key: cord-0771702-8mtdays7 authors: Saif, F. title: COVID-19 Pandemic in Pakistan: Stages and Recommendations date: 2020-05-14 journal: nan DOI: 10.1101/2020.05.11.20098004 sha: f8610fa36c5748375b176b2c6497de6a321ed4da doc_id: 771702 cord_uid: 8mtdays7 We present a real-time forecast of COVID-19 in Pakistan that is important for decision-making to control the spread of the pandemic in the country. The study helps to develop an accurate plan to eradicate the COVID-19 by taking calculated steps at the appropriate time, that are crucial in the absence of a tested medicine. We use four phenomenological mathematical models, namely Discrete Exponential Growth model, the Discrete Generalized Growth model, the Discrete Generalized Logistic Growth, and Discrete Generalize Richards Growth model. Our analysis explains the important characteristics quantitatively. The study leads to understand COVID-19 pandemic in Pakistan in three evolutionary stages, and provides understanding to control its spread in the short time domain and in the long term domain. For the reason the study is helpful in devising the measures to handle the emerging threat of similar outbreaks in other countries. The COVID-19 causes severe acute respiratory syndrome. It have been linked to a live animal seafood market in Wuhan, pointing to a zoonotic origin of the epidemic. Human-to-human transmission, however, has driven its spread in the strongly interconnected human world community [1, 2] . While the transmission potential of novel coronavirus can reach high values the epidemiological features of COVID-19 1 lations we find excellent agreement between the analytical results and the real-time data of coronavirus in Pakistan. The manuscript has the following layout: in section 2 we present the mathematical model for our study, in section 3 we explain the real-time data of confirmed COVID-19 cases and present evolutionary stages of the pandemic in Pakistan. In section 4 we present our conclusions and recommendations. The Exponential Growth model, the Generalized Growth model, the Generalized Logistic Growth, and Generalized Richards Growth model [30] , are expressed by the differential equations, respectively. These have been considered extensively to explain previous epidemics. Here C(t) describes the cumulative number of cases at time t. The equation (4) is the extension of the original Richards growth model [31] which explain the pandemics [32, 33, 34] . Here, r is the growth rate at the early stage, and K is the final epidemic size. Moreover p is a parameter that allows the model to capture different growth profiles. The exponent α measures the deviation from the dynamics of the simple logistic curve. The equation (4) corresponds to the original Richards model for p = 1, that is and reduces to the generalized logistic model for α = 1 and p = 1. Keeping in view the development of data in terms of the positive tests, variations, and deaths on every next day we may consider the change in C over a unit interval of time. We express the rate of change of C, that isĊ(t), in difference form as ∆C ∆t . 3 . 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 14, 2020. . https://doi.org/10.1101/2020.05. 11.20098004 doi: medRxiv preprint Here ∆C = C n+1 − C n is the change in positively tested patients. Thus we reshape the equation (4) in the discrete form as where C n is the cumulative number of cases on the nth day. The discrete generalized Richard model (DGRM) provides an effective way to monitor the pandemic in the form of a mapping, thus connecting the data on nth day with (n + 1)th day. The stable points of the discrete generalized Richards model given in equation (6) are C n = 0, that implies no positively tested patients, and C n = K. The stable points are the same as obtained by the generalized Richards model. We write the discrete generalized growth model (DG 2 M), as which provides exponential growth for p = 1, that is C n+1 = r n 1 C 1 , that relates the number of positively tested patients on the first day with the number of postively tested patients after a number of n days has passed, here r 1 = 1 + r. Hence for the parameter p = 0 we find linear increase with respect to n as C n+1 = C 1 + nr, and sub-exponential growth for 0 < p < 1. To control the COVID-19 pandemic in the absence of medicines, the requirement is to take calculated steps at the appropriate time. Therefore in addition to data analysis, we need a visible understanding, that is necessary for the management of the associated risk to the public life and economy. The day-to-day development of the pandemic in all the provinces of Pakistan describes an exponential increase of the confirmed COVID-19 cases that include active, recovered, and deaths (expressed by blue dots in figure 1) that is verified mathematically using discrete generalized growth model (DG 2 M), discrete logistics growth models (DGM) and discrete generalized Richard model (DGRM). The models have been used to comprehend the COVID-19 outbreak in China, USA, Europe and the other countries of the world [36] . Stage I -February 26 to March 15: On February 26, 2020 first two confirmed coronavirus cases were reported in Pakistan. In the absence of lockdown and public awareness campaign in the country, in the next two weeks the pandemic spread exponentially all over the country. The comparison of the real-time data with the 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. Stage III: April 01-May 08: In the next thirty eight days de-facto quarantining of the provinces by restricting the