) > 0, E(0) > 0, I (0) = 2, I (0) = 2, I (0) = 2, to moderate cases and severity of the disease transmis- A M C sion. H(0) = 0, U(0) = 0, D(0) = 0, R(0) = 0, P(0) = 5000. (2.2) β SP β SI()++ I I β SU()+ H The terms 1 , 2 AM C and 3 de- In this study we explore a human-pathogen model NN N mathematical model with infectious groups, hospital- note the rate at which the susceptible individuals S(t), ized population, human population in intensive care gets infected by the pathogens from environment (P(t)), unit and the fatalities. The study further investigates the infectious humans (IA(t), IM(t) and IC(t)), and hospitalized effects of lifting non-pharmaceutical interventions such humans (U(t),H(t)) respectively. A quarter of reported as school closure, physical distancing and lockdown on cases of COVID-19 are mainly asymptomatic infectious the model. It is envisaged that the dynamics of the re- IA(t), while the larger group is mild infectiousI M(t), with a

Ojiambo et al. J Infect Dis Epidemiol 2020, 6:184 • Page 2 of 8 • DOI: 10.23937/2474-3658/1510184 ISSN: 2474-3658

γA IA Human Population IA

δAωE τA IA

β1 SP β2 S(IA +IM +IC ) β3 S(U+H) N + N + N (1 − δA − δC)ωE τM IM γH H S E IM H R

λH H

τC IC ξ H φU δCωE D λUU

IC U

λC IC

µp P P η1 (IA + IM + IC) + η2(U + H) Pathogens (SARS-CoV-2) Figure 1: Compartmental model of the SEIR model of transmission of COVID-19.

smaller proportion being critical infectious IC(t).  ββ12P+( IAM ++ I I C )( + β3 UH + ) I t R t   A( ) may join the recovery group ( ) or seek medical 0 intervention from H(t). I (t) and I (t) may go to hospital   M C  0  H(t), but upon critical diagnosis be referred to the ICU   U(t) which may result to fatalities D(t) or recovery R(t). Fx()=  0 (3.1) The table of parameters is as shown in Table 1 below.  0  Disease Free Equilibrium and Basic Reproduc-  0 tion Number   ηη12 (IAM++ I I C )( + UH + ) In the Disease Free Equilibrium (DFE) there are no infections from the humans nor the pathogens resulting  ωE  to S = N. This implies that P = IA = IM = IC = U = H = 0 which τ+− γ δω  ()A AAIE A further implies that E = D = R = 0. The Basic Reproduc-  (δδ+− 1) ωEI + τ tion Number (R ) is defined as the average number of AC MM (3.2) 0 =τ +− λ δω secondary infections produced by a typical case of an Vx() (C CC )IE C ()ξλ++ γHI − τ − τ I − τ IU − φ infection in a population where everyone is susceptible H H AA M M CC [6]. This number is affected by the rate of contacts in  ()φλ+−U UH ξ the host population, the probability of infection being   µP P transmitted during contact and the duration of infectiousness. The next generation matrix method is used Evaluating the derivatives of F and V at the Disease Free Equilibrium yields matrix F and V as follows; to obtain the R0. βββββ β Let x = (E, I , I , I , H, U, P )T then the model can be  0 22233 1 A M C  written as  0 0 0 0 0 0 0 dx  =Fx() − Vx (),where 0 0 0 0 0 0 0 dt  F =  0 0 0 0 0 0 0 (3.3)  0 0 0 0 0 0 0   0 0 0 0 0 0 0   0 ηηη111 ηη 22 0

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 ω 0 0 0 0 0 0   δω τ+ γ  -A AA 0 0 0 0 0 (δδ+ -1) ω 0 τ 0 0 0 0 AC M V =  -δωC 0 0 τCC+ λ 0 0 0 (3.4)  0 -τ - τ - τ ξλ++ γ -φ 0 A M C HH  0 0 0 0 -ξ - φλ+ U 0   0 0 0 0 0 0 µP

Substituting, λC + τC = C2, τA + γA = C3 , (φ + λU )−ξφ = C6 −ξφ = C4, ξ + λH + γH = C5, φ + λU = C6 and (ξ + λH + γH ) (φ + λU)

