key: cord-1026786-cgde85eo authors: Nabi, K. N. title: FORECASTING COVID-19 PANDEMIC: A DATA-DRIVEN ANALYSIS date: 2020-05-17 journal: nan DOI: 10.1101/2020.05.12.20099192 sha: 2bdbf5103d46a30921aeb4ecb2fc79736964b855 doc_id: 1026786 cord_uid: cgde85eo In this paper, a new Susceptible-Exposed-Symptomatic Infectious-Asymptomatic Infectious-Quarantined-Hospitalized-Recovered-Dead (SEIDIUQHRD) deterministic compartmental model has been proposed and calibrated for describing the transmission dynamics of the novel coronavirus disease (COVID-19). A calibration process is executed through the solution of an inverse problem with the help of a Trust-Region-Reflective algorithm, used to determine the best parameter values that would fit the model response. The purpose of this study is to give a tentative prediction of the epidemic peak for Russia, Brazil, India and Bangladesh which could become the next COVID-19 hotspots in no time. Based on the publicly available epidemiological data from late January until 10 May, it has been estimated that the number of daily new symptomatic infectious cases for the above mentioned countries could reach the peak around the beginning of June with the peak size of {approx}15,774 symptomatic infectious cases in Russia, {approx}26,449 cases in Brazil, {approx}9,504 cases in India and {approx}2,209 cases in Bangladesh. Based on our analysis, the estimated value of the basic reproduction number (R0) as of May 11, 2020 was found to be {approx}4.234 in Russia, {approx}5.347 in Brazil, {approx}5.218 in India, {approx}4.649 in the United Kingdom and {approx}3.5 in Bangladesh. Moreover, with an aim to quantify the uncertainty of our model parameters, Latin hypercube sampling-partial rank correlation coefficient (LHS-PRCC) which is a global sensitivity analysis (GSA) method is applied which elucidates that, for Russia, the recovery rate of undetected asymptomatic carriers, the rate of getting home-quarantined or self-quarantined and the transition rate from quarantined class to susceptible class are the most influential parameters, whereas the rate of getting home-quarantined or self-quarantined and the inverse of the COVID-19 incubation period are highly sensitive parameters in Brazil, India, Bangladesh and the United Kingdom which could significantly affect the transmission dynamics of the novel coronavirus. Our analysis also suggests that relaxing social distancing restrictions too quickly could exacerbate the epidemic outbreak in the above mentioned countries. • Births and natural deaths in the population are not considered. 126 • The susceptible population are exposed to a latent class . carriers and move to exposed (E) class. Here λ is the relative infectiousness factor of 136 asymptomatic carriers (in comparison to symptomatic individuals). The rate of getting 137 home-quarantined or self-quarantined of S is q, whereas κ is the rate of progression 138 of symptoms of COVID-19 (hence 1 κ is the mean incubation period of COVID-19). Detected symptomatic infected individuals are generated at a proportion σ 1 and un-140 detected asymptomatically-infected cases are generated at a rate σ 2 from the exposed . 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 May 17, 2020. . https://doi.org/10.1101/2020.05.12.20099192 doi: medRxiv preprint illustrated by the following deterministic system of nonlinear differential equations (1). 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 May 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 May 17, 2020. . The disease-free equilibrium (DFE) of (1) can be obtained easily by setting S = 179 E = I D = I U = Q = H = R = D = 0. Therefore the DFE of (1) is : The local stability of the DFE is explored using the next generation operator method The associated basic reproduction number, denoted by R 0 is then given by, , where ρ is the spectral radius of FV −1 . It follows that, Thus, by Theorem 2 of LaSalle (1976), the following result is established. is a prescribed initial condition vector referring to the initial time t 0 of the analysis, the vector p = 8 . 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 May 17, 2020. . (N, β, λ, r 1 , r 2 , η, k, σ 1 , σ 2 , γ, q, φ D , φ U , φ H , δ U , δ H ) ∈ R 16 aggregates the model parameters and f : U ⊂ R 8 × R 16 → R 8 is a nonlinear map which gives the evolution law of this dynamics, defined (for fixed t) on the open set U = (x(t), p) ∈ R 8 × R 16 | x m (t) > 0 and p n > 0, for m = 1, 2, ..., 8and n = 1, ..., 16 The forward problem consists in providing initial conditions (IC) and a set of pa-203 rameters, represented by the pair α = (x 0 , p), and compute by means of numerical 204 integration the model response x(t) from which a scalar observable ψ(α, t) is ob-205 tained. In the forward problem, α represents all IC and system parameters from (1), 206 while ψ(α, t) is the new cases N w system response which can be calculated using daily 207 reported cumulative cases real-time data. Since the map f has a polynomial nature in x, it is continuously differentiable 209 function in x. Thus, the existence and uniqueness theorem for ordinary differential 210 equations guarantees that the initial value problem of (3) has a unique solution. In In this work, the evaluation of the system response in the forward problem is solved 214 numerically by using Runge-kutta (4,5) method and the scalar observable of interest 215 N w is used to assess the simulation when compared with real data of the COVID- In formal terms, given an observation vector y ∈ F and a prediction vector ψ(α) ∈ F , the calibration aims at finding a vector of parameters α * such that 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 May 17, 2020. . This is the inverse problem associated to the epidemic model. In general this type 238 of extremely nonlinear, with none or low regularity, multiple solutions (or even none), where D is a diagonal matrix that depends on α, g, lb, and ub Coleman, (1996) . 