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Use of a Modified SIRD Model to Analyze COVID-19 Data
All of the scientific publishers have made all Covid-19 related papers open sourced, so there is no need to discuss this paper in any detail as interested parties can read it themselves, but here it is: Use of a Modified SIRD Model to Analyze COVID-19 Data (Devosmita Sen and Debasis Sen Industrial & Engineering Chemistry Research 2021 60 (11), 4251-4260.)
Here, anyway, is an excerpt including the definition of "SIRD:"
1. Introduction
ARTICLE SECTIONSJump To
Since the beginning of 2020, the whole world has been experiencing a major and unprecedented global crisis, owing to the outbreak of the COVID-19 pandemic.(1?3) The infection is resulting in severe, and sometimes even fatal, respiratory diseases such as acute respiratory distress syndrome.(4) Such an infectious disease, with a humongous social and economic impact was never seen before, at least in the recent past.(5) COVID-19 arose due to a strain of a novel coronavirus that has rapidly spread throughout the globe,(1,6) originating from and infecting a large number of people in Wuhan, China.(7?9) The spread of this disease has a complex time dependence, which is governed not by the number of infected people alone, but is strongly correlated with aspects such as total population of the country, various norms and measures taken by the nation at a particular time, and many more.(10?14) Because of a lack of previous experience in controlling a similar pandemic with such a high impact in the recent past, it is difficult to anticipate the size of the population that may get affected by this pandemic and the typical time required for its control.
The abovementioned crisis immediately calls for a quantitative understanding of the time evolution of this complex and non-linear process through computer modeling. Statistical and mathematical analysis of reported data can provide valuable insights into the trend of the spread and thus can assist in planning various social measures to contain the spread of the virus as quickly as possible. Further, analysis of reported epidemic data plays a vital role in analyzing the underlying phenomena involved in spreading of the disease and to make predictions about future trends. This enables various organizations to efficiently plan their steps toward containing this spread.
In literature, a few models have been proposed to explain such data. These can primarily be classified into two categories, collective models(12,13,15?18) and networked models.(19?23) Some examples of the former class of models are growth and logistic models,(12) the susceptible–infected–recovered–dead (SIRD) model, and their modifications,(9,16) collectively termed as compartmental models. At this juncture, it is worthy to mention that such a phenomenon has a close resemblance to kinetics of chemical reactions in general,(24) where transition from one state to another is associated with a specific rate. In epidemic modeling, the corresponding rates may be expressed in terms of the instantaneous number of infected, recovered people, and so forth. Owing to the complex interdependence of several processes governing the spread of infections and recovery, a proper mathematical model should be able to simultaneously predict the temporal behavior of infected, recovered, and dead people. As the protection procedures demand quarantine, confinement, social distancing lockdown measures, and so forth,(26) a simple SIRD model only gives a preliminary understanding of the process and is not sufficient to describe such complex processes in general. Here, we model the spread of the present pandemic using a generalized SIRD model, taking into account the fraction of population which is exposed, under quarantine, confined, active-infected, recovered, and expired at time instant t. It is noteworthy that proper modeling calls for a simultaneous corroboration of the time evolution of all the three independent reported data sets, namely, active number of infections and cumulative number of recovered and expired people due to the infection.
In this manuscript, we report the analysis of COVID-19 time series data for five countries—China, Italy, France, the United States, and India (and two of its highly affected states)—using the modified SIRD model. We have shown that this model is capable of explaining the current data significantly well for all these five countries. It should be noted that the present approach is unique because it is capable of explaining simultaneously all the three reported data sets: active, recovered, and dead population. The data have been obtained from https://data.humdata.org/dataset/novel-coronavirus-2019-ncov-cases which is compiled by the Johns Hopkins University Center for Systems Science and Engineering (JHU CCSE) from various sources including the World Health Organization (WHO) and from reported data on Indian state websites https://arogya.maharashtra.gov.in/1175/Novel--Corona-Virus, https://gujcovid19.gujarat.gov.in/.
ARTICLE SECTIONSJump To
Since the beginning of 2020, the whole world has been experiencing a major and unprecedented global crisis, owing to the outbreak of the COVID-19 pandemic.(1?3) The infection is resulting in severe, and sometimes even fatal, respiratory diseases such as acute respiratory distress syndrome.(4) Such an infectious disease, with a humongous social and economic impact was never seen before, at least in the recent past.(5) COVID-19 arose due to a strain of a novel coronavirus that has rapidly spread throughout the globe,(1,6) originating from and infecting a large number of people in Wuhan, China.(7?9) The spread of this disease has a complex time dependence, which is governed not by the number of infected people alone, but is strongly correlated with aspects such as total population of the country, various norms and measures taken by the nation at a particular time, and many more.(10?14) Because of a lack of previous experience in controlling a similar pandemic with such a high impact in the recent past, it is difficult to anticipate the size of the population that may get affected by this pandemic and the typical time required for its control.
The abovementioned crisis immediately calls for a quantitative understanding of the time evolution of this complex and non-linear process through computer modeling. Statistical and mathematical analysis of reported data can provide valuable insights into the trend of the spread and thus can assist in planning various social measures to contain the spread of the virus as quickly as possible. Further, analysis of reported epidemic data plays a vital role in analyzing the underlying phenomena involved in spreading of the disease and to make predictions about future trends. This enables various organizations to efficiently plan their steps toward containing this spread.
In literature, a few models have been proposed to explain such data. These can primarily be classified into two categories, collective models(12,13,15?18) and networked models.(19?23) Some examples of the former class of models are growth and logistic models,(12) the susceptible–infected–recovered–dead (SIRD) model, and their modifications,(9,16) collectively termed as compartmental models. At this juncture, it is worthy to mention that such a phenomenon has a close resemblance to kinetics of chemical reactions in general,(24) where transition from one state to another is associated with a specific rate. In epidemic modeling, the corresponding rates may be expressed in terms of the instantaneous number of infected, recovered people, and so forth. Owing to the complex interdependence of several processes governing the spread of infections and recovery, a proper mathematical model should be able to simultaneously predict the temporal behavior of infected, recovered, and dead people. As the protection procedures demand quarantine, confinement, social distancing lockdown measures, and so forth,(26) a simple SIRD model only gives a preliminary understanding of the process and is not sufficient to describe such complex processes in general. Here, we model the spread of the present pandemic using a generalized SIRD model, taking into account the fraction of population which is exposed, under quarantine, confined, active-infected, recovered, and expired at time instant t. It is noteworthy that proper modeling calls for a simultaneous corroboration of the time evolution of all the three independent reported data sets, namely, active number of infections and cumulative number of recovered and expired people due to the infection.
In this manuscript, we report the analysis of COVID-19 time series data for five countries—China, Italy, France, the United States, and India (and two of its highly affected states)—using the modified SIRD model. We have shown that this model is capable of explaining the current data significantly well for all these five countries. It should be noted that the present approach is unique because it is capable of explaining simultaneously all the three reported data sets: active, recovered, and dead population. The data have been obtained from https://data.humdata.org/dataset/novel-coronavirus-2019-ncov-cases which is compiled by the Johns Hopkins University Center for Systems Science and Engineering (JHU CCSE) from various sources including the World Health Organization (WHO) and from reported data on Indian state websites https://arogya.maharashtra.gov.in/1175/Novel--Corona-Virus, https://gujcovid19.gujarat.gov.in/.
A picture:
The caption:
Figure 2. Schematic representation of the present model.
Enjoy if interested.
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