= C5C6 − ξφ = C1 in matrix V yields  ω 0 0 0 0 0 0  δω  -A C3 0 0 0 0 0 (δδ+ -1) ω 0 τ 0 0 0 0 AC M V =  -δωC 0 0 C2 0 0 0 (3.5)  0 -ττ - - τ C - φ 0 AM C 5  0 0 0 0 -ξ C6 0   0 0 0 0 0 0 µP The inverse of matrix V is determined as

1  0 0 0 0 0 0 ω -δ 1  A 0 0 0 0 0 C3 C3 (c +δ -1) 1  -C 0 0 0 0 0 ττMM  −1 δ 1 (3.6) V =  -C 0 0 0 0 0 CC22 −C(((δ +− δ 1) C − δτ ) CC - τ δ ) τ CCτ CC φ  6AC 3AA 23 C C A 66 C 66 0 CCC231 CC31 C 1 CC 21 C 1 C 1  −ξ(CC (1 −− δ ) τ δ ξτ ξξ ξτ  25A CC A C 0 CCC321 CCCCCCC31 1 21 1 1  1  0 0 0 0 0 0 µP The product FV-1 that results to;

 CC7 9 C 11 C 13 C 15 C 17 C 19   0 0 0 0 0 0 0  0 0 0 0 0 0 0 −1  FV =  0 0 0 0 0 0 0  0 0 0 0 0 0 0 (3.7)   0 0 0 0 0 0 0   CCCCCC8 10 12 14 16 18 0 where

βδ2 A β2(−−+ δAC δ 1) βδ2C β 36C(( δAC+− δ 1) C3 − δτAA ) CC 23 − τ C δ C ) + β 3 ((( δAC +− δ 1)C3 − δτAA ) CC 23 − τ C δ C ) ξ C7 =+ +− C3 τ M C2 CCC231

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ηδ1 A η1(−−+ δAC δ 1) ηδ126C ηC(( δAC+− δ 1) C3 − δτAA ) CC 23 − τ C δ C ) + η 2 ((( δAC +− δ 1)C3 − δτAA ) CC 23 − τ C δ C ) ξ C8 =+ +− C3 τ M C2 CCC231

β2 β36 τAAC β 3 ξτ C9 =++ C3 CC 31 CC 31

η12ητ26AC η ξτ A C10 =++ C3 CC 31 CC 31

β2 β36C βξ 3 C11 =++ τ M CC11

η12η26C ηξ C12 =++ τ M CC11

β2 βτ36CCC βτ 3 ξ C13 =++ C2 CC 21 CC 21

η1 ητ26CCC ητ 2 ξ C14 =++ C2 CC 21 CC 21

β36C βξ 3 C15 = + CC11

η26C ηξ2 C16 = + CC11

βφ3 β 35C C17 = + CC11

ηφ2 η25C C18 = + CC11

β1 C19 = Z (3.8) µP -1 R0 is the spectral radius of the product FV that results to; C 4CC+ C2 R =7 ± 8 19 7 (3.9) 0 22

Here R0 is the sum of three terms representing the average new infections contributed by each of the three infectious classes; pathogens, infectious groups (mild, asymptomatic and critical) and hospitalized groups denoted by β1, β2, and β3 respectively. Results and Discussion Implementation of the NPIs is aimed at reducing the contacts within the population. Reduction of the contacts reduces the R0, which is expressed in terms of the infection transmission ratesβ 1, β2, and β3 in the previous section.

Since low rates of infection transmission implies a low value of R0 then we implement the non-pharmaceutical interventions (NPIs) by multiplying the rates of infection transmissions by a 20% and 30% factor. The interpretation is that the NPIs yield an overall mitigation of the epidemic spread by 20% and 30% respectively. Kenya instituted various mitigation strategies immediately the first case of COVID-19 was confirmed, therefore in this study the R0 at the beginning of epidemic is taken as 1.50. The R0 corresponding to 20% and 30% contact reduction are 1.28 and 1.17 respectively. A simulations study was done using a total population of Kenya, N, as 4.76 × 107. Additionally, an identification rate p of new infectious cases was considered and determined as the ratio of confirmed cases over the total number of tested individuals. At the time of this studyp was 0.022, while the parameter values were taken as shown in

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Table 1. The simulation was initialized at date 13-3-2020 hospitalized cases are reduced by about 49%. However, and run for 365 days with the initial valuesI A(0) = 2, IM(0) there is a likelihood of exceeding the health capacities.