255 Eventually, the trial step is constructed through the subproblem as where ∆ is a scalar associated with the trust region size; Q is a matrix involving D, 257 a Jacobian matrix (also dependent on α, g, lb, and ub) and an approximation 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. The copyright holder for this preprint this version posted May 17, 2020. projection results for Russia from early February to late August are shown in Figure 282 2 and 3. We took real data from February 01 to May 08, 2020 to calibrate the model 283 parameters. 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 May 17, 2020. . https://doi.org/10.1101/2020.05.12.20099192 doi: medRxiv preprint As we can see the results from the proposed model match the real data very well. 285 Based on the proposed model, we want to project that from Figure Table 2 , 297 along with the parameters and IC values resulted from the calibration ("TRR output"). (a) The number of daily detected symptomatic infectious cases measured and fitted from early February to early May, 2020 (b) The number of cumulative detected symptomatic infectious cases cases measured and fitted from early February to early May, 2020 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 May 17, 2020. . https://doi.org/10.1101/2020.05.12.20099192 doi: medRxiv preprint (a) The number of daily detected symptomatic infectious cases measured and projected for Russia from early February to late August, 2020 (b) The number of cumulative detected symptomatic infectious cases measured and projected for Russia from early February to late August, 2020 non-pharmaceutical interventions. The case-fatality rate is hovering around 9.3% as of 314 May 11, which is necessary to assess how much community transmission has occurred 315 and its burden. According to our projection, this ratio could be doubled within two 316 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 May 17, 2020. Table 3 , along 320 with the parameters and IC values resulted from the calibration ("TRR output"). 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. 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 May 17, 2020. . https://doi.org/10.1101/2020.05.12.20099192 doi: medRxiv preprint Table 4 , along with the parameters values resulted from the calibration 348 ("TRR output"). Interestingly, we have found in our analysis that India's case-fatality 349 rate is at 3.5% and the country's recovery rate is at 33% which commensurate with 350 real reported statistics precisely. 17 . 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 May 17, 2020. 18 . 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 May 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 May 17, 2020. The upper and lower bounds used for the parameters were set compatible with the 377 literature suggested intervals and are presented in Table 5 , along with the parameters 378 values resulted from the calibration ("TRR output"). 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. The copyright holder for this preprint this version posted May 17, 2020. . https://doi.org/10.1101/2020.05.12.20099192 doi: medRxiv preprint 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 May 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 May 17, 2020. . https://doi.org/10.1101/2020.05.12.20099192 doi: medRxiv preprint eters, uncertainty analysis can give considerable insights regarding the quantitative re-433 lationship between model responses and model input parameters. However, it is really 434 challenging for complex models to determine the relationship with sufficient accuracy. 435 Importantly, we have got startling yet realistic results from our sensitivity analysis. As we can see from Figure 12 , we found nearly the same qualitative and significant 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 May 17, 2020. . https://doi.org/10.1101/2020.05.12.20099192 doi: medRxiv preprint 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 May 17, 2020. . https://doi.org/10.1101/2020.05.12.20099192 doi: medRxiv preprint For Bangladesh, it has been found in our analysis, home-quarantine rate is the most negatively sensitive parameter on the size of symptomatic infectious individuals and the 478 corresponding PRCC index is −0.68 which is the highest among our five studied cases. Numerical results on the recent COVID-19 data from Russia, Brazil, India, Bangladesh 500 and the UK have been analyzed. Based on the projection as of May 11, 2020, Russia 501 will reach the peak in terms of daily infected cases and death cases around end of May. Brazil and India will reach the peak in terms of daily infected cases and death cases 503 around beginning of June. Based on the projection the United Kingdom may have 504 a second wave of infection provided that lockdown is lifted. To end the pandemic, it 505 is mandatory to actively seek out potential spreaders, particularly the asymptomatic 506 spreaders which requires massive scale testing. Such a level of testing would effectively 507 bring the R 0 below 1 in the above mentioned countries which will eventually cause the 508 pandemic to fade out. 509 27 . 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 May 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 May 17, 2020. Worldometer, https://www.worldometers.info/coronavirus, accessed: 12-05-2020. Modelling the epidemic trend of the 511 2019 novel coronavirus outbreak in China As our proposed epidemic model contains a moderate number of empirical param-Anastassopoulou, C., Russo, L., Tsakris, A., & Siettos, C. (2020). Data-Based Analysis,