key: cord-0970125-2w9jjrji authors: Paul, A.; Chatterjee, S.; Bairagi, N. title: Covid-19 transmission dynamics during the unlock phase and significance of testing date: 2020-08-21 journal: nan DOI: 10.1101/2020.08.18.20176354 sha: fdd2e8bed94a8252e44c16029d0c551f256c66e7 doc_id: 970125 cord_uid: 2w9jjrji The pandemic disease Covid-19 caused by SARS-COV-2, which emerged from Wuhan, China, has established itself as the most devastating disease in the history of infectious disease, affecting 216 countries/territories across the world. Different countries have developed and adopted various policies to contain this epidemic and the most common were the social distancing and lockdown. Though some countries have come out of this pandemic, the infection is still increasing and remains very serious in the rest of the world. Even when the disease is not under control, many countries have withdrawn the lockdown and going through the phase-wise unlocking process, causing a further increment in the infection rate. In such a scenario, the role of the undetected class of infected individuals has become very crucial. The present study is an attempt to understand and estimate the possible epidemic burden during the unlock phase in the presence of an undetected class. We proposed a modified SEIR model and dissected the epidemiological status of different countries with the available data. With the initial establishment of the model with the epidemic data of four countries, which have already attained the epidemic peak, the study focused more on countries like India and the USA, where the epidemic curve is still growing, but the unlock process has started. As a straightforward result, we noticed a significant increase in the undetected and detected infected cases under the ongoing unlock phase. Under such conditions, our recalibration exercise showed that an increase in the testing could revert the existing growth rate of the infected cases to the lower growth rate of the lockdown period. Our present study emphasizes on the implementation of 3T principles, trace, test, and treat, to contain the epidemic. The significance of large scale testing in controlling the epidemic is true for both India and the USA though they have different socio-economic conditions. The use of repurposing drugs may further decrease the infected cases and help the disease controlling process. We believe our proposed strategy obtained through a mathematical model will help to make a better policy for the unlock phase. . It is to be mentioned that an asymptomatic 99 individual may be a member of I d class if Covid-19 infection is confirmed by rapid antigen or ξ in between 0 and 1. A fraction γ (0 < γ < 1) of them join I d class and the remaining fraction (1 − γ) becomes the member of I u class. An individual of undetected class may join the detected 111 class if tested positive later on, and such transformation from I u class to I d class may occur at a 112 rate ω. Transformation from I d class to R d class through recovery occurs at a rate δ d and a similar 113 transformation rate from I u class to R u class is denoted by δ u . The disease related death rates 114 in the I d and I u classes are denoted, respectively, by µ d and µ u , and these individuals join the 115 respective death classes D d and D u . The parameters δ d , δ u , µ d , µ u and ω all lie in between 0 and 1. 116 We assume that the total population (N ) remains constant throughout the study period, a valid 117 assumption if the epidemic period is not too long. The interaction among different classes with 118 these assumptions may be represented by the following system of differential equations: where Here β 0 (1 − ν) is the disease transmission efficiency in the presence of lockdown with β 0 as the 120 baseline disease transmission rate. In fact, the parameter ν encapsulates the effect of lockdown. The basic reproduction number determines whether an infection will spread in the community or 128 not. It is the average number of secondary cases produced by an index case. If this number is 129 greater than 1 then an epidemic can grow, otherwise it dies out [35] . Close to the disease-free Here, and The next generation matrix (N GM ) then can be found as compared with the real data (see Figure 2 ). 6 . CC-BY-NC 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 August 21, 2020. . Table 1: Optimal parameters for BLS, ELS, and LLS time segments, separated by the two critical time points, for the countries Italy , Spain, Germany, and Switzerland. Parameters l, γ, ξ, ω, δ u , µ u remained fixed for each time segment, while the other five parameters differed. The first critical time points are March 10, 14, 23, and 17, respectively, the lockdown starting dates for Italy, Spain, Germany, and Switzerland. The second critical time points for these countries are 37 days, 23 days, 14 days, and 15 days after the first critical point. The population of a country was considered as the initial value of the susceptible population of that country. . CC-BY-NC 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 August 21, 2020. . https://doi.org/10.1101/2020.08.18.20176354 doi: medRxiv preprint Table 1 . Data fitting was relatively poor in the case of Spain because they changed the methodology on April 19 and May 25. In these day daily cases were shown to be negative, and the cumulative cases became lower than its immediate previous day. 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 August 21, 2020. Parameter estimation The lockdown starting dates for India and the US are 25th March and 20th March, respectively, [40] and these dates were used as their first critical time-point. Following the earlier protocol, we 180 generated the optimal parameter set ( Table 2) for India and USA (see Supplementary Information). With these parameters, the model (1) . CC-BY-NC 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 August 21, 2020. . 