= 2, IC(0) = 2, and P (0) = 5,000, while the other variables A 30% effectiveness of the applied NPIs substantially (except S(0)) were initially set to 0. bring the epidemic further down, and as noted in Fig- ure 3 the simulated cumulative infectious cases largely The results of the infectious (I + I + I ) and hospi- A M C coincides with the data of COVID-19 epidemic in Kenya. talized (H + U) cases in Kenya are shown in Figure 2, Moreover, this particular mitigation effort reduce the and epidemic peak values and dates are depicted in cumulative infectious cases from just under 839,510 Table 2. In unmitigated situation, the peak arrives rath- down to around 498,812 cases by date 13-Mar-2021. A er quickly, in about 4 months probably due to the as- similar reduction is also seen in the cumulative number ymptomatics significantly contributing to the epidemic of hospitalized cases. Moreover, the cumulative deaths spread. We note that the Kenyan population is largely attain about 59.4% reduction, from about 6,584 cases in comprised of youth, who are majorly presumed to be unmitigated situation to around 3,909 cases in the 30% an asymptomatic population. Our model predicts that mitigation scenario. Majority of deaths emanate from if the overall control measures achieve 20% effective- those already in intensive care unit (ICU) U, which is pre- ness in slowing the spread of COVID-19, then a delay sumably overwhelmed by the many critically ill patients of slightly 2 months is realized, which gave the health arising from H and IC populations. The inability to access care systems time of gathering resources to manage the the limited ICU resources results to additional deaths epidemic. Consequently, the reported infectious and from H and IC populations.

Table 1: Description of Model Parameters. The parametric values are determined based on the references [5,7,14-19].

Model Parameter Symbol Value

Rate of transmission from S to E due to contact with P β1 0.45

Rate of transmission from S to E due to contact with IA, IM and IC β2 0.75

Rate of transmission from S to E due to contact with U and H β3 0.5

Proportion of asymptomatic infectious people δA 0.75

Proportion of critical symptomatic infectious people δC 0.02

Progression rate from IA to H τA 0.02

Progression rate from IM to H τM 1

Progression rate from IC to H C 0.99 -1 Progression rate from E to either IA, IM or IC ω 0.2 day

Rate of recovery from IA to R γA 0.98

Rate of recovery from H to R γH 0.97 Progression rate from H to U ξ 0.02 Progression rate from U to H φ 0.2

Progression rate from U to D λU 0.9

Progression rate from H to D λH 0.03

Progression rate from IC to D λC 0.02 -1 Rate of virus spread to environment by IA, IM and IC η1 0.55 days -1 Rate of virus spread to environment by U and H η2 0.25 days -1 Natural death rate of pathogens in the environment µP 0.3 days

Table 2: Simulated peaks of infectious and hospitalized cases, with the associated peak dates. The table depicts the predicted peak values of (daily) reported cases and corresponding times. The cases are placed in two categories, namely: infectious (IA +

IM + IC) and hospitalized (H + U).

NPI status Peak Value Peak Time Peak Days Unmitigated (Infectious Cases) 19320 9-Jun-2020 88 Unmitigated (Hospitalized Cases) 5785 10-Jun-2020 89 20% reduction (Infectious Cases) 9522 23-July-2020 132 20% reduction (Hospitalized Cases) 2855 24-July-2020 133 30% reduction (Infectious Cases) 4873 13-Sept-2020 184 30% reduction (Hospitalized Cases) 1462 14-Sept-2020 185

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(a) (b)

Figure 2: Left panels depicts simulation of infectious and hospitalized cases, in unmitigated and mitigated situations. The implementation of NPIs results to a delay and significant reduction in the cases, as shown by the varying peaks. Right panels show the simulated cumulative cases for both infectious and hospitalized individuals. The infectious cases comprise

of individuals in compartments IA, IM , and IC cases. The hospitalized cases comprise of individuals in compartments H and U.

(a) (b)

Figure 3: Left panel depicts the data of the confirmed cases in Kenya against the simulated infectious cases for the first 150 days, in unmitigated and mitigated situations. The simulated results of a 30% NPIs effectiveness coincides with the data. Right panel show the cumulative deaths, which decline significantly as the NPIs take effect.