movement of people, employing social distancing, tracing and tracking, closing educational institutes, parks, and restaurants, limiting air and train travel services, the Government of Pakistan tried to control the COVID-19 spread in the country. This reduced the exponential growth from 0.85 (the stage 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. The copyright holder for this preprint this version posted May 14, 2020. . The measures to eradicate COVID-19 pandemic in Pakistan during stage III resulted in the number of confirmed cases today as 28736, including 20291 active cases, 7809 recovered and 636 deaths. The mathematical analysis displays an intersection of red and blue dashed lines, that corresponds to second week of May in real-time. This implies that the number of confirmed COVID-19 cases were the same today in the absence of any lockdown and public awareness campaign at stage I, if in stage II the country had allowed the people with foreign travel history to enter only after adequate check up and compulsory quarantine. All the measures to ensure lockdown caused a blow to economy of the country at stage II and III. Eventually they appeared to be a cost of the mismanagement in handling the people entry with a foreign travel history. At the same time it displayed the unprepared state to handle the pandemic in Pakistan at the early stages. Stage IV: May 09-May 31: The analysis of the COVID-19 confirmed cases based on DGRM and its extrapolation to May 31 show that with presently adopted lockdown the pandemic size shall increase to around sixty thousands confirmed cases in the next twenty two days (shown in figure 3 , narrow-dashed black line). It further expresses that by intensifying lockdown at this stage we can appreciably slow down the pandemic in Pakistan by end of June, 2020. Thus instead of relaxing the lock-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. The copyright holder for this preprint this version posted May 14, 2020. . down, a strict lockdown is useful at this stage, therefore enabling Pakistan to control the pandemic in next two months. This way the size of the outbreak is restricted to around one hundred thousands confirmed cases, as seen in figure 4 . In case the lockdown disappears completely at stage IV the pandemic size would increase to one hundred twenty thousand confirmed COVID-19 cases in next twenty two days, as indicated by the red line in figure 3 . Lifting the lockdown partially shall bring the numbers of confirmed COVID-19 cases in between sixty thousand and one hundred twenty thousand. Stage V: June 01-: Keeping in view the month of Ramadan and the necessary business requirements in these days, the devised lockdown in stage II and III is relaxed in the stage IV. The pandemic management in next months requires a careful and calculated approach. No lockdown scenario from May 09 to May 31 shall drag the size of pandemic in the country to higher values. By extrapolating the DGRM results we note that a strict lockdown in June shall bring the number of confirmed cases in September around three hundred fifty thousands, with less than one percent increase in new cases per day, as shown by curved black line in figure 4 . The peak is expected to be at the end of June with around two hundred thousands confirmed cases. A compromised lockdown at stage IV shall make it possible to control the COVID-19 pandemic by end of July, with the estimated size of the outbreak around two hundred fifty thousand confirmed cases, as shown by big-dashed black line 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 May 14, 2020. . In order to avoid business melt down and economic depression in Pakistan the Government is easing the lockdown measures from May 09 till May 31. The business centers, shops, and train travel services are opening in these days, anticipating business activities and people transportation. The within-a-city and inter-city movement of people shall make the public vulnerable and take the COVID-19 pandemic to higher levels. We show that by easing the lockdown measures in Pakistan the COVID-19 pandemic may increase four time more than the present value in next three weeks. Therefore with the given relaxation of lockdown in the month of May, a parallel public service campaign is to be launched by the government of Pakistan. This way people must be made concious of the growing pandemic situation in Pakistan all the time. The doctors, subject experts, university faculty, educationalists, and media should play an active role to keep the people well aware of the seriousness of the pandemic and convince them to take every measures essential for their own security. The future risk management requires a stringent lockdown in June to control the pandemic in the country. The effective preparedness on medical, and technical fronts together with optimal allocation of prevention measures, resources, and organization of production activities shall take the country out of the global COVID-19 pandemic. Mismanagement and delayed actions however have tendency of increasing in the size of pandemic and economical loss in next months. . 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 14, 2020. . https://doi.org/10.1101/2020.05.11.20098004 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. (which was not certified by peer review) The copyright holder for this preprint this version posted May 14, 2020. . https://doi.org/10.1101/2020.05.11.20098004 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. 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