10 . CC-BY-NC 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 August 21, 2020. . https://doi.org/10.1101/2020.08.18.20176354 doi: medRxiv preprint To observe the effect of lockdown on the disease transmission rate (β(t)) and the basic reproduction 188 number of India and USA, we plotted their variation (see Figure 5 ) for three-time stages as before. During BLS, these values were very high for both the countries, but it decreased later on and 190 remained in between 1 and 2 for rest of the period, implying that the disease is still not under 191 control. Note that the transmission rate increased in both countries during the unlock period. . CC-BY-NC 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 August 21, 2020. Table 1 and Table 2 13 . CC-BY-NC 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 August 21, 2020. Table 2 ). Fold change is measured taking July 27 value as their bases. The upper row represents the scenario for India and the lower row for the US. 5 Possible policy hypothesis through parameter recalibration 232 We look for policies that could be implemented during the unlock phase to restrict disease spreading. 233 We used parameter recalibration techniques to define such policies that may be adopted to slow Figure 8 shows that α, β 0 1 , 241 β 0 2 , ν 1 and ν 2 all are sensitive parameters. However, these parameters cannot be considered for 242 14 . CC-BY-NC 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 August 21, 2020. . recalibration exercise because during the unlock period one does not have any control over these 243 parameters and the values for the undetected class are completely unknown. We, therefore, looked 244 for other parameters which are sensitive and controllable. Figure 8 shows that the parameters γ 245 and ω, having negative PRCC values, are also sensitive and they have more effect on the undetected 246 class than the detected one. So, we selected γ and ω as the target parameters for our recalibration 247 exercise to hypothesis on the controlling measures. It is mentionable that the parameters γ and After identifying the targeted parameters, we now observe how much these parameters can 251 control the disease progression during unlock period. In this process, we increased separately the 252 15 . CC-BY-NC 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 August 21, 2020. For an example, if the value of γ is increased by 50% of the existing rate, India would be able to 258 reduce the number of detected individuals by 10%, 30%, 40% and undetected infected individuals 259 by 40%, 50%, 60% in the next one, two and three months, respectively and the value even can 260 go below the corresponding value of LLS condition. We also noticed a higher variation in the 261 undetected class, I u , compare to the detected class, I d . Here we investigated the effect of repurposing drugs on Covid-19 disease dynamics. Interestingly, we 268 observed from our global sensitivity analysis that the death rate (δ d ) and recovery rate (µ d ) of the 269 16 . CC-BY-NC 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 August 21, 2020. . https://doi.org/10.1101/2020.08.18.20176354 doi: medRxiv preprint detected class are sensitive parameter, particularly for detected class (see Figure 8) . We, therefore, 17 . CC-BY-NC 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 August 21, 2020. Table 2 (ULS). The world has now started to come out of the lockdown imposed due to Covid-19 pandemic even 18 . CC-BY-NC 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 August 21, 2020. . our study by understanding the effect of lockdown in the countries like Italy, Spain, Germany and Switzerland, which have attained the epidemic peak and the curve is now going down. Gaining 298 experience on the trend of data from these countries, we then studied the epidemiological status of where the effect of lockdown has been observed, but it was insufficient to flatten the curve. Our 328 model simulation captured the disease spreading scenario for these two countries for the period 329 January 22 to July 27, 2020. We noticed that the disease transmission coefficient, β(t), and the 330 lockdown effect measuring parameter, ν, both decreased in the LLS stage from to its previous 331 stage. These decreased parameter values, however, reduced the transmission potentiality measure, 332 R 0 , but could not pull it below 1. Its value remained above 1 for both the countries, indicating that 333 the epidemic is still in its growing stage. Possible reasons for the curve to still grow despite the 334 longer lockdown lie in the observation that the recovery rates for the detected class (δ d ) were low 335 for the US and the value of baseline disease transmission rate (β 0 ) did not change much in India 336 compare to other countries (see Table 2 ). Also to add, these two countries are gradually coming out We have also captured the significance of public perception of disease spreading and observed 361 that it can significantly change the number of infectives. Such effects were observed in both the 362 countries India and the USA despite their socio-economic differences. We have also observed the 363 effect of repurposing drugs in reducing the fatality of the disease. As there is no vaccine and 364 specific drugs for treating SARS-CoV-2 infected individuals, we have to fight against the virus with 365 the available treatments and control strategies in the unlock period. Our study emphasizes that 366 enhancing covid testing and using repurposing drugs, we can significantly reduce the epidemiological 367 burden. We believe our proposed strategy obtained through a mathematical model will help to make 368 a better policy for the unlock phase. CC-BY-NC 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 August 21, 2020. . [32] Li, R., Pei, S., Chen, B., Song, Y., Zhang, T., Yang, W. and Shaman, J., 2020. Substantial . 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