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The control measures were put in place for the en- 5. World Health Organisation (2020) Coronavirus disease tire simulation time, so there was no rebound ofthe 2019 (covid-19): Situation report, 73. infections. A strong one-time social distancing measure 6. Li Q, Guan X, Wu P, Wang X, Zhou L, et al. (2020) Early transmission dynamics in Wuhan, China, of novel corona- would not sufficiently prevent overwhelming of the virus infected pneumonia. N Eng J Med 382: 1199-1207. health care capacities, since it keeps a significant num- 7. Brand S, Aziza R, Kombe I, Agoti C, Hilton J, et al. (2020) ber of the population in susceptible compartment such Forecasting the scale of the covid-19 epidemic in Kenya. that a rebound in infections, after the measure has been MedRXiv. lifted, will lead to an epidemic wave that surpasses the 8. Huang C, Wang Y, Li X, Ren L, Zhao J, et al. (2020) Clinical capacity. Moreover, previous studies have shown that features of patients infected with 2019 novel coronavirus in Wuhan, China. The Lancet 395: 497-506. intermittent application of the NPIs maintains the infec- 9. World Health Organisation (2020) Report of the WHO-Chi- tions within the health care capacities, but prolongs the na joint mission on coronavirus disease 2019 (covid-19). total duration of the epidemic. 10. Ong S, Tan Y, Chia P, Lee T, Ng O, et al. (2020) Air, surface environmental, and personal protective equipment Conclusion contamination by severe acute respiratory syndrome coro- With absence of cure or vaccine for COVID-19 navirus 2 (sars-cov-2) from a symptomatic patient. JAMA non-pharmaceutical that include measures such as con- 323: 1610-1612. tact tracing, quarantine, social distancing, wearing of 11. Hamzaha F, Laub C, Nazric H, Ligotd D, Leee G, et al. (2020) Corona-tracker: Worldwide covid-19 outbreak data face masks, and handwashing should be maintained. analysis and prediction. Mass testing and effective contact tracing has been a 12. UN Department of Economic and Social Affairs Inclusion great challenge in low-income countries due to inade- (2020) Everyone included: Social impact of covid-19. quate testing reagents and lack of proper coordination. 13. Riley S, Fraser C, Donnelly C, Ghani A, Abu-Raddad L, et Therefore, these countries have adopted social dis- al. (2003) Transmission dynamics of the etiological agent tancing measures such as closure of schools, reducing of sars in Hong Kong: Impact of public health interventions. Science 300: 1961-1966. sizes of gatherings, minimizing contact in workplaces, 14. Ferguson N, Laydon D, Nedjati-Gilani G, Imai N, Ainslie K, and imposing curfews. The main aim of such interven- et al. (2020) Impact of non-pharmaceutical interventions tions is to flatten the curve i.e. prevent infection from (NPIs) to reduce covid-19 mortality and healthcare de- spreading fast and bring down the number of infected mand. Imperial College COVID-19 Response Team. cases. Curve flattening is necessary because it avoids 15. Prem K, Liu Y, Russell T, Kucharski A, Eggo R, et al. (2020) overwhelming the health systems and gives them time The effect of control strategies to reduce social mixing on outcomes of the covid-19 epidemic in Wuhan, China: A to develop treatment mechanisms. modelling study. Lancet public Health 5: e261-e270. References 16. Mwalili S, Kimathi M, Ojiambo V, Gathungu D, Mbogo R (2020) SEIR model for covid-19 dynamics incorporating 1. Liu T, Hu J, Kang M, Lin L, Zhong H, et al. (2020) Trans- the environment and social distancing. BMC Res Notes 13: mission dynamics of 2019 novel coronavirus (2019-ncov). 352. BioRXiv. 17. Cao B, Wang Y, Wen D, Liu W, Wang J, et al. (2020) A 2. World Health Organisation (2020) Statement on the sec- trial of lopinavir ritonavir in adults hospitalized with severe ond meeting of the international health regulations (2005) covid-19. N Engl J Med 382: 1787-1799. Emergency committee regarding the outbreak of novel 18. Yang C, Wang J (2020) A mathematical model for the novel coronavirus (2019-ncov). coronavirus epidemic in Wuhan, China. Math Biosci Eng 3. World Health Organisation (2020) Covid-19 situation re- 17: 2708-2724. port, 189. 19. Day M (2020) Covid-19: Four fifths of cases are asymptom- 4. Ministry of Health (2020) First case of coronavirus disease atic, China figures indicate. BMJ 369: m1375. confirmed in Kenya.

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